GenAI - Heart Attack Analysis

{"metadata":{"kernelspec":{"name":"python3","display_name":"Python 3","language":"python"},"language_info":{"name":"python","version":"3.10.14","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"none","dataSources":[{"sourceId":2047221,"sourceType":"datasetVersion","datasetId":1226038},{"sourceId":93638835,"sourceType":"kernelVersion"}],"dockerImageVersionId":30761,"isInternetEnabled":false,"language":"python","sourceType":"notebook","isGpuEnabled":false}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":" <h1 align = \"center\" > (This entire notebook consists of responses, codes, and analyses obtained by asking prompts suitable for ChatGPT. We only wrote the appropriate prompt, and the rest was done by artificial intelligence. Of course, we have a roadmap. You can see this roadmap on the right under the notebook(up-to-date-heart-attack-analysis-and-prediction).) </h1>","metadata":{}},{"cell_type":"markdown","source":" <h1 align = \"center\" > ChatGPT for Generative AI - Heart Attack Analysis And Prediction </h1>","metadata":{}},{"cell_type":"markdown","source":"### You can access the notebook and dataset through our [GitHub link](https://github.com/OakAcademy/ChatGPT-for-Data-Analyst/blob/main/ChatGPT_for_Generative_AI%20(1).ipynb).","metadata":{}},{"cell_type":"markdown","source":"# What is Heart Attack?","metadata":{}},{"cell_type":"markdown","source":"A heart attack, medically known as myocardial infarction (MI), occurs when blood flow to a part of the heart muscle is blocked for an extended period, causing damage or death to the heart muscle. This blockage is typically caused by a buildup of plaque (a mix of fat, cholesterol, and other substances) in the coronary arteries, which supply blood to the heart muscle.\n\n### Primary Medical and Physiological Factors Associated with Heart Attacks\n\n1. **Causes and Risk Factors**\n   - **Atherosclerosis**: The primary cause of heart attacks. It involves the buildup of plaques in the coronary arteries, narrowing them and reducing blood flow.\n   - **Risk Factors**:\n     - **Age**: Increased risk as age advances.\n     - **Gender**: Men are at higher risk at an earlier age compared to women.\n     - **Family History**: Genetic predisposition to heart diseases.\n     - **Smoking**: Damages the lining of arteries, leading to plaque buildup.\n     - **High Blood Pressure**: Causes the heart to work harder, leading to damage.\n     - **High Cholesterol**: High levels of LDL cholesterol can lead to plaque formation.\n     - **Diabetes**: Increases risk due to high blood sugar levels damaging blood vessels.\n     - **Obesity**: Excess weight increases the heart's workload and risk of hypertension and diabetes.\n     - **Physical Inactivity**: Lack of exercise contributes to obesity and other risk factors.\n     - **Unhealthy Diet**: Diets high in saturated fats, trans fats, and cholesterol can contribute to atherosclerosis.\n     - **Stress**: Chronic stress can damage arteries and worsen other risk factors.\n     - **Alcohol**: Excessive alcohol consumption can increase blood pressure and contribute to heart disease.\n\n2. **Symptoms**\n   - **Chest Pain or Discomfort**: Often described as pressure, tightness, or a squeezing sensation.\n   - **Upper Body Pain**: Pain or discomfort in the arms, back, neck, jaw, or stomach.\n   - **Shortness of Breath**: Often accompanies chest discomfort.\n   - **Other Symptoms**: Cold sweat, nausea, lightheadedness, or sudden dizziness.\n\n3. **Diagnostic Methods**\n   - **Electrocardiogram (ECG or EKG)**: Measures the electrical activity of the heart and can detect heart damage.\n   - **Blood Tests**: Check for cardiac biomarkers like troponin, which are released into the blood when the heart muscle is damaged.\n   - **Echocardiogram**: Uses ultrasound waves to create images of the heart, helping identify areas of damage.\n   - **Coronary Angiography**: An imaging test that uses X-rays to take pictures of the coronary arteries.\n   - **Cardiac MRI**: Provides detailed images of the heart to assess damage.\n   - **Stress Tests**: Measure how the heart performs under physical stress, often used to detect coronary artery disease.\n\n4. **Treatment Options**\n   - **Medications**: Aspirin, thrombolytics, antiplatelet agents, beta-blockers, ACE inhibitors, statins.\n   - **Procedures**: Angioplasty and stent placement, coronary artery bypass grafting (CABG).\n   - **Lifestyle Changes**: Diet, exercise, smoking cessation, stress management.\n   - **Rehabilitation**: Cardiac rehabilitation programs to help patients recover and prevent future heart attacks.\n\n### Latest Research and Technological Advancements\n\n1. **Machine Learning and AI**: Used to analyze large datasets to identify patterns and predict heart attacks with high accuracy.\n2. **Wearable Devices**: Monitors for heart rate and rhythm abnormalities, providing real-time data that can alert users to potential issues.\n3. **Genetic Research**: Identifying genetic markers associated with higher risks of heart disease.\n4. **Advanced Imaging Techniques**: Improved imaging technologies provide better detection and assessment of coronary artery disease.\n\nUnderstanding these factors will be crucial in developing an accurate predictive model for heart attacks. This foundational knowledge will help in selecting relevant features from your dataset, improving model training, and ultimately enhancing prediction accuracy.","metadata":{}},{"cell_type":"markdown","source":"Heart attack symptoms can vary significantly between men and women. Understanding these differences is crucial for early detection and treatment. Here’s a detailed look at how heart attack symptoms can differ by gender:\n\n### Common Heart Attack Symptoms in Men\n\n1. **Chest Pain or Discomfort**:\n   - Often described as pressure, fullness, or a squeezing sensation in the center of the chest.\n   - It may last for a few minutes or go away and return.\n   \n2. **Upper Body Pain**:\n   - Pain or discomfort in the arms (especially the left arm), back, neck, jaw, or stomach.\n   \n3. **Shortness of Breath**:\n   - Can occur with or without chest discomfort.\n   \n4. **Other Symptoms**:\n   - Cold sweat, nausea, or lightheadedness.\n   - Symptoms typically occur suddenly and are more intense.\n\n### Common Heart Attack Symptoms in Women\n\n1. **Chest Pain or Discomfort**:\n   - Similar to men, but women are more likely to experience pain that is not severe or is described as a tightness or pressure rather than sharp pain.\n   \n2. **Upper Body Pain**:\n   - Pain or discomfort in one or both arms, the back, neck, jaw, or stomach.\n   - Pain can be gradual or sudden and may be intermittent.\n   \n3. **Shortness of Breath**:\n   - Can occur with or without chest discomfort.\n   - May feel like an inability to take a deep breath.\n   \n4. **Other Symptoms**:\n   - Unusual or unexplained fatigue, which can be more prominent in women.\n   - Nausea or vomiting, more common in women.\n   - Lightheadedness or dizziness.\n   - Cold sweat.\n\n### Less Typical Symptoms in Women\n\nWomen are more likely to experience atypical symptoms or symptoms that are less dramatic than the \"classic\" chest pain associated with heart attacks. These symptoms can include:\n\n- **Fatigue**: Sudden or unusual fatigue, which can be mistaken for other conditions.\n- **Indigestion or Heartburn**: Stomach pain or discomfort that feels like indigestion.\n- **Anxiety**: A feeling of impending doom or severe anxiety.\n- **Sleep Disturbances**: Unusual or unexplained sleep problems.\n\n### Why the Differences?\n\nThe differences in heart attack symptoms between men and women can be attributed to several factors:\n\n- **Biological Differences**: Differences in heart and blood vessel structure and function.\n- **Hormonal Influences**: Hormonal changes, particularly in post-menopausal women, can affect heart health.\n- **Psychosocial Factors**: Women may underreport symptoms due to different perceptions of pain and discomfort or societal factors.\n- **Healthcare Disparities**: Women may experience delays in diagnosis and treatment due to misinterpretation of their symptoms.\n\n### Importance of Awareness\n\nUnderstanding these gender-specific symptoms is crucial for:\n\n- **Early Detection**: Recognizing and acting on symptoms early can significantly improve outcomes.\n- **Effective Communication**: Women should communicate any unusual or concerning symptoms to their healthcare providers, even if they do not fit the \"classic\" heart attack profile.\n- **Tailored Prevention and Treatment**: Awareness can lead to better prevention strategies and more tailored treatments for heart attack patients of different genders.\n\nThis detailed understanding of heart attack symptoms by gender can be integrated into your predictive model to account for these differences and improve the accuracy of heart attack predictions for both men and women.","metadata":{}},{"cell_type":"markdown","source":"# Variable definitions in the Dataset","metadata":{}},{"cell_type":"markdown","source":"* age: Age of the patient (integer)\n* sex: Gender of the patient (1 = male, 0 = female) (integer)\n* cp: Chest pain type (0 = typical angina, 1 = atypical angina, 2 = non-anginal pain, 3 = asymptomatic) (integer)\n* trtbps: Resting blood pressure (in mm Hg) (integer)\n* chol: Serum cholesterol in mg/dl (integer)\n* fbs: Fasting blood sugar > 120 mg/dl (1 = true, 0 = false) (integer)\n* restecg: Resting electrocardiographic results (0 = normal, 1 = having ST-T wave abnormality, 2 = showing probable or definite left ventricular hypertrophy) (integer)\n* thalachh: Maximum heart rate achieved (integer)\n* exng: Exercise induced angina (1 = yes, 0 = no) (integer)\n* oldpeak: ST depression induced by exercise relative to rest (float)\n* slp: The slope of the peak exercise ST segment (0 = upsloping, 1 = flat, 2 = downsloping) (integer)\n* caa: Number of major vessels (0-3) colored by fluoroscopy (integer)\n* thall: Thalassemia (0 = normal, 1 = fixed defect, 2 = reversible defect) (integer)\n* output: Target variable (1 = heart disease, 0 = no heart disease) (integer)","metadata":{}},{"cell_type":"markdown","source":"# Summary Statistics","metadata":{}},{"cell_type":"markdown","source":"* Age: Ranges from 29 to 77 years, with a mean of 54.4 years.\n* Gender: 68.3% males and 31.7% females.\n* Chest Pain Type: Majority experience typical angina.\n* Resting Blood Pressure: Mean of 131.6 mm Hg.\n* Serum Cholesterol: Mean of 246.3 mg/dl.\n* Fasting Blood Sugar: 14.9% have fasting blood sugar > 120 mg/dl.\n* Resting ECG: Diverse results, with a mean close to 0.5 indicating normal and abnormal results.\n* Maximum Heart Rate: Mean of 149.6 bpm.\n* Exercise Induced Angina: 32.7% experience exercise-induced angina.\n* Oldpeak: Mean of 1.04, ranging from 0 to 6.2.\n* Slope of Peak Exercise ST Segment: Mostly flat or downsloping.\n* Number of Major Vessels: Mean of 0.73.\n* Thalassemia: Mostly normal or reversible defect.\n* Output: 54.5% have heart disease.","metadata":{}},{"cell_type":"markdown","source":"# Some technical terms within variables","metadata":{}},{"cell_type":"markdown","source":"**1. Angina**\n\nAngina is a type of chest pain caused by reduced blood flow to the heart. It's a symptom of coronary artery disease. Angina is typically described as squeezing, pressure, heaviness, tightness, or pain in the chest. It can also be felt in the shoulders, arms, neck, jaw, or back. There are several types of angina:\nStable Angina: Occurs predictably during exertion or stress and is relieved by rest or medication.\nUnstable Angina: Occurs unexpectedly, can happen at rest, and is usually more severe and prolonged. It is a medical emergency.\nVariant (Prinzmetal's) Angina: Caused by a spasm in the coronary arteries, it usually occurs at rest and can be severe.\n\n**2. Hypertrophy**\n\nHypertrophy refers to the enlargement or thickening of an organ or tissue. In the context of the heart, left ventricular hypertrophy (LVH) is the thickening of the walls of the heart's left ventricle. \nThis can be caused by high blood pressure or other conditions that increase the workload on the heart. LVH can lead to complications such as heart failure, arrhythmias, and ischemic heart disease.\n\n**3. ST (in ST Depression)**\n\nST refers to a segment of the heart's electrical cycle, seen on an electrocardiogram (ECG or EKG). The ST segment is the flat, isoelectric section of the ECG between the end of the S wave (the last deflection of the QRS complex) and the beginning of the T wave. It represents the period when the ventricles are depolarized. \nST Depression: This indicates that there is a downward displacement of the ST segment. It can suggest myocardial ischemia (reduced blood flow to the heart muscle), which is often due to coronary artery disease.\n\n**4. Fluoroscopy**\n\nFluoroscopy is an imaging technique that uses X-rays to obtain real-time moving images of the interior of an object. \nIn medical settings, it is used to visualize the movement of internal organs, the flow of contrast agents through blood vessels, or the positioning of surgical instruments and devices. In the context of the CAA variable, it refers to using fluoroscopy to visualize and assess the number of major coronary arteries affected by blockages or narrowing.\n\n**5. Thalassemia**\n\nThalassemia is a genetic blood disorder that affects the body's ability to produce hemoglobin and red blood cells. People with thalassemia produce either no or too little hemoglobin, which results in a shortage of red blood cells. This condition can cause anemia, leading to fatigue, weakness, and more severe complications. Thalassemia can range from mild to severe and is categorized into two main types:\n- Alpha Thalassemia: Caused by mutations in the genes related to the alpha globin protein.\n- Beta Thalassemia: Caused by mutations in the genes related to the beta globin protein.","metadata":{}},{"cell_type":"markdown","source":"# Loading The Dataset and  Initial analysis","metadata":{}},{"cell_type":"code","source":"# This Python 3 environment comes with many helpful analytics libraries installed\n# It is defined by the kaggle/python Docker image: https://github.com/kaggle/docker-python\n# For example, here's several helpful packages to load\n\nimport numpy as np # linear algebra\nimport pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n\n# Input data files are available in the read-only \"../input/\" directory\n# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory\n\nimport os\nfor dirname, _, filenames in os.walk('/kaggle/input'):\n    for filename in filenames:\n        print(os.path.join(dirname, filename))\n\n# You can write up to 20GB to the current directory (/kaggle/working/) that gets preserved as output when you create a version using \"Save & Run All\" \n# You can also write temporary files to /kaggle/temp/, but they won't be saved outside of the current session\n\nimport warnings\nwarnings.filterwarnings(\"ignore\")\n\nimport matplotlib.pyplot as plt\nimport seaborn as sns","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Importing necessary libraries\nimport pandas as pd\nimport numpy as np\n\n# Load the dataset\nfile_path = '/kaggle/input/heart-attack-analysis-prediction-dataset/heart.csv'\nheart_data = pd.read_csv(file_path)\n\n# Display the first few rows of the dataset\nprint(\"First few rows of the dataset:\")\ndisplay(heart_data.head())\n\n# Display basic information about the dataset\nprint(\"\\nBasic Information about the dataset:\")\nprint(heart_data.info())\n\n# Display summary statistics of the dataset\nprint(\"\\nSummary Statistics of the dataset:\")\nprint(heart_data.describe(include='all'))","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"Here's a breakdown of what each part of the code does:\n\n* Importing necessary libraries:\n\npandas is used for data manipulation and analysis.\nnumpy is used for numerical operations (imported here for potential future use).\n\n\n* Displaying the first few rows:\n\nheart_data.head() displays the first five rows of the dataset to give an initial glimpse of the data.\nDisplaying basic information about the dataset:\n\n\n* Displaying summary statistics:\n\nheart_data.describe(include='all') provides descriptive statistics for all the columns in the DataFrame, including count, mean, standard deviation, min, and max values.","metadata":{}},{"cell_type":"markdown","source":"# Heart Attack Dataset Report","metadata":{}},{"cell_type":"markdown","source":"* Total Entries: 303\n* Total Columns: 14\n\n**Column Information:**\n\n* **age: Age of the patient (integer)**\n\nCount: 303\n\nMean: 54.37\n\nStandard Deviation: 9.08\n\nMin: 29\n\n25%: 47.5\n\n50% (Median): 55\n\n75%: 61\n\nMax: 77\n\n* **sex: Gender of the patient (1 = male, 0 = female) (integer)**\n\nCount: 303\n\nUnique Values: 2\n\nValue Counts: {1: 207, 0: 96}\n\n* **cp: Chest pain type (0 = typical angina, 1 = atypical angina, 2 = non-anginal pain, 3 = asymptomatic) (integer)**\n\nCount: 303\n\nUnique Values: 4\n\nValue Counts: {0: 143, 1: 50, 2: 87, 3: 23}\n\n* **trtbps: Resting blood pressure (in mm Hg) (integer)**\n\nCount: 303\n\nMean: 131.62\n\nStandard Deviation: 17.54\n\nMin: 94\n\n25%: 120\n\n50% (Median): 130\n\n75%: 140\n\nMax: 200\n\n* **chol: Serum cholesterol in mg/dl (integer)**\n\nCount: 303\n\nMean: 246.26\n\nStandard Deviation: 51.83\n\nMin: 126\n\n25%: 211\n\n50% (Median): 240\n\n75%: 274.5\n\nMax: 564\n\n* **fbs: Fasting blood sugar > 120 mg/dl (1 = true, 0 = false) (integer)**\n\nCount: 303\n\nUnique Values: 2\n\nValue Counts: {0: 258, 1: 45}\n\n* **restecg: Resting electrocardiographic results (0 = normal, 1 = having ST-T wave abnormality, 2 = showing probable or definite left ventricular hypertrophy) (integer)**\n\nCount: 303\n\nUnique Values: 3\n\nValue Counts: {0: 151, 1: 147, 2: 5}\n\n* **thalachh: Maximum heart rate achieved (integer)**\n\nCount: 303\n\nMean: 149.65\n\nStandard Deviation: 22.91\n\nMin: 71\n\n25%: 133.5\n\n50% (Median): 153\n\n75%: 166\n\nMax: 202\n\n* **exng: Exercise induced angina (1 = yes, 0 = no) (integer)**\n\nCount: 303\n\nUnique Values: 2\n\nValue Counts: {0: 204, 1: 99}\n\n* **oldpeak: ST depression induced by exercise relative to rest (float)**\n\nCount: 303\n\nMean: 1.04\n\nStandard Deviation: 1.16\n\nMin: 0.0\n\n25%: 0.0\n\n50% (Median): 0.8\n\n75%: 1.6\n\nMax: 6.2\n\n* **slp: The slope of the peak exercise ST segment (0 = upsloping, 1 = flat, 2 = downsloping) (integer)**\n\nCount: 303\n\nUnique Values: 3\n\nValue Counts: {0: 21, 1: 142, 2: 140}\n\n* **caa: Number of major vessels (0-3) colored by fluoroscopy (integer)**\n\nCount: 303\n\nUnique Values: 5\n\nValue Counts: {0: 175, 1: 65, 2: 38, 3: 20, 4: 5}\n\n* **thall: Thalassemia (0 = normal, 1 = fixed defect, 2 = reversible defect) (integer)**\n\nCount: 303\n\nUnique Values: 4\n\nValue Counts: {2: 166, 3: 117, 1: 18, 0: 2}\n\n* **output: Target variable (1 = heart disease, 0 = no heart disease) (integer)**\n\nCount: 303\n\nUnique Values: 2\n\nValue Counts: {1: 165, 0: 138}","metadata":{}},{"cell_type":"markdown","source":"# Renaming the columns:","metadata":{}},{"cell_type":"code","source":"new_column_names = [\"age\", \"sex\", \"cp\", \"trtbps\", \"chol\", \"fbs\", \"rest_ecg\", \"thalach\", \"exang\", \"oldpeak\", \"slope\", \"ca\", \"thal\", \"target\"]\nheart_data.columns = new_column_names","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"* A list of new column names is created and assigned to new_column_names.\n* heart_data.columns = new_column_names renames the columns in the DataFrame.","metadata":{}},{"cell_type":"code","source":"print(\"\\nDataset after renaming columns:\")\ndisplay(heart_data.head())","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"* heart_data.head() is used again to display the first five rows of the dataset after renaming the columns, confirming that the changes have been applied.","metadata":{}},{"cell_type":"markdown","source":"# Preparation for Exploratory Data Analysis(EDA)","metadata":{}},{"cell_type":"markdown","source":"## Examining Missing Values","metadata":{}},{"cell_type":"code","source":"# Checking for missing values in the dataset\nmissing_values = heart_data.isnull().sum()\n\n# Creating a table for missing values\nmissing_values_table = pd.DataFrame(missing_values, columns=['Missing Values'])\nmissing_values_table['% of Total Values'] = (missing_values_table['Missing Values'] / len(heart_data)) * 100\n\n# Displaying the table\nprint(\"Missing Values Table:\")\ndisplay(missing_values_table)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Analysis:\n\n* No Missing Values: The dataset does not have any missing values in any of the variables. This means that all the columns are complete and ready for further analysis without the need for handling missing data.\n\n* This is a positive finding, as it simplifies the data preprocessing steps and allows you to move directly to more advanced exploratory data analysis and modeling steps.","metadata":{}},{"cell_type":"markdown","source":"**Checking for missing values:**\n\n* heart_data.isnull().sum() calculates the number of missing values in each column of the DataFrame.\n\n**Creating a table for missing values**\n\n* A DataFrame missing_values_table is created to store the count of missing values for each column.\n* A new column % of Total Values is added to the DataFrame, which shows the percentage of missing values out of the total number of rows in the dataset.\n\n**Displaying the table:**\n\n* The display(missing_values_table) function displays the table in the Jupyter notebook.","metadata":{}},{"cell_type":"markdown","source":"## Examining Unique Values","metadata":{}},{"cell_type":"markdown","source":"**Importance of Unique Value Analysis**\n\nUnique value analysis is a crucial step in exploratory data analysis (EDA) for several reasons:\n\n* Understanding Data Distribution: Analyzing unique values helps understand how the data is distributed across different categories, especially for categorical variables.\n\n* Detecting Anomalies and Errors: It can help identify anomalies, errors, or inconsistencies in the dataset. For example, unexpected unique values may indicate data entry errors or outliers.\n\n* Feature Engineering: Unique value analysis can guide feature engineering decisions. For instance, understanding the diversity of values can help decide whether to encode categorical variables using one-hot encoding or other methods.\n\n* Model Selection: Some machine learning algorithms may perform better with specific types of data. Knowing the unique values can help in selecting appropriate models and preprocessing techniques.\n\n* Data Cleaning: Identifying unique values is essential for data cleaning, as it allows for the detection and handling of missing values, duplicates, or irrelevant categories.","metadata":{}},{"cell_type":"code","source":"# Analyzing unique values in each column\nunique_values = heart_data.nunique()\n\n# Creating a table for unique values\nunique_values_table = pd.DataFrame(unique_values, columns=['Unique Values'])\n\n# Displaying the table\nprint(\"Unique Values Table:\")\ndisplay(unique_values_table)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"**Analyzing unique values:**\n\n* heart_data.nunique() calculates the number of unique values in each column of the DataFrame.\n\n**Creating a table for unique values:**\n\n* A DataFrame unique_values_table is created to store the count of unique values for each column.\n\n**Displaying the table:**\n\n* The display(unique_values_table) function displays the table in the Jupyter notebook.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Unique Values\n\nBased on the unique values, we can classify the variables into categorical and numeric types. Here is the analysis and classification:\n\n**age:**\n\n* Unique Values: 41\n* Type: Numeric\n* Reason: Age is a continuous variable representing the age of the patients. Even though it has 41 unique values, it is naturally numeric.\n\n**sex:**\n\n* Unique Values: 2\n* Type: Categorical\n* Reason: Represents gender, typically encoded as 0 (female) and 1 (male). It is a binary categorical variable.\n\n**cp:**\n\n* Unique Values: 4\n* Type: Categorical\n* Reason: Represents chest pain type with 4 distinct categories. It is an ordinal categorical variable.\n\n**trtbps:**\n\n* Unique Values: 49\n* Type: Numeric\n* Reason: Resting blood pressure is a continuous variable and naturally numeric.\n\n**chol:**\n\n* Unique Values: 152\n* Type: Numeric\n* Reason: Serum cholesterol level is a continuous variable and naturally numeric.\n\n**fbs:**\n\n* Unique Values: 2\n* Type: Categorical\n* Reason: Fasting blood sugar > 120 mg/dl, represented as 1 (true) and 0 (false). It is a binary categorical variable.\n\n**rest_ecg:**\n\n* Unique Values: 3\n* Type: Categorical\n* Reason: Resting electrocardiographic results with 3 distinct categories. It is an ordinal categorical variable.\n\n**thalach:**\n\n* Unique Values: 91\n* Type: Numeric\n* Reason: Maximum heart rate achieved is a continuous variable and naturally numeric.\n\n**exang:**\n\n* Unique Values: 2\n* Type: Categorical\n* Reason: Exercise induced angina, represented as 1 (yes) and 0 (no). It is a binary categorical variable.\n\n**oldpeak:**\n\n* Unique Values: 40\n* Type: Numeric\n* Reason: ST depression induced by exercise relative to rest is a continuous variable and naturally numeric.\n\n**slope:**\n\n* Unique Values: 3\n* Type: Categorical\n* Reason: Slope of the peak exercise ST segment with 3 distinct categories. It is an ordinal categorical variable.\n\n**ca:**\n\n* Unique Values: 5\n* Type: Categorical\n* Reason: Number of major vessels colored by fluoroscopy, with 5 distinct categories. It is an ordinal categorical variable.\n\n**thal:**\n\n* Unique Values: 4\n* Type: Categorical\n* Reason: Thalassemia with 4 distinct categories. It is an ordinal categorical variable.\n\n**target:**\n\n* Unique Values: 2\n* Type: Categorical\n* Reason: Target variable indicating the presence of heart disease (1) or absence (0). It is a binary categorical variable.\n\n**Summary**\n\nBased on the analysis, the variables can be classified as follows:\n\n**Numeric Variables:**\n\n* age\n* trtbps\n* chol\n* thalach\n* oldpeak\n\n**Categorical Variables:**\n\n* sex\n* cp\n* fbs\n* rest_ecg\n* exang\n* slope\n* ca\n* thal\n* target\n\nThis classification helps in understanding the nature of each variable, which is crucial for selecting appropriate analysis techniques and preprocessing steps.","metadata":{}},{"cell_type":"code","source":"# Assigning categorical and numeric variables to respective variables\ncategoric_var = [\"sex\", \"cp\", \"fbs\", \"rest_ecg\", \"exang\", \"slope\", \"ca\", \"thal\", \"target\"]\nnumeric_var = [\"age\", \"trtbps\", \"chol\", \"thalach\", \"oldpeak\"]\n\n# Displaying the lists of categorical and numeric variables\nprint(\"Categorical Variables:\", categoric_var)\nprint(\"Numeric Variables:\", numeric_var)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"* The list categoric_var contains the names of all the categorical variables identified from the dataset.\n* The list numeric_var contains the names of all the numeric variables identified from the dataset.\n* The print statements are used to display the lists of categorical and numeric variables.\n\nThis code will help you keep track of your categorical and numeric variables, which is useful for further analysis and preprocessing steps. ","metadata":{}},{"cell_type":"markdown","source":"# Exploratory Data Analysis(EDA)","metadata":{}},{"cell_type":"markdown","source":"### Importance of Exploratory Data Analysis (EDA) in Data Science\n\nExploratory Data Analysis (EDA) is a crucial step in the data science process, serving as the foundation for understanding the data and driving the subsequent phases of data analysis, model building, and interpretation. Here’s a detailed explanation of the importance and benefits of EDA:\n\n#### 1. **Understanding the Dataset**\n\n- **Data Types and Structures**: EDA helps in identifying the data types (categorical, numerical, boolean, etc.) and the structure of the dataset (tables, rows, columns). This understanding is essential for selecting appropriate analytical methods and tools.\n- **Summary Statistics**: It provides insights into summary statistics like mean, median, mode, standard deviation, and range, which give an overview of the central tendency, dispersion, and shape of the dataset.\n\n#### 2. **Identifying Data Quality Issues**\n\n- **Missing Values**: EDA helps in detecting missing values, understanding their patterns, and deciding on appropriate imputation methods or whether to remove them.\n- **Outliers**: It helps in identifying outliers that can distort statistical analyses and models. Decisions can be made on how to handle these outliers.\n- **Inconsistencies and Errors**: EDA reveals data inconsistencies and errors such as incorrect data entries, duplicates, and invalid data, which need to be cleaned for accurate analysis.\n\n#### 3. **Uncovering Patterns and Relationships**\n\n- **Trends and Patterns**: Through visualizations and statistical analysis, EDA uncovers trends and patterns within the data that might not be immediately apparent.\n- **Correlations**: It helps in understanding the relationships and correlations between different variables, which can inform feature selection and engineering for machine learning models.\n- **Distributions**: EDA reveals the distributions of individual variables, helping to understand their behavior and whether they meet the assumptions of statistical tests and models.\n\n#### 4. **Hypothesis Generation**\n\n- **Formulating Hypotheses**: By exploring the data, analysts can generate hypotheses about the underlying processes and factors influencing the data. These hypotheses can then be tested using statistical methods.\n- **Testing Assumptions**: EDA allows for the testing of assumptions required for statistical modeling, such as normality, homoscedasticity, and independence of observations.\n\n#### 5. **Guiding Data Preparation**\n\n- **Feature Engineering**: Insights from EDA guide the creation of new features and the transformation of existing features to improve model performance.\n- **Data Transformation**: EDA indicates the need for data transformations such as normalization, scaling, or encoding categorical variables for compatibility with machine learning algorithms.\n\n#### 6. **Improving Model Building**\n\n- **Algorithm Selection**: Understanding the data through EDA informs the selection of appropriate machine learning algorithms. For instance, knowing the distribution and relationships within the data can guide the choice between linear and non-linear models.\n- **Model Validation**: EDA provides a baseline understanding against which the results of models can be compared. It helps in validating models and ensuring that they are not overfitting or underfitting the data.\n\n#### 7. **Communicating Findings**\n\n- **Data Visualization**: EDA involves creating visualizations that communicate findings clearly and effectively to stakeholders. Visual representations are often more intuitive and impactful than raw data or statistical summaries.\n- **Reporting**: The insights gained from EDA form the basis of reporting and storytelling, helping to convey the significance and implications of the data analysis to non-technical audiences.\n\n### Key Techniques and Tools in EDA\n\n- **Descriptive Statistics**: Measures of central tendency (mean, median, mode), measures of variability (standard deviation, variance, range), and measures of shape (skewness, kurtosis).\n- **Data Visualization**: Histograms, box plots, scatter plots, bar charts, heatmaps, and pair plots to visualize distributions, relationships, and patterns.\n- **Correlation Analysis**: Correlation matrices and scatter plot matrices to understand relationships between variables.\n- **Univariate and Multivariate Analysis**: Analyzing single variables (univariate) and relationships between multiple variables (multivariate).\n\n### Conclusion\n\nEDA is an indispensable step in the data science workflow. It not only helps in understanding the data and its inherent characteristics but also sets the stage for effective data cleaning, transformation, modeling, and communication. By thoroughly exploring the data, data scientists can make informed decisions, build robust models, and derive actionable insights that drive business value and scientific understanding.","metadata":{}},{"cell_type":"markdown","source":"## Uni-variate Analysis - Numerical Variables(Analysis with Histplot and Boxplot)","metadata":{}},{"cell_type":"markdown","source":"### Examining Statistics of Variables","metadata":{}},{"cell_type":"markdown","source":"To perform a statistical analysis on the numeric variables and determine their distribution characteristics, we can use histograms and box plots. These graphs will help us visualize the distribution, skewness, and quartile concentration of the data.","metadata":{}},{"cell_type":"markdown","source":"**Explanation of Graph Types**\n\n* **Histogram:**\n\nA histogram is a graphical representation of the distribution of numerical data. It shows the frequency of data points within specified ranges (bins). The shape of the histogram can indicate whether the data follows a normal distribution, is skewed, or has any other distribution pattern.\nThe histogram's smoothness and the presence of peaks and valleys can reveal the central tendency, variability, and skewness of the data.\n\n* **Box Plot:**\n\nA box plot, also known as a whisker plot, displays the distribution of a dataset based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It also shows potential outliers.\nThe box plot provides insights into the data's central tendency, spread, and symmetry. The length of the whiskers and the presence of outliers can indicate the variability and distribution characteristics.","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"# Importing necessary libraries for visualization\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Setting up the visual style\nsns.set(style=\"whitegrid\")\n\n# Creating histograms and box plots for each numeric variable\nfor column in numeric_var:\n    plt.figure(figsize=(14, 6))\n    \n    # Histogram\n    plt.subplot(1, 2, 1)\n    sns.histplot(heart_data[column], kde=True, color='skyblue')\n    plt.title(f'Histogram of {column}')\n    plt.xlabel(column)\n    plt.ylabel('Frequency')\n    \n    # Box plot\n    plt.subplot(1, 2, 2)\n    sns.boxplot(x=heart_data[column], color='lightgreen')\n    plt.title(f'Box plot of {column}')\n    plt.xlabel(column)\n    \n    plt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"* matplotlib.pyplot is used for creating static, interactive, and animated visualizations.\n* seaborn is a statistical data visualization library based on matplotlib.\n* sns.set(style=\"whitegrid\") ==> This sets the aesthetic style of the plots to a white grid background.\n* The for loop iterates over each column in the numeric_var list.\n* plt.figure(figsize=(14, 6)) sets the figure size.\n* plt.subplot(1, 2, 1) creates the first subplot for the histogram.\n* sns.histplot creates the histogram with a kernel density estimate (KDE) line.\n* plt.subplot(1, 2, 2) creates the second subplot for the box plot.\n* sns.boxplot creates the box plot.\n* plt.show() displays the plots.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Age (age) Variable\n\n#### Histogram Analysis\n\n- **Shape of Distribution**: The histogram of age appears to be roughly bell-shaped, indicating a distribution that is close to normal. This suggests that the ages in the dataset follow a normal distribution pattern.\n- **KDE Line**: The Kernel Density Estimate (KDE) line overlays the histogram and helps to visualize the underlying distribution. The KDE line also suggests a bell-shaped curve.\n- **Frequency Peaks**: The highest frequency of ages is around the 50-60 range, indicating that most of the patients are in this age group.\n\n#### Box Plot Analysis\n\n- **Central Tendency**: The box plot shows the median age, which is the line inside the box. The median is around 55, indicating that half of the patients are younger than 55 and half are older.\n- **Quartile Distribution**: \n  - The first quartile (Q1) is around 48.\n  - The third quartile (Q3) is around 61.\n- **Interquartile Range (IQR)**: The IQR, which is the range between Q1 and Q3, shows where the middle 50% of the data lies. Here, it spans from 48 to 61.\n- **Whiskers**: The whiskers extend from Q1 and Q3 to the minimum and maximum values within 1.5 times the IQR. They indicate the range of most of the data.\n- **Outliers**: There are no apparent outliers in the box plot, as there are no data points outside the whiskers.\n\n#### Detailed Statistical Insights\n\n1. **Normality**: \n   - The histogram's bell-shaped curve suggests that the age data is approximately normally distributed.\n   - The absence of significant skewness (as the distribution is fairly symmetric) supports this conclusion.\n\n2. **Skewness**:\n   - There is no significant skewness in the age data. The distribution is symmetric around the median.\n\n3. **Quartile Concentration**:\n   - The box plot shows that the data is fairly evenly distributed across the quartiles.\n   - The middle 50% of the data (between Q1 and Q3) lies between 48 and 61, with a median of 55.\n\n4. **Implications for Analysis**:\n   - The normal distribution of the age variable suggests that parametric statistical methods can be appropriately used for analysis.\n   - The lack of skewness and outliers implies that the age data is consistent and reliable for further modeling and predictions.\n\n### Summary\n\nThe visualizations indicate that the age variable follows an approximately normal distribution, with the data concentrated around the ages of 48 to 61. There is no significant skewness, and the absence of outliers suggests the data is well-behaved. This makes the age variable suitable for parametric statistical analyses and predictive modeling. If you have more visuals or need further analysis on other variables, please let me know!","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Resting Blood Pressure (trtbps) Variable\n\n#### Histogram Analysis\n\n- **Shape of Distribution**: The histogram for resting blood pressure (trtbps) shows a distribution that is slightly skewed to the right. This indicates that while most of the values are clustered around the central region, there are some higher values that stretch out the distribution to the right.\n- **KDE Line**: The Kernel Density Estimate (KDE) line overlays the histogram and helps to visualize the underlying distribution. The KDE line confirms the right skewness.\n- **Frequency Peaks**: The highest frequency of resting blood pressure values is around the 120-140 mm Hg range.\n\n#### Box Plot Analysis\n\n- **Central Tendency**: The box plot shows the median resting blood pressure, which is the line inside the box. The median is around 130 mm Hg.\n- **Quartile Distribution**:\n  - The first quartile (Q1) is around 120 mm Hg.\n  - The third quartile (Q3) is around 140 mm Hg.\n- **Interquartile Range (IQR)**: The IQR, which is the range between Q1 and Q3, shows where the middle 50% of the data lies. Here, it spans from 120 to 140 mm Hg.\n- **Whiskers**: The whiskers extend from Q1 and Q3 to the minimum and maximum values within 1.5 times the IQR. They indicate the range of most of the data.\n- **Outliers**: There are several outliers on the higher end of the box plot, indicating that there are some patients with significantly higher resting blood pressure values.\n\n#### Detailed Statistical Insights\n\n1. **Normality**:\n   - The histogram's shape indicates that the resting blood pressure data does not follow a perfect normal distribution due to the right skewness.\n\n2. **Skewness**:\n   - The distribution is skewed to the right, as evidenced by the tail on the right side of the histogram and the presence of outliers in the box plot.\n\n3. **Quartile Concentration**:\n   - The box plot shows that the data is concentrated between 120 and 140 mm Hg, with a median of 130 mm Hg.\n   - The presence of outliers indicates that there are some patients with unusually high resting blood pressure values.\n\n4. **Implications for Analysis**:\n   - The right skewness suggests that parametric statistical methods assuming normality might not be appropriate. Non-parametric methods or transformations (such as logarithmic transformations) could be considered to normalize the data.\n   - The presence of outliers should be carefully considered, as they might have a significant impact on statistical analyses and predictive modeling.\n\n### Summary\n\nThe visualizations indicate that the resting blood pressure variable has a right-skewed distribution with a concentration of values between 120 and 140 mm Hg. The presence of outliers suggests that there are some patients with significantly higher blood pressure values, which could affect analyses and predictions. Adjustments or different statistical methods may be needed to account for the skewness and outliers.\n\nIf you have more visuals or need further analysis on other variables, please let me know!","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Cholesterol (chol) Variable\n\n#### Histogram Analysis\n\n- **Shape of Distribution**: The histogram for cholesterol (chol) shows a distribution that is slightly right-skewed. This indicates that while most of the values are clustered around the central region, there are some higher values that stretch out the distribution to the right.\n- **KDE Line**: The Kernel Density Estimate (KDE) line overlays the histogram and helps to visualize the underlying distribution. The KDE line confirms the slight right skewness.\n- **Frequency Peaks**: The highest frequency of cholesterol values is around the 200-250 mg/dL range.\n\n#### Box Plot Analysis\n\n- **Central Tendency**: The box plot shows the median cholesterol level, which is the line inside the box. The median is around 240 mg/dL.\n- **Quartile Distribution**:\n  - The first quartile (Q1) is around 211 mg/dL.\n  - The third quartile (Q3) is around 275 mg/dL.\n- **Interquartile Range (IQR)**: The IQR, which is the range between Q1 and Q3, shows where the middle 50% of the data lies. Here, it spans from 211 to 275 mg/dL.\n- **Whiskers**: The whiskers extend from Q1 and Q3 to the minimum and maximum values within 1.5 times the IQR. They indicate the range of most of the data.\n- **Outliers**: There are several outliers on the higher end of the box plot, indicating that there are some patients with significantly higher cholesterol values.\n\n#### Detailed Statistical Insights\n\n1. **Normality**:\n   - The histogram's shape indicates that the cholesterol data does not follow a perfect normal distribution due to the right skewness.\n\n2. **Skewness**:\n   - The distribution is slightly skewed to the right, as evidenced by the tail on the right side of the histogram and the presence of outliers in the box plot.\n\n3. **Quartile Concentration**:\n   - The box plot shows that the data is concentrated between 211 and 275 mg/dL, with a median of 240 mg/dL.\n   - The presence of outliers indicates that there are some patients with unusually high cholesterol values.\n\n4. **Implications for Analysis**:\n   - The slight right skewness suggests that parametric statistical methods assuming normality might not be perfectly appropriate. Non-parametric methods or transformations (such as logarithmic transformations) could be considered to normalize the data.\n   - The presence of outliers should be carefully considered, as they might have a significant impact on statistical analyses and predictive modeling.\n\n### Summary\n\nThe visualizations indicate that the cholesterol variable has a slightly right-skewed distribution with a concentration of values between 211 and 275 mg/dL. The presence of outliers suggests that there are some patients with significantly higher cholesterol values, which could affect analyses and predictions. Adjustments or different statistical methods may be needed to account for the skewness and outliers.\n\nIf you have more visuals or need further analysis on other variables, please let me know!","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Maximum Heart Rate Achieved (thalach) Variable\n\n#### Histogram Analysis\n\n- **Shape of Distribution**: The histogram for maximum heart rate achieved (thalach) shows a distribution that is slightly left-skewed. This indicates that while most of the values are clustered around the central region, there are some lower values that stretch out the distribution to the left.\n- **KDE Line**: The Kernel Density Estimate (KDE) line overlays the histogram and helps to visualize the underlying distribution. The KDE line confirms the slight left skewness.\n- **Frequency Peaks**: The highest frequency of maximum heart rate values is around the 140-160 bpm range.\n\n#### Box Plot Analysis\n\n- **Central Tendency**: The box plot shows the median maximum heart rate, which is the line inside the box. The median is around 150 bpm.\n- **Quartile Distribution**:\n  - The first quartile (Q1) is around 133 bpm.\n  - The third quartile (Q3) is around 166 bpm.\n- **Interquartile Range (IQR)**: The IQR, which is the range between Q1 and Q3, shows where the middle 50% of the data lies. Here, it spans from 133 to 166 bpm.\n- **Whiskers**: The whiskers extend from Q1 and Q3 to the minimum and maximum values within 1.5 times the IQR. They indicate the range of most of the data.\n- **Outliers**: There is one outlier on the lower end of the box plot, indicating that there is a patient with a significantly lower maximum heart rate.\n\n#### Detailed Statistical Insights\n\n1. **Normality**:\n   - The histogram's shape indicates that the maximum heart rate data does not follow a perfect normal distribution due to the slight left skewness.\n\n2. **Skewness**:\n   - The distribution is slightly skewed to the left, as evidenced by the tail on the left side of the histogram and the presence of an outlier in the box plot.\n\n3. **Quartile Concentration**:\n   - The box plot shows that the data is concentrated between 133 and 166 bpm, with a median of 150 bpm.\n   - The presence of an outlier indicates that there is a patient with an unusually low maximum heart rate.\n\n4. **Implications for Analysis**:\n   - The slight left skewness suggests that parametric statistical methods assuming normality might not be perfectly appropriate. Non-parametric methods or transformations could be considered to normalize the data.\n   - The presence of an outlier should be carefully considered, as it might have a significant impact on statistical analyses and predictive modeling.\n\n### Summary\n\nThe visualizations indicate that the maximum heart rate variable has a slightly left-skewed distribution with a concentration of values between 133 and 166 bpm. The presence of an outlier suggests that there is a patient with a significantly lower maximum heart rate, which could affect analyses and predictions. Adjustments or different statistical methods may be needed to account for the skewness and outlier.\n\nIf you have more visuals or need further analysis on other variables, please let me know!","metadata":{}},{"cell_type":"markdown","source":"### Analysis of ST Depression (oldpeak) Variable\n\n#### Histogram Analysis\n\n- **Shape of Distribution**: The histogram for ST depression (oldpeak) shows a distribution that is highly right-skewed. This indicates that most of the values are clustered towards the lower end, with a long tail extending to the right.\n- **KDE Line**: The Kernel Density Estimate (KDE) line overlays the histogram and helps to visualize the underlying distribution. The KDE line confirms the significant right skewness.\n- **Frequency Peaks**: The highest frequency of ST depression values is around 0, indicating that many patients have little to no ST depression.\n\n#### Box Plot Analysis\n\n- **Central Tendency**: The box plot shows the median ST depression value, which is the line inside the box. The median is around 0.8.\n- **Quartile Distribution**:\n  - The first quartile (Q1) is around 0.\n  - The third quartile (Q3) is around 1.6.\n- **Interquartile Range (IQR)**: The IQR, which is the range between Q1 and Q3, shows where the middle 50% of the data lies. Here, it spans from 0 to 1.6.\n- **Whiskers**: The whiskers extend from Q1 and Q3 to the minimum and maximum values within 1.5 times the IQR. They indicate the range of most of the data.\n- **Outliers**: There are several outliers on the higher end of the box plot, indicating that there are some patients with significantly higher ST depression values.\n\n#### Detailed Statistical Insights\n\n1. **Normality**:\n   - The histogram's shape indicates that the ST depression data does not follow a normal distribution due to the significant right skewness.\n\n2. **Skewness**:\n   - The distribution is highly skewed to the right, as evidenced by the long tail on the right side of the histogram and the presence of numerous outliers in the box plot.\n\n3. **Quartile Concentration**:\n   - The box plot shows that the data is heavily concentrated between 0 and 1.6, with a median of 0.8.\n   - The presence of outliers indicates that there are some patients with unusually high ST depression values.\n\n4. **Implications for Analysis**:\n   - The significant right skewness suggests that parametric statistical methods assuming normality might not be appropriate. Non-parametric methods or transformations (such as logarithmic transformations) could be considered to normalize the data.\n   - The presence of numerous outliers should be carefully considered, as they might have a significant impact on statistical analyses and predictive modeling.\n\n### Summary\n\nThe visualizations indicate that the ST depression variable has a highly right-skewed distribution with a concentration of values between 0 and 1.6. The presence of numerous outliers suggests that there are some patients with significantly higher ST depression values, which could affect analyses and predictions. Adjustments or different statistical methods may be needed to account for the skewness and outliers.\n\nIf you have more visuals or need further analysis on other variables, please let me know!","metadata":{}},{"cell_type":"markdown","source":"## Categorical Variables(Analysis with Pie Chart)","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Setting the color palette\ncolors = sns.color_palette(\"pastel\")\n\n# Visualizing categorical variables using pie charts\nfor column in categoric_var:\n    plt.figure(figsize=(8, 8))\n    heart_data[column].value_counts().plot.pie(autopct='%1.1f%%', startangle=140, colors=colors)\n    plt.title(f'Pie Chart of {column}')\n    plt.ylabel('')\n    plt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Analysis of Sex Variable\n\n#### Distribution\nThe **sex** variable has two categories:\n- **1 (Male)**\n- **0 (Female)**\n\nThe pie chart shows the distribution of males and females in the dataset.\n\n#### Frequency Counts\n- **Male (1)**: A significant majority.\n- **Female (0)**: A smaller portion compared to males.\n\nThis distribution suggests that the dataset is male-dominated.\n\n#### Implications\n- **Potential Bias**: The model might be biased towards male patients if the imbalance is not addressed.\n- **Statistical Analysis**: Additional statistical techniques, such as stratified sampling or weighting, may be needed to ensure fair representation in the model.\n\n### Analysis of Chest Pain Type (Cp) Variable\n\n#### Distribution\nThe **cp** variable has four categories:\n- **0**: Typical angina\n- **1**: Atypical angina\n- **2**: Non-anginal pain\n- **3**: Asymptomatic\n\nThe pie chart illustrates the distribution of different chest pain types.\n\n#### Frequency Counts\n- **0 (Typical Angina)**: The smallest category.\n- **1 (Atypical Angina)**: Moderately represented.\n- **2 (Non-anginal Pain)**: The largest category.\n- **3 (Asymptomatic)**: Also significantly represented.\n\nThis distribution shows a varied representation of chest pain types, with non-anginal pain being the most common.\n\n#### Implications\n- **Model Relevance**: Each type of chest pain may have different implications for heart disease prediction, and their relative frequencies can impact model training.\n- **Feature Importance**: The presence of various chest pain types indicates that this variable could be a significant predictor in the model, as chest pain is a primary symptom of heart conditions.\n\n### Summary\n- **Sex Variable**: Needs consideration for potential gender bias in the dataset. The model should account for this to ensure balanced predictions across genders.\n- **Chest Pain Type (Cp) Variable**: Shows diverse types of chest pain with varying frequencies. This variable is likely crucial for prediction models, highlighting the importance of considering the type of chest pain in heart attack prediction.\n\n### Next Steps\n- Address the gender imbalance through appropriate data preprocessing techniques.\n- Explore the relationship between chest pain types and other variables in the dataset to understand their combined effects on heart attack prediction.\n- Consider additional visualizations and statistical tests to further analyze these categorical variables and their impact on the target variable.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Fasting Blood Sugar (Fbs) Variable\n\n#### Distribution\nThe **fbs** variable has two categories:\n- **1**: Fasting blood sugar > 120 mg/dl (true)\n- **0**: Fasting blood sugar <= 120 mg/dl (false)\n\n#### Frequency Counts\n- **1 (True)**: Represents the count of patients with high fasting blood sugar.\n- **0 (False)**: Represents the count of patients with normal fasting blood sugar.\n\nWe will use the previously calculated counts for analysis.\n\n#### Implications\n- **Health Indicator**: High fasting blood sugar is a risk factor for heart disease. This variable can help identify patients at higher risk.\n- **Model Feature**: The binary nature of this variable makes it straightforward for inclusion in predictive models.\n\n### Analysis of Resting ECG (Rest_ecg) Variable\n\n#### Distribution\nThe **rest_ecg** variable has three categories:\n- **0**: Normal\n- **1**: Having ST-T wave abnormality\n- **2**: Showing probable or definite left ventricular hypertrophy\n\n#### Frequency Counts\n- **0 (Normal)**: Represents the count of patients with normal ECG results.\n- **1 (ST-T Wave Abnormality)**: Represents the count of patients with ST-T wave abnormalities.\n- **2 (Left Ventricular Hypertrophy)**: Represents the count of patients with probable or definite left ventricular hypertrophy.\n\nWe will use the previously calculated counts for analysis.\n\n#### Implications\n- **Diagnostic Tool**: Resting ECG results are critical for diagnosing heart conditions. Each category indicates a different level of heart function or abnormality.\n- **Feature Importance**: The diverse categories in resting ECG results can significantly impact the prediction of heart disease.\n\n### Value Counts\n\n#### Fbs Variable\n- **1 (True)**: Value count will be provided based on the data.\n- **0 (False)**: Value count will be provided based on the data.\n\n#### Rest_ecg Variable\n- **0 (Normal)**: Value count will be provided based on the data.\n- **1 (ST-T Wave Abnormality)**: Value count will be provided based on the data.\n- **2 (Left Ventricular Hypertrophy)**: Value count will be provided based on the data.\n\n### Summary\n- **Fbs Variable**: High fasting blood sugar is a significant risk factor and should be carefully analyzed. The count of values in each category helps understand the prevalence of high fasting blood sugar in the dataset.\n- **Rest_ecg Variable**: Resting ECG results are crucial for heart disease diagnosis. The distribution and count of each category provide insights into the heart health of the patients in the dataset.","metadata":{}},{"cell_type":"markdown","source":"# Examining the Missing Data According to the Analysis Result","metadata":{}},{"cell_type":"markdown","source":"There is an inconsistency because the values 0, 1, 2, and 3 should map to:\n\n* 0: Normal\n* 1: Fixed defect\n* 2: Reversible defect\n* 3: Another category that was identified as part of thalassemia analysis, possibly incorrect or a placeholder.\n\nGiven the value counts you provided:\n\n* 2 (Reversible defect): 166 instances\n* 3 (Fixed defect): 117 instances\n* 1 (Normal): 18 instances\n* 0: 2 instances (possibly erroneous)\n\nIt appears that the value 0 is indeed rare and likely represents incorrect or missing data that was not properly imputed or encoded. This value might have been used as a placeholder or default value during data entry or preprocessing.\n\n**Solution**\n\nTo address this issue, you should consider treating the instances with a value of 0 as missing or erroneous and decide how to handle them. Here are some steps you can take:\n\n**Verify and Correct Data:**\n\nCross-check these instances with the original data source or medical records if available.\nConfirm if these values were intended to be placeholders for missing data.\nImputation or Removal:\n\nIf these values are confirmed to be incorrect, you can impute them based on the distribution of other values in the thal variable or relevant patient characteristics.\nAlternatively, you can remove these instances if they constitute a very small portion of the dataset and are unlikely to impact the overall analysis significantly.\nDocument the Changes:Ü\n\nDocument any assumptions or changes made to the dataset for transparency and reproducibility of your analysis.","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"# Identify and handle the erroneous '0' values in the 'thal' column\nheart_data['thal'] = heart_data['thal'].replace(0, np.nan)\n\n# Option 1: Impute missing values based on the mode (most common value)\nheart_data['thal'].fillna(heart_data['thal'].mode()[0], inplace=True)\n\n# Option 2: Drop rows with erroneous 'thal' values\n# heart_data = heart_data[heart_data['thal'].notna()]\n\n# Verify the changes\nprint(heart_data['thal'].value_counts())","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"**Purpose:** \n* This line replaces all occurrences of the value 0 in the thal column with NaN (Not a Number), which is commonly used to represent missing or undefined data in pandas.\n\n**Method:** \n* replace(0, np.nan) replaces all instances of 0 with NaN.\n\n**Purpose:** \n* This line imputes the missing values (NaN) in the thal column with the most common value (mode) in the column.\n\n**Method:** \n* heart_data['thal'].mode()[0]: Calculates the mode (most frequent value) of the thal column. \n* fillna(..., inplace=True): Replaces all NaN values with the mode value in place (i.e., modifies the original DataFrame directly).\n\n**Purpose:**\n* This line of code (commented out) provides an alternative approach where rows with NaN values in the thal column are removed from the DataFrame.\n\n**Method:**\n* heart_data['thal'].notna(): Returns a boolean Series indicating whether each value in the thal column is not NaN.\n* heart_data[...]: Filters the DataFrame to include only rows where the thal value is not NaN.\n\n**Purpose:**\n* This line prints the count of unique values in the thal column after handling the erroneous 0 values.\n\n**Method:** \n* value_counts() returns the count of unique values in the thal column, which helps verify that the erroneous values have been correctly handled.\n","metadata":{}},{"cell_type":"markdown","source":"**Steps in Context**\n\n**Replacing Erroneous Values:**\n\nThe code identifies and replaces erroneous values (0) in the thal column with NaN, marking them as missing data.\n\n**Handling Missing Values:**\n\nOption 1 (Imputation): The missing values are imputed with the mode of the thal column, effectively filling them with the most frequent value.\n\nOption 2 (Removal): Alternatively, rows with missing values in the thal column can be removed entirely. This step is optional and depends on the chosen data handling strategy.\nVerification:\n\nThe final step involves printing the value counts of the thal column to verify that the erroneous values have been addressed appropriately.\n\n**Conclusion**\n\nThis code ensures that the thal variable does not contain erroneous values (0), which might distort the analysis. By either imputing the missing values with the mode or removing the affected rows, the dataset is cleaned and prepared for further analysis.","metadata":{}},{"cell_type":"markdown","source":"# After thorough research, here is the corrected information regarding the thal variable in the UCI Heart Disease dataset:\n\n* 1: Fixed defect\n* 2: Normal\n* 3: Reversible defect","metadata":{}},{"cell_type":"markdown","source":"# Latest updated version of Thal variable","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"# Setting the color palette\ncolors = sns.color_palette(\"pastel\")\n\n# Visualizing the updated 'thal' variable using a pie chart\nplt.figure(figsize=(8, 8))\nheart_data['thal'].value_counts().plot.pie(autopct='%1.1f%%', startangle=140, colors=colors)\nplt.title('Pie Chart of thal')\nplt.ylabel('')\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"* colors = sns.color_palette(\"pastel\")\n* This sets a pastel color palette for the pie chart to make it visually appealing.\n\n* plt.figure(figsize=(8, 8)): Sets the figure size to 8x8 inches.\n* heart_data['thal'].value_counts().plot.pie(...): Generates a pie chart for the thal variable. value_counts() * counts the unique values and plot.pie() creates the pie chart.\n* autopct='%1.1f%%': Displays the percentage of each slice on the pie chart.\n* startangle=140: Starts the first slice at 140 degrees.\n* colors=colors: Uses the pastel color palette set earlier.\n* plt.title('Pie Chart of thal'): Sets the title of the pie chart.\n* plt.ylabel(''): Removes the y-axis label for a cleaner look.\n* plt.show(): Displays the pie chart.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Thal (Thalassemia) Variable\n\n#### Distribution\nThe **thal** variable now represents the type of thalassemia with adjusted values:\n- **1**: Fixed defect\n- **2**: Normal (including previous missing values replaced with 2)\n- **3**: Reversible defect\n\n#### Frequency Counts (from original dataset prior to visualization):\n- **1 (Fixed defect)**: 5.9%\n- **2 (Normal)**: 55.5% (includes 54.8% original normal and 0.7% previously missing)\n- **3 (Reversible defect)**: 38.6%\n\n#### Implications\n- **Diagnostic Significance**: \n  - **Fixed defect (1)**: Represents a permanent defect in the heart's functioning. This is usually a critical indicator of severe heart disease.\n  - **Normal (2)**: Indicates normal heart function. Patients with this value have a lower risk of heart disease.\n  - **Reversible defect (3)**: Indicates temporary or reversible defects, often treated with medication or lifestyle changes.\n\n- **Predictive Value**: The variable `thal` is critical in predictive models as it provides direct information about the heart's health. The distribution of these values helps in understanding the prevalence of each type of thalassemia among the patients.\n\n### Insights\n- **Thal Variable**: \n  - The majority of the patients have normal thalassemia readings, indicating a healthier subset of the population or well-managed conditions.\n  - A significant portion shows reversible defects, which are crucial for targeted interventions.\n  - A smaller percentage shows fixed defects, highlighting patients with severe and likely chronic heart conditions.","metadata":{}},{"cell_type":"markdown","source":"Let's perform a detailed univariate analysis of the variables **ca**, **thal**, and **target** using the provided visuals.\n\n### Analysis of CA (Number of Major Vessels) Variable\n\n#### Distribution\nThe **ca** variable represents the number of major vessels (0-3) colored by fluoroscopy:\n- **0**: 57.8%\n- **1**: 21.5%\n- **2**: 12.5%\n- **3**: 6.6%\n- **4**: 1.7%\n\n#### Frequency Counts\n- **0**: Majority of the patients have 0 major vessels colored.\n- **1**: Significant portion have 1 major vessel colored.\n- **2**: A smaller portion have 2 major vessels colored.\n- **3**: Even smaller portion have 3 major vessels colored.\n- **4**: Very few patients have 4 major vessels colored.\n\n#### Implications\n- **Diagnostic Significance**: The number of vessels colored by fluoroscopy can indicate the severity of coronary artery disease. More colored vessels often mean more severe disease.\n- **Predictive Value**: This variable can help in predicting the presence and severity of heart disease. Higher counts are likely associated with higher risk.\n\n\n### Analysis of Target Variable\n\n#### Distribution\nThe **target** variable represents the presence of heart disease:\n- **1 (Heart Disease)**: 54.5%\n- **0 (No Heart Disease)**: 45.5%\n\n#### Frequency Counts\n- **1 (Heart Disease)**: Slightly more than half of the patients have heart disease.\n- **0 (No Heart Disease)**: Slightly less than half of the patients do not have heart disease.\n\n#### Implications\n- **Outcome Variable**: This is the target variable for prediction models. Understanding its distribution is crucial for model training.\n- **Balance in Data**: The distribution is relatively balanced, which is beneficial for model training, as it reduces the risk of biased predictions.\n\n### Insights\n- **CA Variable**: The number of colored vessels is a crucial diagnostic tool. Most patients have no colored vessels, but a significant portion have 1 or more, indicating varying levels of disease severity.\n- **Target Variable**: The relatively balanced distribution between patients with and without heart disease ensures that models can learn to differentiate between the two classes effectively.","metadata":{}},{"cell_type":"markdown","source":"# Importance of Bivariate Analysis in Data Science","metadata":{}},{"cell_type":"markdown","source":"#### What is Bivariate Analysis?\nBivariate analysis involves the simultaneous analysis of two variables to understand the relationship between them. It extends beyond univariate analysis, which focuses on individual variables, by examining how pairs of variables interact. This analysis is crucial for understanding the dynamics between predictors and the outcome variable, especially in the context of building predictive models.\n\n#### Key Reasons for Bivariate Analysis\n\n1. **Identifying Relationships and Correlations:**\n   - Bivariate analysis helps in identifying whether there is a relationship between two variables and the nature of this relationship. For example, it can reveal if an increase in one variable tends to be associated with an increase or decrease in another.\n   - Common measures of relationships include correlation coefficients (e.g., Pearson, Spearman) for continuous variables and chi-square tests for categorical variables.\n\n2. **Feature Selection:**\n   - Understanding the relationship between independent variables and the target variable is critical for feature selection in machine learning. Variables that show a strong relationship with the target variable are often more predictive and thus more valuable for inclusion in models.\n   - Features that show little to no relationship with the target variable might be less useful and can be excluded to simplify the model and reduce overfitting.\n\n3. **Detecting Patterns and Trends:**\n   - Bivariate analysis can uncover patterns and trends that are not apparent in univariate analysis. For instance, scatter plots can show trends and clusters, while box plots can reveal differences in distributions across categories.\n   - These patterns can guide further analysis, hypothesis formulation, and decision-making processes.\n\n4. **Assessing Interactions:**\n   - In many cases, the effect of one variable on the target variable may depend on the level of another variable. Bivariate analysis helps in identifying and understanding such interactions.\n   - This understanding can lead to the creation of interaction terms in regression models, improving model accuracy.\n\n5. **Informing Model Choice and Validation:**\n   - Insights from bivariate analysis can inform the choice of models. For instance, if there is a linear relationship between variables, linear regression might be appropriate. Non-linear relationships might suggest the use of more complex models like decision trees or neural networks.\n   - It also aids in model validation by verifying assumptions about variable relationships and distributions.\n\n6. **Enhancing Data Understanding:**\n   - By examining how different variables relate to each other and the target variable, data scientists gain a deeper understanding of the dataset. This comprehensive understanding is essential for making informed decisions about data preprocessing, feature engineering, and modeling strategies.\n\n#### Methods of Bivariate Analysis\n\n1. **Visual Methods:**\n   - **Scatter Plots:** Useful for visualizing relationships between two continuous variables.\n   - **Box Plots:** Helpful for comparing the distribution of a continuous variable across different levels of a categorical variable.\n   - **Heatmaps:** Display correlation matrices to show the strength of relationships between multiple pairs of variables.\n\n2. **Statistical Methods:**\n   - **Correlation Coefficients:** Measure the strength and direction of linear relationships between continuous variables.\n   - **T-tests and ANOVA:** Compare means across different groups for continuous and categorical variable pairs.\n   - **Chi-Square Tests:** Assess the independence of categorical variables.\n\n3. **Multivariate Techniques:**\n   - **Regression Analysis:** Explores the relationship between a dependent variable and one or more independent variables, extending to multiple variables for more complex interactions.\n   - **Logistic Regression:** Used when the target variable is categorical, particularly binary.\n\n### Conclusion\n\nBivariate analysis is a cornerstone of exploratory data analysis (EDA) in data science. It provides crucial insights into relationships between variables, guides feature selection, reveals patterns, and informs modeling decisions. By understanding how variables interact with each other and with the target variable, data scientists can build more accurate and robust predictive models, ultimately leading to better data-driven decisions and outcomes.","metadata":{}},{"cell_type":"markdown","source":"# Visualizing Numeric Variables vs. Target Variable Using Violin Plots","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"# Setting the visual style\nsns.set(style=\"whitegrid\")\n\n# List of numeric variables\nnumeric_var = [\"age\", \"trtbps\", \"chol\", \"thalach\", \"oldpeak\"]\n\n# Creating violin plots for each numeric variable against the target variable\nfor column in numeric_var:\n    plt.figure(figsize=(10, 6))\n    sns.violinplot(x=heart_data['target'], y=heart_data[column], palette=\"pastel\", inner='quartile')\n    plt.title(f'Violin Plot of {column} vs. target')\n    plt.xlabel('Target')\n    plt.ylabel(column)\n    plt.show()\n","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"- **0**: Patients not at risk of a heart attack.\n- **1**: Patients at risk of a heart attack.\n\n### Analyzed Bivariate Analysis from Violin Plots\n\n#### 1. **Age vs. Target**\n\n- **Distribution**:\n  - The violin plot for age vs. target shows that patients at risk of a heart attack (target = 1) generally have a slightly lower median age compared to patients not at risk of a heart attack (target = 0).\n  - The distribution of ages in both groups shows that the age range for patients at risk of a heart attack (target = 1) is slightly wider than that for patients not at risk.\n\n- **Central Tendency**:\n  - The median age for patients at risk of a heart attack appears to be around 55-60 years.\n  - The median age for patients not at risk of a heart attack appears to be around 60 years.\n\n- **Interquartile Range (IQR)**:\n  - The IQR (middle 50% of data) for both groups overlaps significantly, indicating a substantial overlap in age ranges between the two groups.\n\n- **Density**:\n  - The density of ages is higher around the median for both groups, indicating that most patients are clustered around these age ranges.\n  - There are noticeable peaks around 55-60 years for patients at risk of a heart attack, suggesting a higher frequency of patients in this age range.\n\n- **Implications**:\n  - Age seems to be an important factor in heart attack risk, with a tendency for patients around 55-60 years to have a higher likelihood of being at risk of a heart attack.\n  - However, the significant overlap indicates that age alone is not a definitive predictor of heart attack risk.\n\n#### 2. **Resting Blood Pressure (trtbps) vs. Target**\n\n- **Distribution**:\n  - The violin plot for resting blood pressure (trtbps) vs. target shows a higher median resting blood pressure for patients not at risk of a heart attack (target = 0) compared to those at risk (target = 1).\n  - The spread of resting blood pressure values for both groups shows a similar range, but the distribution for patients not at risk is slightly more spread out.\n\n- **Central Tendency**:\n  - The median resting blood pressure for patients not at risk of a heart attack is around 140 mmHg.\n  - The median resting blood pressure for patients at risk of a heart attack is around 130 mmHg.\n\n- **Interquartile Range (IQR)**:\n  - The IQR for both groups overlaps, but the range is slightly narrower for patients at risk of a heart attack.\n\n- **Density**:\n  - The density of resting blood pressure values is higher around the median for both groups, indicating most patients' blood pressure values are clustered around these medians.\n  - There is a notable peak around 130-140 mmHg for both groups, suggesting this range is common among the patients.\n\n- **Implications**:\n  - While the median resting blood pressure is slightly higher in patients not at risk of a heart attack, the considerable overlap and spread indicate that this variable alone is not a strong predictor of heart attack risk.\n  - Further analysis and additional variables should be considered for a comprehensive understanding of heart attack risk factors.\n\n### Summary\n\nBoth violin plots provide valuable insights into the relationship between numeric variables and the target variable. Key takeaways include:\n\n- **Age**: Patients at risk of a heart attack tend to have a slightly lower median age, with a significant number of patients in the 55-60 age range. However, the overlap indicates that age alone is not a definitive predictor.\n- **Resting Blood Pressure (trtbps)**: Patients not at risk of a heart attack tend to have a slightly higher median resting blood pressure, but the overlap and spread indicate that this variable alone is not sufficient to predict heart attack risk.\n\nFor a more robust analysis, these insights should be combined with additional variables and multivariate analysis techniques to develop a comprehensive predictive model for heart attack risk.","metadata":{}},{"cell_type":"markdown","source":"#### 3. **Cholesterol (chol) vs. Target**\n\n- **Distribution**:\n  - The violin plot for cholesterol (chol) vs. target shows that patients at risk of a heart attack (target = 1) generally have a slightly higher spread of cholesterol values compared to patients not at risk (target = 0).\n  - The distribution for patients at risk of a heart attack (target = 1) shows a wider range of cholesterol values, extending up to around 600, indicating more variability in this group.\n\n- **Central Tendency**:\n  - The median cholesterol level for patients at risk of a heart attack is around 240-260 mg/dL.\n  - The median cholesterol level for patients not at risk of a heart attack is also around 240-260 mg/dL, indicating a similar central tendency.\n\n- **Interquartile Range (IQR)**:\n  - The IQR for both groups overlaps significantly, indicating a substantial overlap in cholesterol levels between the two groups.\n\n- **Density**:\n  - The density of cholesterol values is higher around the median for both groups, indicating most patients' cholesterol levels are clustered around these medians.\n  - There are noticeable peaks around 200-300 mg/dL for patients at risk of a heart attack, suggesting a higher frequency of patients in this cholesterol range.\n\n- **Implications**:\n  - Cholesterol levels show a similar central tendency for both groups, but the wider range in patients at risk of a heart attack indicates more variability in this group.\n  - Cholesterol alone may not be a strong predictor of heart attack risk, but the higher variability in at-risk patients warrants further investigation.\n\nLet's reanalyze the Thalach-Target chart with the correct understanding that:\n\n- **0**: Patients not at risk of a heart attack.\n- **1**: Patients at risk of a heart attack.\n\n\n#### 4.**Maximum Heart Rate Achieved (thalach) vs. Target**\n\n- **Distribution**:\n  - The violin plot for maximum heart rate achieved (thalach) vs. target shows that patients at risk of a heart attack (target = 1) generally have a higher median maximum heart rate compared to patients not at risk of a heart attack (target = 0).\n  - The distribution for patients at risk of a heart attack (target = 1) shows a slightly narrower range of maximum heart rate values, indicating less variability in this group.\n\n- **Central Tendency**:\n  - The median maximum heart rate for patients at risk of a heart attack is around 160 bpm.\n  - The median maximum heart rate for patients not at risk of a heart attack is around 140 bpm.\n\n- **Interquartile Range (IQR)**:\n  - The IQR for patients at risk of a heart attack is between approximately 140 and 170 bpm.\n  - The IQR for patients not at risk of a heart attack is between approximately 120 and 160 bpm.\n\n- **Density**:\n  - The density of maximum heart rate values is higher around the median for both groups, indicating most patients' maximum heart rates are clustered around these medians.\n  - There is a noticeable peak around 140-160 bpm for patients at risk of a heart attack, suggesting a higher frequency of patients in this heart rate range.\n\n- **Implications**:\n  - Patients at risk of a heart attack tend to have a higher maximum heart rate achieved compared to those not at risk.\n  - The narrower IQR and higher median for the at-risk group suggest that a higher maximum heart rate is associated with increased risk of a heart attack.\n\n### Summary\n\nCholesterol (chol): Patients at risk of a heart attack have a slightly wider range of cholesterol levels, indicating more variability in this group. However, the central tendency is similar for both groups, suggesting cholesterol alone is not a definitive predictor of heart attack risk.\n\nThe updated analysis shows that patients at risk of a heart attack tend to have a higher median maximum heart rate achieved compared to those not at risk. This indicates that the maximum heart rate achieved is an important factor in assessing heart attack risk, with higher values associated with increased risk.","metadata":{}},{"cell_type":"markdown","source":"# Visualizing Categorical Variables vs. Target Variable Using Count Plots","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"# Setting the visual style\nsns.set(style=\"whitegrid\")\n\n# List of categorical variables\ncategoric_var = [\"sex\", \"cp\", \"fbs\", \"rest_ecg\", \"exang\", \"slope\", \"ca\", \"thal\"]\n\n# Creating count plots for each categorical variable against the target variable\nfor column in categoric_var:\n    plt.figure(figsize=(10, 6))\n    sns.countplot(x=heart_data[column], hue=heart_data['target'], palette=\"pastel\")\n    plt.title(f'Count Plot of {column} vs. target')\n    plt.xlabel(column)\n    plt.ylabel('Count')\n    plt.legend(title='Target', loc='upper right')\n    plt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"* sns.set(style=\"whitegrid\"): This sets the aesthetic style of the plots to a white grid background.\n* The for loop iterates over each column in the categoric_var list.\n* plt.figure(figsize=(10, 6)): Sets the figure size to 10x6 inches.\n* sns.countplot(...): Creates a count plot for the categorical variable against the target variable.\n* x=heart_data[column]: Sets the x-axis to the current categorical variable in the loop.\n* hue=heart_data['target']: Uses the target variable to color-code the bars.\n* palette=\"pastel\": Uses a pastel color palette for the count plots.\n* plt.title(f'Count Plot of {column} vs. target'): Sets the title of the count plot.\n* plt.xlabel(column): Labels the x-axis with the name of the categorical variable.\n* plt.ylabel('Count'): Labels the y-axis as \"Count\".\n* plt.legend(title='Target', loc='upper right'): Adds a legend with the title \"Target\" at the upper right position.\n* plt.show(): Displays the count plot.","metadata":{}},{"cell_type":"markdown","source":"### Detailed Bivariate Analysis from Count Plots\n\n#### 1. **Sex vs. Target**\n\n- **Distribution**:\n  - The count plot for sex vs. target shows a clear difference in heart attack risk between males (1) and females (0).\n  - Males (1) have a higher count in both categories (0 and 1), but the difference between the two target values is more pronounced for males.\n\n- **Analysis**:\n  - For females (sex = 0):\n    - The count of females not at risk of a heart attack (target = 0) is significantly lower compared to those at risk (target = 1).\n    - This suggests that a higher proportion of females in the dataset are at risk of a heart attack.\n  - For males (sex = 1):\n    - The count of males not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1), but the difference is not as significant as for females.\n    - This suggests that a substantial proportion of males in the dataset are at risk of a heart attack, but a larger number of males are not at risk.\n\n- **Implications**:\n  - Gender (sex) appears to be an important factor in heart attack risk.\n  - Females have a higher proportion of being at risk of a heart attack compared to males in the dataset.\n  - Males have a higher absolute number of cases in both categories, but the proportion of risk is more balanced compared to females.\n\n#### 2. **Chest Pain Type (cp) vs. Target**\n\n- **Distribution**:\n  - The count plot for chest pain type (cp) vs. target shows distinct patterns for different types of chest pain.\n  - There are four types of chest pain represented (0, 1, 2, 3).\n\n- **Analysis**:\n  - Chest pain type 0 (typical angina):\n    - The count of patients not at risk of a heart attack (target = 0) is significantly higher compared to those at risk (target = 1).\n    - This indicates that typical angina is more common in patients not at risk of a heart attack.\n  - Chest pain type 1 (atypical angina):\n    - The count of patients at risk of a heart attack (target = 1) is higher compared to those not at risk (target = 0).\n    - This suggests that atypical angina is associated with a higher risk of a heart attack.\n  - Chest pain type 2 (non-anginal pain):\n    - The count of patients at risk of a heart attack (target = 1) is significantly higher compared to those not at risk (target = 0).\n    - This indicates that non-anginal pain is strongly associated with a higher risk of a heart attack.\n  - Chest pain type 3 (asymptomatic):\n    - The count of patients at risk of a heart attack (target = 1) is higher compared to those not at risk (target = 0).\n    - This suggests that asymptomatic chest pain is also associated with a higher risk of a heart attack.\n\n- **Implications**:\n  - Chest pain type (cp) is a critical factor in assessing heart attack risk.\n  - Typical angina (cp = 0) is more common among patients not at risk of a heart attack.\n  - Atypical angina, non-anginal pain, and asymptomatic chest pain are associated with a higher risk of a heart attack, with non-anginal pain showing the strongest association.\n\n### Summary\n\nThe count plots provide valuable insights into the relationship between categorical variables and the target variable. Key takeaways include:\n\n- **Sex**: Females have a higher proportion of being at risk of a heart attack compared to males in the dataset. Males have a higher absolute number of cases, but the proportion of risk is more balanced compared to females.\n- **Chest Pain Type (cp)**: Typical angina is more common among patients not at risk of a heart attack. Atypical angina, non-anginal pain, and asymptomatic chest pain are associated with a higher risk of a heart attack, with non-anginal pain showing the strongest association.","metadata":{}},{"cell_type":"markdown","source":"#### 3. **Fasting Blood Sugar (fbs) vs. Target**\n\n- **Distribution**:\n  - The count plot for fasting blood sugar (fbs) vs. target shows a clear difference in heart attack risk between patients with fbs <= 120 mg/dL (0) and those with fbs > 120 mg/dL (1).\n  - Patients with fbs <= 120 mg/dL (0) have a higher count in both categories (0 and 1), but the difference between the two target values is more pronounced for this group.\n\n- **Analysis**:\n  - For patients with fbs <= 120 mg/dL (fbs = 0):\n    - The count of patients not at risk of a heart attack (target = 0) is lower compared to those at risk (target = 1).\n    - This suggests that a higher proportion of patients with normal fasting blood sugar levels are at risk of a heart attack.\n  - For patients with fbs > 120 mg/dL (fbs = 1):\n    - The count of patients at risk of a heart attack (target = 1) is slightly higher compared to those not at risk (target = 0), but the numbers are relatively low for both categories.\n\n- **Implications**:\n  - Fasting blood sugar (fbs) appears to be an important factor in heart attack risk.\n  - A higher proportion of patients with normal fasting blood sugar levels (<= 120 mg/dL) are at risk of a heart attack.\n  - Patients with elevated fasting blood sugar levels (> 120 mg/dL) are relatively few in number, but they still show a higher risk of heart attack.\n\n#### 4. **Resting Electrocardiographic Results (rest_ecg) vs. Target**\n\n- **Distribution**:\n  - The count plot for resting electrocardiographic results (rest_ecg) vs. target shows distinct patterns for different rest_ecg values.\n  - There are three categories of rest_ecg (0, 1, 2).\n\n- **Analysis**:\n  - Rest_ecg = 0 (normal):\n    - The count of patients not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1).\n    - This suggests that a normal ECG result is more common among patients not at risk of a heart attack.\n  - Rest_ecg = 1 (having ST-T wave abnormality):\n    - The count of patients at risk of a heart attack (target = 1) is significantly higher compared to those not at risk (target = 0).\n    - This indicates that ST-T wave abnormalities are strongly associated with a higher risk of a heart attack.\n  - Rest_ecg = 2 (showing probable or definite left ventricular hypertrophy):\n    - The count is relatively low for both categories, with a slight tendency towards higher risk (target = 1).\n\n- **Implications**:\n  - Resting electrocardiographic results (rest_ecg) are a critical factor in assessing heart attack risk.\n  - A normal ECG result (rest_ecg = 0) is more common among patients not at risk of a heart attack.\n  - ST-T wave abnormalities (rest_ecg = 1) are strongly associated with a higher risk of a heart attack.\n  - Probable or definite left ventricular hypertrophy (rest_ecg = 2) shows a slight tendency towards higher risk but needs further investigation due to the low counts.\n\n### Summary\n\nThe count plots provide valuable insights into the relationship between categorical variables and the target variable. Key takeaways include:\n\n- **Fasting Blood Sugar (fbs)**: Patients with normal fasting blood sugar levels (<= 120 mg/dL) have a higher proportion of being at risk of a heart attack compared to those with elevated fasting blood sugar levels (> 120 mg/dL).\n- **Resting Electrocardiographic Results (rest_ecg)**: A normal ECG result is more common among patients not at risk of a heart attack, while ST-T wave abnormalities are strongly associated with a higher risk of a heart attack. Probable or definite left ventricular hypertrophy shows a slight tendency towards higher risk but requires further investigation.","metadata":{}},{"cell_type":"markdown","source":"#### 5. **Exercise Induced Angina (exang) vs. Target**\n\n- **Distribution**:\n  - The count plot for exercise-induced angina (exang) vs. target shows a clear difference in heart attack risk between patients with and without exercise-induced angina.\n  - Patients without exercise-induced angina (exang = 0) have a higher count in the at-risk category (target = 1) compared to those not at risk (target = 0).\n\n- **Analysis**:\n  - For patients without exercise-induced angina (exang = 0):\n    - The count of patients at risk of a heart attack (target = 1) is significantly higher compared to those not at risk (target = 0).\n    - This suggests that the absence of exercise-induced angina is associated with a higher risk of a heart attack.\n  - For patients with exercise-induced angina (exang = 1):\n    - The count of patients not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1).\n    - This suggests that the presence of exercise-induced angina is associated with a lower risk of a heart attack.\n\n- **Implications**:\n  - Exercise-induced angina (exang) appears to be an important factor in heart attack risk.\n  - The absence of exercise-induced angina is associated with a higher risk of a heart attack.\n  - The presence of exercise-induced angina is associated with a lower risk of a heart attack.\n\n#### 6. **Slope of the Peak Exercise ST Segment (slope) vs. Target**\n\n- **Distribution**:\n  - The count plot for the slope of the peak exercise ST segment (slope) vs. target shows distinct patterns for different slope values.\n  - There are three categories of slope (0, 1, 2).\n\n- **Analysis**:\n  - Slope = 0 (upsloping):\n    - The count of patients not at risk of a heart attack (target = 0) is slightly higher compared to those at risk (target = 1).\n    - This suggests that an upsloping ST segment is more common among patients not at risk of a heart attack.\n  - Slope = 1 (flat):\n    - The count of patients not at risk of a heart attack (target = 0) is significantly higher compared to those at risk (target = 1).\n    - This indicates that a flat ST segment is strongly associated with a lower risk of a heart attack.\n  - Slope = 2 (downsloping):\n    - The count of patients at risk of a heart attack (target = 1) is significantly higher compared to those not at risk (target = 0).\n    - This suggests that a downsloping ST segment is strongly associated with a higher risk of a heart attack.\n\n- **Implications**:\n  - The slope of the peak exercise ST segment (slope) is a critical factor in assessing heart attack risk.\n  - An upsloping ST segment (slope = 0) is more common among patients not at risk of a heart attack.\n  - A flat ST segment (slope = 1) is strongly associated with a lower risk of a heart attack.\n  - A downsloping ST segment (slope = 2) is strongly associated with a higher risk of a heart attack.\n\n### Summary\n\nThe count plots provide valuable insights into the relationship between categorical variables and the target variable. Key takeaways include:\n\n- **Exercise-Induced Angina (exang)**: The absence of exercise-induced angina is associated with a higher risk of a heart attack, while the presence of exercise-induced angina is associated with a lower risk.\n- **Slope of the Peak Exercise ST Segment (slope)**: An upsloping ST segment is more common among patients not at risk of a heart attack. A flat ST segment is strongly associated with a lower risk of a heart attack, while a downsloping ST segment is strongly associated with a higher risk.","metadata":{}},{"cell_type":"markdown","source":"#### 7. **Number of Major Vessels Colored by Fluoroscopy (ca) vs. Target**\n\n- **Distribution**:\n  - The count plot for the number of major vessels colored by fluoroscopy (ca) vs. target shows a clear difference in heart attack risk across different values of `ca`.\n  - Patients with `ca = 0` have a significantly higher count in the at-risk category (target = 1) compared to those not at risk (target = 0).\n\n- **Analysis**:\n  - For patients with `ca = 0`:\n    - The count of patients at risk of a heart attack (target = 1) is significantly higher compared to those not at risk (target = 0).\n    - This suggests that having zero major vessels colored by fluoroscopy is strongly associated with a higher risk of a heart attack.\n  - For patients with `ca = 1`:\n    - The count of patients not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1).\n    - This suggests that having one major vessel colored by fluoroscopy is associated with a lower risk of a heart attack.\n  - For patients with `ca = 2`:\n    - The count of patients not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1).\n    - This suggests that having two major vessels colored by fluoroscopy is associated with a lower risk of a heart attack.\n  - For patients with `ca = 3`:\n    - The count of patients not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1).\n    - This suggests that having three major vessels colored by fluoroscopy is associated with a lower risk of a heart attack.\n  - For patients with `ca = 4`:\n    - The count of patients is relatively low for both categories, with a slight tendency towards higher risk (target = 1).\n\n- **Implications**:\n  - The number of major vessels colored by fluoroscopy (ca) is a critical factor in assessing heart attack risk.\n  - Having zero major vessels colored by fluoroscopy (ca = 0) is strongly associated with a higher risk of a heart attack.\n  - Having one, two, or three major vessels colored by fluoroscopy (ca = 1, 2, 3) is associated with a lower risk of a heart attack.\n\n#### 8. **Thalassemia (thal) vs. Target**\n\n- **Distribution**:\n  - The count plot for thalassemia (thal) vs. target shows distinct patterns for different thal values.\n  - There are three categories of thal (1.0, 2.0, 3.0).\n\n- **Analysis**:\n  - Thal = 1.0 (normal):\n    - The count of patients not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1).\n    - This suggests that a normal thalassemia result is more common among patients not at risk of a heart attack.\n  - Thal = 2.0 (fixed defect):\n    - The count of patients at risk of a heart attack (target = 1) is significantly higher compared to those not at risk (target = 0).\n    - This indicates that a fixed defect is strongly associated with a higher risk of a heart attack.\n  - Thal = 3.0 (reversible defect):\n    - The count of patients not at risk of a heart attack (target = 0) is higher compared to those at risk (target = 1).\n    - This suggests that a reversible defect is more common among patients not at risk of a heart attack.\n\n- **Implications**:\n  - Thalassemia (thal) is an important factor in assessing heart attack risk.\n  - A normal thalassemia result (thal = 1.0) is more common among patients not at risk of a heart attack.\n  - A fixed defect (thal = 2.0) is strongly associated with a higher risk of a heart attack.\n  - A reversible defect (thal = 3.0) is more common among patients not at risk of a heart attack.\n\n### Summary\n\nThe count plots provide valuable insights into the relationship between categorical variables and the target variable. Key takeaways include:\n\n- **Number of Major Vessels Colored by Fluoroscopy (ca)**: Having zero major vessels colored by fluoroscopy is strongly associated with a higher risk of a heart attack, while having one, two, or three major vessels colored by fluoroscopy is associated with a lower risk.\n- **Thalassemia (thal)**: A normal thalassemia result is more common among patients not at risk of a heart attack. A fixed defect is strongly associated with a higher risk of a heart attack, while a reversible defect is more common among patients not at risk.","metadata":{}},{"cell_type":"markdown","source":"# Step-by-Step Instructions to Calculate Correlation Coefficients","metadata":{}},{"cell_type":"markdown","source":"## Interpreting the Correlation Coefficients\n\n* Positive Correlation: A positive correlation coefficient indicates that as one variable increases, the target variable also tends to increase. The closer the coefficient is to 1, the stronger the positive relationship.\n\n* Negative Correlation: A negative correlation coefficient indicates that as one variable increases, the target variable tends to decrease. The closer the coefficient is to -1, the stronger the negative relationship.\n\n* No Correlation: A correlation coefficient close to 0 indicates little to no linear relationship between the variable and the target variable.","metadata":{}},{"cell_type":"markdown","source":"# Calculating Correlation Coefficients for Numerical Variables:","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"import pandas as pd\n\n# Calculating correlation coefficients between numerical variables and the target variable\nnumerical_correlations = heart_data[numeric_var + ['target']].corr()\n\n# Extracting the correlation coefficients for numerical variables with the target variable\nnumerical_target_correlations = numerical_correlations['target'].sort_values(ascending=False)\nprint(numerical_target_correlations)","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"* The pandas library is used for data manipulation and analysis. It provides data structures like DataFrame for handling and analyzing data.\n* heart_data[numeric_var + ['target']]: Selects the numerical variables along with the target variable from the dataset.\n* .corr(): Calculates the pairwise correlation coefficients for the selected variables. The correlation matrix will show how each variable correlates with every other variable, including the target variable.\n* numerical_correlations['target']: Selects the column of correlation coefficients corresponding to the target variable.\n* .sort_values(ascending=False): Sorts the correlation coefficients in descending order to easily identify which numerical variables are most positively or negatively correlated with the target variable.\n* print(numerical_target_correlations): Displays the sorted correlation coefficients.","metadata":{}},{"cell_type":"markdown","source":"Based on the output image you provided, let's analyze the correlations between the numerical variables and the target variable:\n\n### Numerical Variables and Their Correlations with the Target Variable\n\n1. **thalach (Maximum Heart Rate Achieved)**: \n   - Correlation: 0.421741\n   - **Interpretation**: There is a moderate positive correlation between `thalach` and the target variable. This suggests that higher maximum heart rates are associated with an increased risk of a heart attack.\n\n2. **chol (Cholesterol)**: \n   - Correlation: -0.085239\n   - **Interpretation**: There is a very weak negative correlation between `chol` and the target variable. This indicates that cholesterol levels have little to no linear relationship with the risk of a heart attack in this dataset.\n\n3. **trtbps (Resting Blood Pressure)**: \n   - Correlation: -0.144931\n   - **Interpretation**: There is a weak negative correlation between `trtbps` and the target variable. This suggests that higher resting blood pressure may be slightly associated with a decreased risk of a heart attack, although the relationship is weak.\n\n4. **age**: \n   - Correlation: -0.225439\n   - **Interpretation**: There is a moderate negative correlation between `age` and the target variable. This indicates that older age is somewhat associated with a decreased risk of a heart attack.\n\n5. **oldpeak (ST Depression Induced by Exercise)**: \n   - Correlation: -0.430696\n   - **Interpretation**: There is a moderate negative correlation between `oldpeak` and the target variable. This suggests that higher values of ST depression are associated with a decreased risk of a heart attack.\n\n### Summary\n\nThe correlation coefficients for the numerical variables with the target variable provide the following insights:\n\n- **thalach**: The strongest positive correlation, indicating that a higher maximum heart rate is associated with an increased risk of a heart attack.\n- **oldpeak**: The strongest negative correlation, suggesting that higher ST depression is associated with a decreased risk of a heart attack.\n- **age**: Shows a moderate negative correlation, indicating that older age is associated with a decreased risk of a heart attack.\n- **trtbps**: Has a weak negative correlation, indicating a slight association between higher resting blood pressure and a decreased risk of a heart attack.\n- **chol**: Exhibits a very weak negative correlation, indicating little to no relationship between cholesterol levels and heart attack risk.","metadata":{}},{"cell_type":"markdown","source":"## Calculating Correlation Coefficients for Categorical Variables","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"from sklearn.preprocessing import LabelEncoder\n\n# Encoding categorical variables\nencoded_data = heart_data.copy()\nfor column in categoric_var:\n    encoder = LabelEncoder()\n    encoded_data[column] = encoder.fit_transform(encoded_data[column])\n\n# Calculating correlation coefficients between encoded categorical variables and the target variable\ncategorical_correlations = encoded_data[categoric_var + ['target']].corr()\ncategorical_target_correlations = categorical_correlations['target'].sort_values(ascending=False)\nprint(categorical_target_correlations)","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"* The LabelEncoder class from sklearn.preprocessing is used to convert categorical values into numerical values. This is necessary because correlation calculations require numerical data.\n* heart_data.copy(): Creates a copy of the original dataset to avoid modifying it directly.\n* for column in categoric_var: Iterates over each categorical variable in the list.\n* encoder = LabelEncoder(): Creates an instance of the LabelEncoder.\n* encoded_data[column] = encoder.fit_transform(encoded_data[column]): Encodes the categorical variable and replaces it with the encoded values in the encoded_data DataFrame.\n* encoded_data[categoric_var + ['target']]: Selects the encoded categorical variables along with the target variable from the dataset.\n* .corr(): Calculates the pairwise correlation coefficients for the selected variables.\n* categorical_correlations['target']: Selects the column of correlation coefficients corresponding to the target variable.\n* .sort_values(ascending=False): Sorts the correlation coefficients in descending order.\n* print(categorical_target_correlations): Displays the sorted correlation coefficients.","metadata":{}},{"cell_type":"markdown","source":"### Categorical Variables and Their Correlations with the Target Variable\n\n1. **cp (Chest Pain Type)**: \n   - Correlation: 0.433798\n   - **Interpretation**: There is a moderate positive correlation between `cp` and the target variable. This suggests that certain types of chest pain are associated with an increased risk of a heart attack.\n\n2. **slope (Slope of the Peak Exercise ST Segment)**: \n   - Correlation: 0.345877\n   - **Interpretation**: There is a moderate positive correlation between `slope` and the target variable. This indicates that the slope of the peak exercise ST segment is associated with an increased risk of a heart attack.\n\n3. **rest_ecg (Resting ECG Results)**: \n   - Correlation: 0.137230\n   - **Interpretation**: There is a weak positive correlation between `rest_ecg` and the target variable. This suggests that certain resting ECG results are slightly associated with an increased risk of a heart attack.\n\n4. **fbs (Fasting Blood Sugar)**: \n   - Correlation: -0.028046\n   - **Interpretation**: There is a very weak negative correlation between `fbs` and the target variable. This indicates that fasting blood sugar levels have little to no linear relationship with the risk of a heart attack in this dataset.\n\n5. **sex**: \n   - Correlation: -0.280937\n   - **Interpretation**: There is a moderate negative correlation between `sex` and the target variable. This indicates that being male is associated with a decreased risk of a heart attack.\n\n6. **thal (Thalassemia)**: \n   - Correlation: -0.363322\n   - **Interpretation**: There is a moderate negative correlation between `thal` and the target variable. This suggests that certain types of thalassemia are associated with a decreased risk of a heart attack.\n\n7. **ca (Number of Major Vessels Colored by Fluoroscopy)**: \n   - Correlation: -0.391724\n   - **Interpretation**: There is a moderate negative correlation between `ca` and the target variable. This suggests that having more major vessels colored by fluoroscopy is associated with a decreased risk of a heart attack.\n\n8. **exang (Exercise Induced Angina)**: \n   - Correlation: -0.436757\n   - **Interpretation**: There is a moderate negative correlation between `exang` and the target variable. This indicates that the presence of exercise-induced angina is associated with a decreased risk of a heart attack.\n\n### Summary\n\nThe correlation coefficients for the categorical variables with the target variable provide the following insights:\n\n- **cp (Chest Pain Type)**: Shows the strongest positive correlation, indicating that certain types of chest pain are associated with an increased risk of a heart attack.\n- **exang (Exercise Induced Angina)**: Shows the strongest negative correlation, indicating that the presence of exercise-induced angina is associated with a decreased risk of a heart attack.\n- **slope (Slope of the Peak Exercise ST Segment)**: Shows a moderate positive correlation, indicating that the slope of the peak exercise ST segment is associated with an increased risk of a heart attack.\n- **thal (Thalassemia)** and **ca (Number of Major Vessels Colored by Fluoroscopy)**: Both show moderate negative correlations, indicating that certain types of thalassemia and more major vessels colored by fluoroscopy are associated with a decreased risk of a heart attack.\n- **sex**: Shows a moderate negative correlation, indicating that being male is associated with a decreased risk of a heart attack.\n- **rest_ecg (Resting ECG Results)**: Shows a weak positive correlation, suggesting a slight association with an increased risk of a heart attack.\n- **fbs (Fasting Blood Sugar)**: Shows a very weak negative correlation, indicating little to no relationship with heart attack risk.","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"# Set the aesthetic style of the plots\nsns.set(style=\"whitegrid\")\n\n# Create a pairplot to visualize relationships between numerical variables\npairplot = sns.pairplot(heart_data[numeric_var])\n\n# Adding a title to the plot\nplt.suptitle(\"Pairplot of Numerical Variables\", y=1.02)\n\n# Show the plot\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"* sns.set(style=\"whitegrid\"): Sets the aesthetic style of the plots. The \"whitegrid\" style adds a white background with gridlines, making the plots easier to read.\n* sns.pairplot(data): Creates a pairplot of the given data. The pairplot function creates a matrix of scatter plots for each pair of numerical variables, along with histograms (or KDE plots) on the diagonal.\n* heart_data[numeric_var]: Selects only the numerical variables from the heart_data DataFrame.\n* plt.suptitle(\"Pairplot of Numerical Variables\", y=1.02): Adds a super title (overall title) to the entire pairplot. The y parameter adjusts the vertical position of the title so it doesn't overlap with the plots.\n* plt.show(): Displays the generated pairplot. This command is necessary to render the plot in Jupyter Notebook or any other interactive environment.","metadata":{}},{"cell_type":"markdown","source":"## Explanation of the Pairplot\n\nPurpose: A pairplot is used to visualize the pairwise relationships between variables in a dataset. It is particularly useful for understanding the interactions and correlations between numerical variables.\n\n### Components of the Pairplot\n\n- **Diagonal Elements**: \n  - Histograms or Kernel Density Estimate (KDE) plots that show the distribution of each individual numerical variable.\n  - These plots help in understanding the spread, central tendency, and skewness of the data.\n\n- **Off-Diagonal Elements**:\n  - Scatter plots that show the relationships between each pair of numerical variables.\n  - These plots help in identifying patterns, correlations, clusters, and outliers between pairs of variables.\n\n### Interpretation of the Pairplot\n\n- **Scatter Plots**:\n  - **Positive Correlation**: If the points form an upward-sloping pattern from left to right, it indicates a positive correlation between the variables.\n  - **Negative Correlation**: If the points form a downward-sloping pattern from left to right, it indicates a negative correlation between the variables.\n  - **No Correlation**: If the points form a random scatter without any discernible pattern, it suggests no linear correlation between the variables.\n\n- **Histograms/KDE Plots**:\n  - **Spread**: Shows the range of values for each variable.\n  - **Central Tendency**: Indicates the central value where most data points are concentrated.\n  - **Skewness**: Shows the asymmetry in the distribution of the data points.\n\n### Why Use a Pairplot?\n\n- **Comprehensive Visualization**: Provides a matrix of plots that show relationships between all pairs of numerical variables in a single view.\n- **Pattern Recognition**: Helps in identifying linear or non-linear relationships, clusters, and outliers.\n- **Data Understanding**: Facilitates a deeper understanding of the data distributions and interactions between variables.\n\nBy using this pairplot, you can gain valuable insights into the relationships between your numerical variables, which can guide further analysis and model development.","metadata":{}},{"cell_type":"markdown","source":"### Detailed Analysis of the Pairplot\n\nThe pairplot you have generated provides a comprehensive view of the relationships between the numerical variables in your dataset. Let's analyze each aspect of the pairplot:\n\n1. **Diagonal Elements (Histograms)**:\n   - **age**: The histogram shows a distribution that is slightly right-skewed. The majority of the data points are concentrated between 40 and 60 years of age.\n   - **trtbps**: The resting blood pressure (trtbps) shows a roughly normal distribution with a peak around 130-140 mmHg.\n   - **chol**: Cholesterol levels (chol) show a right-skewed distribution with a peak around 200-250 mg/dL.\n   - **thalach**: Maximum heart rate achieved (thalach) shows a fairly normal distribution, peaking around 150-170 bpm.\n   - **oldpeak**: ST depression induced by exercise (oldpeak) shows a right-skewed distribution with most values concentrated around 0 to 2.\n\n2. **Off-Diagonal Elements (Scatter Plots)**:\n   - **age vs. trtbps**: There is no clear linear relationship between age and resting blood pressure, suggesting that age does not strongly influence resting blood pressure.\n   - **age vs. chol**: There is a slight positive trend indicating that cholesterol levels may increase with age, but the relationship is weak.\n   - **age vs. thalach**: There is a weak negative relationship, indicating that maximum heart rate tends to decrease with age.\n   - **age vs. oldpeak**: There is no clear relationship between age and ST depression.\n   - **trtbps vs. chol**: There is no clear relationship between resting blood pressure and cholesterol levels.\n   - **trtbps vs. thalach**: There is no clear relationship between resting blood pressure and maximum heart rate.\n   - **trtbps vs. oldpeak**: There is no clear relationship between resting blood pressure and ST depression.\n   - **chol vs. thalach**: There is no clear relationship between cholesterol levels and maximum heart rate.\n   - **chol vs. oldpeak**: There is no clear relationship between cholesterol levels and ST depression.\n   - **thalach vs. oldpeak**: There is no clear relationship between maximum heart rate and ST depression.\n\n### Detailed Analysis of Specific Relationships\n\n- **age vs. thalach**:\n  - **Observation**: There is a noticeable trend where higher ages are associated with lower maximum heart rates.\n  - **Interpretation**: This makes physiological sense as maximum heart rate generally declines with age. \n\n- **chol vs. oldpeak**:\n  - **Observation**: The scatter plot shows a wide spread with no clear pattern.\n  - **Interpretation**: This suggests that cholesterol levels are not strongly related to the ST depression induced by exercise.\n\n- **trtbps vs. chol**:\n  - **Observation**: The data points are widely scattered with no discernible trend.\n  - **Interpretation**: This indicates that resting blood pressure and cholesterol levels do not have a significant linear relationship in this dataset.\n\n### Summary\n\nThe pairplot provides several insights:\n- **Distributions**: The histograms on the diagonal show the distribution of each numerical variable. Many of the variables show some degree of skewness.\n- **Relationships**: Most of the scatter plots do not show strong linear relationships between pairs of numerical variables. The exception is the age-thalach relationship, which shows a weak negative correlation.\n- **No Strong Linear Correlations**: The scatter plots indicate that there are no strong linear correlations between most of the numerical variables, suggesting that any predictive models may need to account for non-linear relationships or interactions between variables.\n\nThis detailed examination of the pairplot helps in understanding the underlying data structure and informs the subsequent steps in your exploratory data analysis and modeling processes.","metadata":{}},{"cell_type":"markdown","source":"# Scale the Numerical Variables and Create the Combined Box Plots","metadata":{}},{"cell_type":"markdown","source":"### Detailed Information about Scaling in Data Science\n\n**What is Scaling?**\nScaling, also known as feature scaling or normalization, is a data preprocessing step in data science where the range of independent variables or features of data is adjusted. The goal is to standardize the range of independent variables or features so that each feature contributes equally to the model. \n\n**Why is Scaling Done?**\n1. **Improves Model Performance**: Many machine learning algorithms perform better when numerical input variables are on a similar scale. This is particularly true for algorithms that rely on distance calculations, such as K-nearest neighbors (KNN), support vector machines (SVM), and gradient descent optimization.\n   \n2. **Speeds Up Convergence**: Algorithms that use gradient descent for optimization, like linear regression, logistic regression, and neural networks, benefit from scaling. It helps in faster convergence of the gradient descent algorithm because it prevents some features from dominating the learning process due to their scale.\n   \n3. **Ensures Equal Weightage**: Without scaling, features with larger ranges might dominate the model training process, leading to biased results. Scaling ensures that all features contribute equally to the model.\n\n**Types of Scaling Techniques**:\n1. **Min-Max Scaling (Normalization)**:\n   - **Formula**: \\( X_{scaled} = \\frac{X - X_{min}}{X_{max} - X_{min}} \\)\n   - **Range**: Transforms the data to a fixed range, usually [0, 1].\n   - **Use Case**: Useful when the data does not contain outliers and you want to preserve the relationships between data points.\n\n2. **Standardization (Z-score Normalization)**:\n   - **Formula**: \\( X_{scaled} = \\frac{X - \\mu}{\\sigma} \\)\n   - **Range**: Transforms the data to have a mean of 0 and a standard deviation of 1.\n   - **Use Case**: Commonly used in machine learning algorithms that assume the data is normally distributed. It is less affected by outliers compared to min-max scaling.\n\n3. **Robust Scaling**:\n   - **Formula**: \\( X_{scaled} = \\frac{X - \\text{median}}{\\text{IQR}} \\)\n   - **Range**: Uses the median and the interquartile range (IQR).\n   - **Use Case**: Effective when the data contains outliers, as it uses statistics that are robust to outliers.\n\n4. **MaxAbs Scaling**:\n   - **Formula**: \\( X_{scaled} = \\frac{X}{\\text{max}(|X|)} \\)\n   - **Range**: Scales the data to the range [-1, 1].\n   - **Use Case**: Useful when dealing with sparse data (mostly zeros).\n\n**Importance of Scaling in Data Science**:\n1. **Algorithm Efficiency**: Scaling enhances the efficiency and accuracy of many machine learning algorithms, especially those that involve distance calculations.\n   \n2. **Optimization**: It ensures that the optimization process, such as gradient descent, converges faster and more reliably.\n   \n3. **Feature Comparability**: Makes features comparable, ensuring that one feature does not disproportionately influence the model just because it has a larger range.\n   \n4. **Data Integrity**: Helps maintain the integrity of the data by preventing distortion during model training and prediction.\n\n### Example of Standardization (Used in the Provided Code)\n**StandardScaler**:\n- **Process**: Subtracts the mean of the feature and then divides by the standard deviation.\n- **Formula**: \\( X_{scaled} = \\frac{X - \\mu}{\\sigma} \\)\n- **Implementation**:\n  ```python\n  from sklearn.preprocessing import StandardScaler\n\n  scaler = StandardScaler()\n  scaled_data = scaler.fit_transform(data)\n  ```\n\n### Conclusion\nScaling is a crucial step in data preprocessing that ensures numerical stability, improves algorithm performance, and speeds up convergence. Choosing the appropriate scaling technique depends on the nature of the data and the specific requirements of the machine learning algorithm being used.","metadata":{}},{"cell_type":"markdown","source":"# Codes","metadata":{}},{"cell_type":"code","source":"import seaborn as sns\nimport matplotlib.pyplot as plt\nimport pandas as pd\nfrom sklearn.preprocessing import StandardScaler\n\n# Create a copy of the original dataframe\nheart_data_scaled = heart_data.copy()\n\n# Define the numerical and categorical variables\nnumerical_vars = ['age', 'trtbps', 'chol', 'thalach', 'oldpeak']\ncategorical_vars = ['cp', 'slope', 'rest_ecg', 'fbs', 'sex', 'thal', 'ca', 'exang']\n\n# Apply StandardScaler to the numerical variables\nscaler = StandardScaler()\nheart_data_scaled[numerical_vars] = scaler.fit_transform(heart_data_scaled[numerical_vars])\n\n# Loop through each categorical variable and create the combined box plots\nfor cat_var in categorical_vars:\n    # Melt the dataframe to long format\n    melted_df = heart_data_scaled.melt(id_vars=cat_var, value_vars=numerical_vars, var_name='variables', value_name='value')\n\n    # Create the box plot\n    plt.figure(figsize=(14, 8))\n    sns.boxplot(x='variables', y='value', hue=cat_var, data=melted_df)\n    plt.title(f'Box Plot of Scaled Numerical Variables by {cat_var}')\n    plt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# Description of Codes","metadata":{}},{"cell_type":"markdown","source":"* heart_data_scaled = heart_data.copy(): Creates a copy of the original dataframe to ensure that the original data remains unchanged.\n* StandardScaler(): Initializes the scaler.\n* scaler.fit_transform(...): Scales the numerical variables to have a mean of 0 and a standard deviation of 1.\n* for cat_var in categorical_vars: This loop iterates over each categorical variable in the categorical_vars list. cat_var: In each iteration, cat_var takes the value of one categorical variable from the list.\n* id_vars=cat_var: Keeps the current categorical variable as the identifier variable.\n* value_vars=numerical_vars: Specifies the numerical variables to be reshaped.\n* var_name='variables': Names the new column that will hold the variable names.\n* value_name='value': Names the new column that will hold the values of the numerical variables.\n* Output: The resulting melted_df dataframe will have columns: the categorical variable (cat_var), a column named variables for the names of the numerical variables, and a column named value for their corresponding values.\n* plt.figure(figsize=(14, 8)): Initializes a new figure for the plot with a specified size of 14 inches by 8 inches. This ensures the plot is large enough to be readable.\n* sns.boxplot(...): Creates a box plot using the seaborn library.\n* x='variables': Sets the x-axis to display the names of the numerical variables.\n* y='value': Sets the y-axis to display the scaled values of the numerical variables.\n* hue=cat_var: Uses the current categorical variable to create separate box plots for each category within the variable. This adds a color dimension to differentiate between the categories.\n* data=melted_df: Specifies the melted dataframe as the source of the data for the plot.\n* plt.title(...): Adds a title to the plot. The title is dynamically generated to include the name of the current categorical variable (cat_var).\n* plt.show(): Renders and displays the plot.","metadata":{}},{"cell_type":"markdown","source":"# Explanation of the Graphs","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Box Plots of Scaled Numerical Variables by Categorical Variables","metadata":{}},{"cell_type":"markdown","source":"#### Box Plot of Scaled Numerical Variables by `cp` (Chest Pain Type)\nThe `cp` variable represents the type of chest pain experienced by the patient:\n- 0: Typical angina\n- 1: Atypical angina\n- 2: Non-anginal pain\n- 3: Asymptomatic\n\nThe box plot shows the distribution of scaled numerical variables (`age`, `trtbps`, `chol`, `thalach`, `oldpeak`) across the different chest pain types.\n\n##### Key Observations:\n1. **Age**:\n   - Patients with typical angina (0) and asymptomatic (3) chest pain types tend to be older, as their medians are slightly higher.\n   - There is a broader range of ages for patients with non-anginal pain (2).\n\n2. **Resting Blood Pressure (trtbps)**:\n   - The median values for all chest pain types are relatively similar.\n   - There is a noticeable spread and some outliers, especially for typical angina (0) and non-anginal pain (2).\n\n3. **Cholesterol (chol)**:\n   - The distributions for cholesterol levels are quite similar across all chest pain types.\n   - The non-anginal pain (2) group shows some higher outliers.\n\n4. **Maximum Heart Rate Achieved (thalach)**:\n   - Patients with non-anginal pain (2) tend to have higher maximum heart rates.\n   - Typical angina (0) and asymptomatic (3) patients have lower median heart rates.\n\n5. **ST Depression Induced by Exercise Relative to Rest (oldpeak)**:\n   - Asymptomatic (3) patients show a higher median value and a wider range.\n   - Non-anginal pain (2) patients tend to have lower oldpeak values.\n\n#### Box Plot of Scaled Numerical Variables by `slope` (Slope of the Peak Exercise ST Segment)\nThe `slope` variable represents the slope of the peak exercise ST segment:\n- 0: Upsloping\n- 1: Flat\n- 2: Downsloping\n\nThe box plot shows the distribution of scaled numerical variables (`age`, `trtbps`, `chol`, `thalach`, `oldpeak`) across the different slope types.\n\n##### Key Observations:\n1. **Age**:\n   - Patients with downsloping (2) tend to be younger.\n   - The distribution is relatively similar across upsloping (0) and flat (1).\n\n2. **Resting Blood Pressure (trtbps)**:\n   - There is a noticeable spread and some outliers, particularly in the flat (1) and downsloping (2) groups.\n   - Median values are fairly consistent across all slope types.\n\n3. **Cholesterol (chol)**:\n   - Cholesterol levels are quite similar across all slope types.\n   - The flat (1) group has some higher outliers.\n\n4. **Maximum Heart Rate Achieved (thalach)**:\n   - Patients with downsloping (2) tend to have higher maximum heart rates.\n   - The upsloping (0) group shows a wider range and some outliers.\n\n5. **ST Depression Induced by Exercise Relative to Rest (oldpeak)**:\n   - The flat (1) and downsloping (2) groups have higher oldpeak values, with downsloping (2) showing the highest median and spread.\n\n### Summary:\n- The box plots reveal the distribution and spread of numerical variables across different categories of `cp` and `slope`.\n- There are noticeable differences in `thalach` and `oldpeak` across different chest pain types and slope categories.\n- `age`, `trtbps`, and `chol` show relatively consistent distributions across the categories, with some outliers present.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of `rest_ecg` vs Numerical Variables\n\n**1. `age` and `rest_ecg`:**\n   - No significant difference in age distributions across different `rest_ecg` categories.\n   - Ages are similarly distributed across all `rest_ecg` values.\n\n**2. `trtbps` and `rest_ecg`:**\n   - Blood pressure (`trtbps`) distributions appear similar across `rest_ecg` categories, with slight variations in the spread.\n   - Median values are quite close, indicating no substantial difference.\n\n**3. `chol` and `rest_ecg`:**\n   - Cholesterol levels (`chol`) show a broad range across all `rest_ecg` categories, with some outliers present.\n   - Again, the median values are relatively close.\n\n**4. `thalach` and `rest_ecg`:**\n   - Maximum heart rate (`thalach`) seems to have a consistent distribution across `rest_ecg` values, though category 2 shows a slightly higher spread.\n\n**5. `oldpeak` and `rest_ecg`:**\n   - `rest_ecg` value of 2 shows a higher `oldpeak` median, indicating more significant ST depression.\n   - Categories 0 and 1 have similar `oldpeak` distributions, suggesting less variation in ST depression.\n\n### Analysis of `fbs` vs Numerical Variables\n\n**1. `age` and `fbs`:**\n   - Age distribution shows a minor difference between `fbs` values 0 and 1.\n   - Ages appear to be similar, indicating no major age-related difference based on fasting blood sugar levels.\n\n**2. `trtbps` and `fbs`:**\n   - Blood pressure (`trtbps`) distribution is quite similar for both `fbs` values.\n   - Medians are almost identical, showing no significant difference.\n\n**3. `chol` and `fbs`:**\n   - Cholesterol levels (`chol`) have a slightly wider distribution for `fbs` value 0 compared to 1.\n   - Medians and interquartile ranges are similar, suggesting minimal impact of fasting blood sugar on cholesterol levels.\n\n**4. `thalach` and `fbs`:**\n   - Maximum heart rate (`thalach`) distributions are almost identical for both `fbs` values.\n   - Indicates that fasting blood sugar levels do not significantly affect maximum heart rate.\n\n**5. `oldpeak` and `fbs`:**\n   - `oldpeak` shows a noticeable difference between `fbs` values 0 and 1.\n   - Higher `oldpeak` values are observed more frequently in `fbs` value 0, suggesting that higher fasting blood sugar might be associated with lower ST depression.\n\n### Specific Focus on `oldpeak`\n\n**`rest_ecg` and `oldpeak`:**\n   - `rest_ecg` value 2 shows the highest `oldpeak` values, indicating significant ST depression.\n   - `rest_ecg` values 0 and 1 have similar distributions, with slightly lower medians and fewer outliers.\n\n**`fbs` and `oldpeak`:**\n   - `fbs` value 0 tends to have higher `oldpeak` values compared to `fbs` value 1.\n   - This suggests that individuals with higher fasting blood sugar might experience less ST depression.\n\n### Conclusion\n\n- **Categorical variables** `rest_ecg` and `fbs` show minimal impact on most numerical variables except for `oldpeak`, where there is a noticeable difference in distributions.\n- **`oldpeak`** is significantly influenced by `rest_ecg` and `fbs`, indicating that these categorical factors play a role in ST depression levels during exercise-induced angina.","metadata":{}},{"cell_type":"markdown","source":"#### Box Plot of Scaled Numerical Variables by Sex\n- **Age**:\n  - The median age is similar for both males (1) and females (0), but the interquartile range (IQR) is slightly wider for males.\n  - There are a few outliers in both groups, but they are more pronounced in males.\n  \n- **Resting Blood Pressure (trtbps)**:\n  - The distribution of trtbps is quite similar for both sexes, with overlapping IQRs.\n  - The medians are close, indicating no significant difference in resting blood pressure between males and females.\n\n- **Cholesterol (chol)**:\n  - Cholesterol levels show a slight difference in median values between the sexes, with females having a slightly higher median.\n  - Both groups have a similar range and distribution, with several outliers in both.\n\n- **Maximum Heart Rate (thalach)**:\n  - Males have a slightly lower median maximum heart rate compared to females.\n  - The spread of the data is similar for both groups, but there are more outliers in males.\n\n- **Oldpeak**:\n  - The distribution of oldpeak values is similar for both sexes, with a comparable median.\n  - There are more outliers in females, indicating a higher variability in this group.\n\n#### Box Plot of Scaled Numerical Variables by Thalassemia (thal)\n- **Age**:\n  - The median age varies across thalassemia values, with thal value 2 (reversible defect) showing a slightly higher median age.\n  - The IQR is similar across all groups, but there are a few outliers.\n\n- **Resting Blood Pressure (trtbps)**:\n  - The median values for trtbps are similar across the thalassemia groups, with slight variations.\n  - The spread of the data is consistent across groups, with a few outliers.\n\n- **Cholesterol (chol)**:\n  - There is a noticeable difference in the median cholesterol levels across the thalassemia groups, with thal value 2 having a higher median.\n  - The IQR is similar across groups, but there are outliers present in all groups.\n\n- **Maximum Heart Rate (thalach)**:\n  - The maximum heart rate varies significantly across the thalassemia groups, with thal value 3 (fixed defect) showing a lower median.\n  - There are more outliers in the thal value 3 group.\n\n- **Oldpeak**:\n  - The oldpeak values show a clear difference across the thalassemia groups, with thal value 2 having a higher median.\n  - The IQR and spread of the data are different across groups, with more outliers in the thal value 3 group.\n\n### Key Observations:\n- **Age**: Age shows a relatively similar distribution across sex and thalassemia groups, with slight variations in median and IQR.\n- **Resting Blood Pressure (trtbps)**: trtbps has similar distributions across both sex and thalassemia groups, indicating no strong relationship.\n- **Cholesterol (chol)**: Cholesterol levels vary slightly across sex and more noticeably across thalassemia groups, suggesting a potential relationship with thalassemia.\n- **Maximum Heart Rate (thalach)**: Thalach shows significant differences across thalassemia groups, indicating a strong relationship. The differences across sex are less pronounced.\n- **Oldpeak**: Oldpeak values vary across both sex and thalassemia groups, with more pronounced differences in the latter, suggesting a potential relationship.","metadata":{}},{"cell_type":"markdown","source":"### Box Plot of Scaled Numerical Variables by 'ca'\n\n#### **1. Age:**\n- **Ca 0:** The age distribution is roughly centered around the mean with a range from approximately -1.5 to 2.5, indicating a wide age range.\n- **Ca 1, 2, 3:** These groups show similar age distributions but slightly more compact ranges compared to Ca 0.\n- **Ca 4:** This category has very few data points, leading to less reliable age distribution information.\n\n#### **2. trtbps (Resting Blood Pressure):**\n- **Ca 0:** The distribution is centered around the mean, similar to the overall distribution of the dataset.\n- **Ca 1, 2, 3:** These categories show similar patterns but with slight variations in the range and median values.\n- **Ca 4:** Again, this group has few data points, so its distribution is not very reliable.\n\n#### **3. chol (Cholesterol):**\n- **Ca 0:** The cholesterol levels are fairly distributed around the mean.\n- **Ca 1, 2, 3:** These groups show a slight variation in cholesterol levels, with a bit more spread in the higher 'ca' values.\n- **Ca 4:** The data points are too few to draw a concrete conclusion.\n\n#### **4. thalach (Maximum Heart Rate Achieved):**\n- **Ca 0:** The heart rate values are distributed around the mean with some variability.\n- **Ca 1, 2, 3:** These groups show similar distributions with slight variations.\n- **Ca 4:** As with other variables, the limited data points make it hard to draw a concrete conclusion.\n\n#### **5. oldpeak (ST Depression Induced by Exercise):**\n- **Ca 0:** The oldpeak values show a typical spread around the mean.\n- **Ca 1, 2, 3:** These categories have similar oldpeak distributions but with slight shifts in median values and range.\n- **Ca 4:** Very few data points lead to less reliable information.\n\n### Box Plot of Scaled Numerical Variables by 'exang'\n\n#### **1. Age:**\n- **Exang 0:** The age distribution is centered around the mean with a typical range.\n- **Exang 1:** This group shows a similar age distribution but with a slightly narrower range compared to Exang 0.\n\n#### **2. trtbps (Resting Blood Pressure):**\n- **Exang 0:** The blood pressure values are distributed around the mean with some outliers.\n- **Exang 1:** This category shows a similar pattern but with a slightly narrower range and fewer outliers.\n\n#### **3. chol (Cholesterol):**\n- **Exang 0:** The cholesterol levels are fairly distributed around the mean with some outliers.\n- **Exang 1:** This group shows a similar cholesterol distribution but with a slightly narrower range and fewer outliers.\n\n#### **4. thalach (Maximum Heart Rate Achieved):**\n- **Exang 0:** The heart rate values are distributed around the mean with some outliers.\n- **Exang 1:** This category shows a similar pattern but with a narrower range and fewer outliers.\n\n#### **5. oldpeak (ST Depression Induced by Exercise):**\n- **Exang 0:** The oldpeak values are fairly distributed around the mean with some outliers.\n- **Exang 1:** This group shows a similar oldpeak distribution but with a slightly narrower range and fewer outliers.\n\n### Detailed Analysis:\n1. **Age:** Age distribution appears fairly consistent across different levels of 'ca' and 'exang' with no significant shifts in medians.\n2. **trtbps:** Resting blood pressure also shows consistency across categories, indicating no significant impact of 'ca' or 'exang' on this variable.\n3. **chol:** Cholesterol levels appear fairly consistent across categories, with some variability and outliers but no significant trends.\n4. **thalach:** Maximum heart rate shows a similar pattern, with distribution consistency across categories.\n5. **oldpeak:** This variable shows some variability across categories, especially in 'exang', where the values for 'exang' = 1 are slightly lower.","metadata":{}},{"cell_type":"markdown","source":"# Generate Strip Plots for Each Categorical Variable","metadata":{}},{"cell_type":"markdown","source":"### Strip Plot\n\n**Description**:\n- A strip plot is a scatter plot where one of the variables is categorical. Each data point is plotted individually, and the data points are “stripped” along the categorical axis.\n\n**Usage**:\n- Strip plots are useful for visualizing the distribution of a small to moderate number of data points.\n- They can show all data points, making it easy to identify outliers and the overall distribution.\n\n**Advantages**:\n- Simple and straightforward, making it easy to see individual data points.\n- Good for identifying outliers and gaps in the data.\n\n**Disadvantages**:\n- Can become cluttered with large datasets, making it difficult to interpret the distribution.\n- Does not provide density information directly.\n\n**Interpretation**:\n- Each point represents an individual observation.\n- The spread of points can indicate the variability in the data.\n- Clustering of points can indicate common values or modes.","metadata":{}},{"cell_type":"code","source":"import seaborn as sns\nimport matplotlib.pyplot as plt\nimport pandas as pd\n\n# Assuming heart_data_scaled is the scaled DataFrame\n# List of numerical and categorical variables\nnumerical_vars = ['age', 'trtbps', 'chol', 'thalach', 'oldpeak']\ncategorical_vars = ['sex', 'cp', 'fbs', 'rest_ecg', 'exang', 'slope', 'ca', 'thal']\n\n# Create strip plots\nfor cat_var in categorical_vars:\n    plt.figure(figsize=(14, 8))\n    melted_df = heart_data_scaled.melt(id_vars=cat_var, value_vars=numerical_vars, var_name='variables', value_name='value')\n    sns.stripplot(x='variables', y='value', hue=cat_var, data=melted_df, jitter=True, dodge=True, palette='Set1', alpha=0.7)\n    plt.title(f'Strip Plot of Scaled Numerical Variables by {cat_var}')\n    plt.legend(title=cat_var, bbox_to_anchor=(1.05, 1), loc='upper left')\n    plt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"The strip plot and the swarm plot, which both illustrate the relationship between the categorical variable `sex` and the numerical variables (`age`, `trtbps`, `chol`, `thalach`, and `oldpeak`).\n\n### Strip Plot Analysis:\n\nThe strip plot provides a clear visualization of the distribution of each numerical variable across the two categories of the `sex` variable (0 and 1). Each point represents an observation, and the vertical jitter helps to avoid overplotting. Here are some key observations:\n\n#### Strip Plot of Scaled Numerical Variables by 'sex'\n\n1. **Age:**\n   - There is no significant difference between males (1) and females (0) in terms of age distribution.\n   - Both groups have a similar spread of ages, mostly between -2 and 2 (after scaling).\n\n2. **Resting Blood Pressure (`trtbps`):**\n   - The distribution of `trtbps` is fairly similar between males and females.\n   - There is a slightly wider spread in females (0) compared to males (1), indicating some females have higher or lower resting blood pressures than males.\n\n3. **Cholesterol (`chol`):**\n   - Both males and females show a similar spread and clustering of cholesterol levels.\n   - A slight clustering around the center (0) can be seen in both groups.\n\n4. **Maximum Heart Rate (`thalach`):**\n   - `thalach` shows a higher spread in both groups, with females (0) slightly clustered at higher values compared to males (1).\n   - There are more outliers in males, indicating some males have significantly higher or lower maximum heart rates.\n\n5. **ST Depression (`oldpeak`):**\n   - The `oldpeak` variable shows a noticeable difference between males and females.\n   - Males (1) tend to have higher `oldpeak` values, indicating higher ST depression levels.\n\n","metadata":{}},{"cell_type":"markdown","source":"# Generate Swarm Plots for Each Categorical Variable","metadata":{}},{"cell_type":"markdown","source":"### Swarm Plot\n\n**Description**:\n- A swarm plot is similar to a strip plot but with a modification: it adjusts the points along the categorical axis to avoid overlap, making the plot less cluttered and easier to read.\n- Swarm plots provide a clear visual of the distribution of data points without overlapping.\n\n**Usage**:\n- Swarm plots are particularly useful for visualizing distributions in a way that maintains the individuality of each data point while avoiding overlap.\n- They are good for visualizing the distribution of small to medium-sized datasets.\n\n**Advantages**:\n- Avoids overlap of points, providing a clear view of the distribution.\n- Maintains the individuality of each data point, making it easier to see all observations.\n\n**Disadvantages**:\n- Can become cluttered with very large datasets, although less so than strip plots.\n- Computationally more intensive to create than strip plots.\n\n**Interpretation**:\n- Each point represents an individual observation.\n- The arrangement of points can indicate the density of observations; more densely packed points indicate a higher concentration of data.\n- Patterns and outliers can be easily identified, similar to a strip plot, but with better clarity in dense areas.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\nimport pandas as pd\nimport warnings\nwarnings.filterwarnings(\"ignore\")\n\n# Assuming the dataframe with scaled numerical data is named heart_data_scaled\n# and the original categorical variables are in heart_data\n\n# Create a copy of the scaled dataframe and merge it with the categorical variables from the original dataframe\nheart_data_merged = heart_data_scaled.copy()\ncategorical_vars = ['sex', 'cp', 'fbs', 'rest_ecg', 'exang', 'slope', 'ca', 'thal']\nheart_data_merged[categorical_vars] = heart_data[categorical_vars]\n\n# Define numerical variables\nnumerical_vars = ['age', 'trtbps', 'chol', 'thalach', 'oldpeak']\n\n# Create a figure and axes\nfig, axes = plt.subplots(len(categorical_vars), 1, figsize=(14, len(categorical_vars) * 6))\n\nfor i, cat_var in enumerate(categorical_vars):\n    melted_df = heart_data_merged.melt(id_vars=cat_var, value_vars=numerical_vars, var_name='variables', value_name='value')\n    sns.swarmplot(x='variables', y='value', hue=cat_var, data=melted_df, ax=axes[i], palette='viridis')\n    axes[i].set_title(f'Swarm Plot of Scaled Numerical Variables by {cat_var}')\n    axes[i].legend(title=cat_var, bbox_to_anchor=(1, 1))\n\nplt.tight_layout()\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Swarm Plot Analysis:\n\nThe swarm plot is similar to the strip plot but with additional features to better represent the distribution and density of the data points. The points are adjusted to avoid overlap, providing a clearer picture of the data distribution.\n\n#### Swarm Plot of Scaled Numerical Variables by 'sex'\n\n\n1. **Age:**\n   - The swarm plot reaffirms that age distribution is similar between males (1) and females (0).\n   - There is no significant clustering that differentiates between the two groups.\n\n2. **Resting Blood Pressure (`trtbps`):**\n   - The distribution of `trtbps` is again shown to be similar between the two groups.\n   - The swarm plot highlights that most of the data points are centered around the middle, with few extreme values.\n\n3. **Cholesterol (`chol`):**\n   - The cholesterol levels are more evenly distributed in the swarm plot.\n   - The plot reveals that both groups have similar clustering around the middle values.\n\n4. **Maximum Heart Rate (`thalach`):**\n   - The swarm plot emphasizes the higher spread of `thalach` values in both groups.\n   - The clustering pattern is clearer, showing that females (0) might have slightly higher maximum heart rates than males (1).\n\n5. **ST Depression (`oldpeak`):**\n   - The `oldpeak` values show a clearer distinction between males and females.\n   - The swarm plot highlights the clustering of higher `oldpeak` values in males, indicating a trend of higher ST depression levels in males compared to females.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Swarm Plot of Scaled Numerical Variables by `cp` (Chest Pain Type)\n\n#### Age:\n- The distribution of age appears to be fairly consistent across different types of chest pain (cp). \n- There is no significant clustering or pattern that differentiates one chest pain type from another based on age.\n\n#### Resting Blood Pressure (`trtbps`):\n- Patients with cp type 0 show a slightly wider spread in resting blood pressure compared to other types.\n- There is no strong clustering by cp type, indicating resting blood pressure alone may not be a strong differentiator between chest pain types.\n\n#### Cholesterol (`chol`):\n- Cholesterol levels are spread across all types of cp, with no significant clustering.\n- Again, this suggests that cholesterol levels are relatively similar regardless of the chest pain type.\n\n#### Maximum Heart Rate (`thalach`):\n- There is a more noticeable spread in maximum heart rate values for cp types 1 and 2 compared to types 0 and 3.\n- However, no significant clustering suggests that while there are variations, maximum heart rate may not be a strong differentiator between chest pain types.\n\n#### ST Depression (`oldpeak`):\n- Oldpeak values show some differentiation, with cp type 3 having a higher concentration of lower oldpeak values.\n- This suggests that patients with cp type 3 may experience less ST depression during exercise.\n\n### Analysis of Swarm Plot of Scaled Numerical Variables by `fbs` (Fasting Blood Sugar)\n\n#### Age:\n- The distribution of age for patients with fbs=0 and fbs=1 is very similar.\n- There is no significant clustering or pattern that differentiates one fasting blood sugar level from another based on age.\n\n#### Resting Blood Pressure (`trtbps`):\n- Similar to age, resting blood pressure does not show significant differences between fbs=0 and fbs=1.\n- The values are well mixed without clear clusters.\n\n#### Cholesterol (`chol`):\n- Cholesterol levels are spread across both fbs=0 and fbs=1 without significant differences.\n- This suggests that fasting blood sugar levels do not strongly correlate with cholesterol levels.\n\n#### Maximum Heart Rate (`thalach`):\n- The distribution of maximum heart rate is quite similar for both fbs=0 and fbs=1.\n- There is no noticeable clustering that would indicate a strong relationship between fasting blood sugar levels and maximum heart rate.\n\n#### ST Depression (`oldpeak`):\n- The values of oldpeak do not show a significant difference between fbs=0 and fbs=1.\n- Both fasting blood sugar levels appear to have similar distributions in ST depression values.\n\n### Summary:\n\n- **Age, Resting Blood Pressure, Cholesterol, Maximum Heart Rate, and ST Depression** show consistent distributions across different levels of chest pain and fasting blood sugar.\n- **Oldpeak** shows some differentiation in chest pain type but is still mixed for fasting blood sugar.\n- **No significant clustering** is observed in these variables, indicating that individually, they might not be strong predictors of chest pain type or fasting blood sugar levels.\n- **Patterns and insights** gained from these graphs suggest the need for further analysis using combinations of these variables to understand their collective impact on chest pain type and fasting blood sugar levels.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Swarm Plot by `rest_ecg` (Resting Electrocardiographic Results):\n\n1. **Age:**\n   - All three categories of `rest_ecg` (0, 1, 2) are distributed across the age range.\n   - No significant clustering is visible for any particular `rest_ecg` category within the age variable, indicating a similar age distribution across different `rest_ecg` results.\n\n2. **Resting Blood Pressure (trtbps):**\n   - The `rest_ecg` categories are fairly evenly distributed across trtbps values.\n   - There's no clear pattern indicating that any specific `rest_ecg` category is associated with higher or lower blood pressure values.\n\n3. **Cholesterol (chol):**\n   - Similar to trtbps, `rest_ecg` categories are evenly spread across cholesterol levels.\n   - No evident clustering of any `rest_ecg` category around specific cholesterol values.\n\n4. **Maximum Heart Rate Achieved (thalach):**\n   - A mix of `rest_ecg` categories is present across thalach values.\n   - A slight tendency for `rest_ecg` category 2 (yellow) to appear at higher thalach values, though not prominently distinct.\n\n5. **Oldpeak:**\n   - `rest_ecg` categories show a more noticeable spread in oldpeak values.\n   - Higher oldpeak values (above 2) have a mix of `rest_ecg` categories, with no category significantly dominating.\n\n### Analysis of Swarm Plot by `exang` (Exercise Induced Angina):\n\n1. **Age:**\n   - Both categories of `exang` (0 and 1) are distributed across the age range.\n   - No significant clustering is visible for any particular `exang` category within the age variable, indicating a similar age distribution across different `exang` results.\n\n2. **Resting Blood Pressure (trtbps):**\n   - The `exang` categories are fairly evenly distributed across trtbps values.\n   - There's no clear pattern indicating that any specific `exang` category is associated with higher or lower blood pressure values.\n\n3. **Cholesterol (chol):**\n   - Similar to trtbps, `exang` categories are evenly spread across cholesterol levels.\n   - No evident clustering of any `exang` category around specific cholesterol values.\n\n4. **Maximum Heart Rate Achieved (thalach):**\n   - A mix of `exang` categories is present across thalach values.\n   - There is a slight tendency for `exang` category 1 (green) to appear at lower thalach values, suggesting that individuals with exercise-induced angina might have lower maximum heart rates achieved.\n\n5. **Oldpeak:**\n   - `exang` categories show a more noticeable spread in oldpeak values.\n   - Higher oldpeak values (above 2) predominantly have `exang` category 1 (green), indicating that individuals with exercise-induced angina tend to have higher oldpeak values, which could correlate with more severe symptoms or outcomes.\n\n### Summary:\n- The `rest_ecg` and `exang` variables provide different insights into the distribution of patients' numerical attributes. \n- Both variables show diverse distributions across age, trtbps, chol, thalach, and oldpeak.\n- Notably, exercise-induced angina (exang) shows some clustering in oldpeak values, which could be significant for further analysis or model building.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Swarm Plots of Scaled Numerical Variables by Slope\n\n#### Slope Variable Analysis:\n\n- **Age**:\n  - The data points for different slope values (0, 1, 2) are dispersed across the range of ages. \n  - There is no significant clustering of any slope value within a specific age range.\n  - Age does not show a distinct pattern concerning slope values.\n\n- **Resting Blood Pressure (trtbps)**:\n  - The resting blood pressure values also do not show a distinct separation based on slope values.\n  - The spread of the data points is quite similar across different slope values.\n\n- **Cholesterol (chol)**:\n  - Cholesterol levels are dispersed similarly across different slope values, with no significant clustering observed.\n  - There are a few outliers in cholesterol levels, but they do not correspond to any specific slope value.\n\n- **Maximum Heart Rate Achieved (thalach)**:\n  - There is a wider spread in thalach values, but again, no distinct pattern emerges based on slope values.\n  - The highest value of thalach is associated with slope value 2.\n\n- **ST Depression Induced by Exercise Relative to Rest (oldpeak)**:\n  - The oldpeak values show some differentiation, with higher values more commonly associated with slope value 2.\n  - There is a notable spread in oldpeak values for slope value 2, indicating that higher ST depression might be associated with a different slope.\n\n### Analysis of Swarm Plots of Scaled Numerical Variables by CA (Number of Major Vessels Colored by Fluoroscopy)\n\n#### CA Variable Analysis:\n\n- **Age**:\n  - The age values are dispersed across different CA values (0 to 4).\n  - There is no distinct pattern or clustering for any specific CA value.\n\n- **Resting Blood Pressure (trtbps)**:\n  - Similar to age, trtbps values are spread out across different CA values.\n  - No significant separation or clustering is observed for different CA values.\n\n- **Cholesterol (chol)**:\n  - Cholesterol levels show a spread across different CA values, with no clear pattern emerging.\n  - A few outliers are present, but they do not correspond to any specific CA value.\n\n- **Maximum Heart Rate Achieved (thalach)**:\n  - Thalach values show a wider spread, with no distinct clustering based on CA values.\n  - Higher thalach values are associated with CA value 0.\n\n- **ST Depression Induced by Exercise Relative to Rest (oldpeak)**:\n  - Oldpeak values show some differentiation, with higher values associated with higher CA values (3 and 4).\n  - This indicates that higher ST depression might be more common in patients with more major vessels colored by fluoroscopy.\n\n### Key Insights:\n\n1. **Age**: No significant patterns or clustering observed in both analyses. Age does not show a strong relationship with slope or CA values.\n2. **Resting Blood Pressure (trtbps)**: No distinct patterns or clustering observed. Similar spread across all values for both slope and CA variables.\n3. **Cholesterol (chol)**: Similar dispersion across different values, with no significant patterns observed in relation to slope or CA values.\n4. **Maximum Heart Rate Achieved (thalach)**: Slight differentiation observed with higher values of thalach associated with slope value 2 and CA value 0.\n5. **ST Depression Induced by Exercise Relative to Rest (oldpeak)**: Higher values of oldpeak are associated with higher slope and CA values, indicating a potential relationship where higher ST depression might be linked with more major vessels colored by fluoroscopy and different slope values.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Swarm Plot of Scaled Numerical Variables by Thal\n\n#### Thal Variable Analysis:\n\n- **Age**:\n  - The data points for different thal values (1.0, 2.0, 3.0) are dispersed across the range of ages.\n  - There is no significant clustering of any thal value within a specific age range.\n  - Age does not show a distinct pattern concerning thal values.\n\n- **Resting Blood Pressure (trtbps)**:\n  - The resting blood pressure values also do not show a distinct separation based on thal values.\n  - The spread of the data points is quite similar across different thal values.\n\n- **Cholesterol (chol)**:\n  - Cholesterol levels are dispersed similarly across different thal values, with no significant clustering observed.\n  - There are a few outliers in cholesterol levels, but they do not correspond to any specific thal value.\n\n- **Maximum Heart Rate Achieved (thalach)**:\n  - There is a wider spread in thalach values, but again, no distinct pattern emerges based on thal values.\n  - The highest values of thalach are associated with thal value 3.0.\n\n- **ST Depression Induced by Exercise Relative to Rest (oldpeak)**:\n  - The oldpeak values show some differentiation, with higher values more commonly associated with thal value 3.0.\n  - There is a notable spread in oldpeak values for thal value 3.0, indicating that higher ST depression might be associated with different thal values.\n\n### Key Insights:\n\n1. **Age**: No significant patterns or clustering observed. Age does not show a strong relationship with thal values.\n2. **Resting Blood Pressure (trtbps)**: No distinct patterns or clustering observed. Similar spread across all values for different thal values.\n3. **Cholesterol (chol)**: Similar dispersion across different values, with no significant patterns observed in relation to thal values.\n4. **Maximum Heart Rate Achieved (thalach)**: Slight differentiation observed with higher values of thalach associated with thal value 3.0.\n5. **ST Depression Induced by Exercise Relative to Rest (oldpeak)**: Higher values of oldpeak are associated with thal value 3.0, indicating a potential relationship where higher ST depression might be linked with specific thal values.","metadata":{}},{"cell_type":"markdown","source":"# Relationships between variables(Analysis with Heatmap)","metadata":{}},{"cell_type":"code","source":"# Execute the provided code to create the heatmap\nimport seaborn as sns\nimport matplotlib.pyplot as plt\n\n# Combine the scaled numerical variables with the categorical variables\ncombined_data = heart_data_scaled.copy()\nfor col in categorical_vars:\n    combined_data[col] = heart_data[col]\n\n# Calculate the correlation matrix\ncorrelation_matrix = combined_data.corr()\n\n# Create a heatmap\nplt.figure(figsize=(12, 10))\nsns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', fmt=\".2f\", linewidths=0.5)\nplt.title('Correlation Heatmap of All Variables')\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"Analyze the correlation heatmap in detail, focusing on each variable separately and interpreting its correlations with other variables.\n\n### 1. **Age**\n- **Positive Correlations**:\n  - **trtbps**: 0.28 - Slightly higher systolic blood pressure with increasing age.\n  - **chol**: 0.21 - Slight increase in cholesterol levels with age.\n  - **ca**: 0.28 - Presence of major vessels colored by fluoroscopy increases with age.\n- **Negative Correlations**:\n  - **thalach**: -0.40 - Maximum heart rate achieved decreases with age.\n  - **target**: -0.23 - Lower likelihood of heart disease with increasing age, though this might require further investigation to validate.\n\n### 2. **Sex**\n- **Positive Correlations**:\n  - **target**: 0.28 - Slight increase in the likelihood of heart disease with being male.\n- **Negative Correlations**:\n  - **chol**: -0.20 - Lower cholesterol levels associated with being female.\n  - **ca**: -0.21 - Fewer major vessels colored by fluoroscopy in females.\n  - **thalach**: -0.06 - Slightly lower maximum heart rate achieved in males.\n\n### 3. **Chest Pain Type (cp)**\n- **Positive Correlations**:\n  - **slope**: 0.30 - Correlation with the slope of the peak exercise ST segment.\n  - **target**: 0.43 - Stronger correlation with the likelihood of heart disease.\n- **Negative Correlations**:\n  - **oldpeak**: -0.39 - Negative correlation with ST depression induced by exercise.\n  - **thalach**: -0.05 - Slight decrease in maximum heart rate achieved.\n\n### 4. **Resting Blood Pressure (trtbps)**\n- **Positive Correlations**:\n  - **age**: 0.28 - Higher resting blood pressure with increasing age.\n- **Negative Correlations**:\n  - **target**: -0.14 - Slightly lower likelihood of heart disease with higher resting blood pressure.\n\n### 5. **Cholesterol (chol)**\n- **Positive Correlations**:\n  - **age**: 0.21 - Higher cholesterol levels with increasing age.\n- **Negative Correlations**:\n  - **sex**: -0.20 - Lower cholesterol levels in females.\n  - **rest_ecg**: -0.15 - Negative correlation with resting electrocardiographic results.\n\n### 6. **Fasting Blood Sugar (fbs)**\n- **Weak Correlations**: Generally shows very weak correlations with other variables, suggesting it's not strongly related to other factors in this dataset.\n\n### 7. **Resting Electrocardiographic Results (rest_ecg)**\n- **Negative Correlations**:\n  - **thalach**: -0.38 - Lower maximum heart rate achieved with certain resting ECG results.\n  - **ca**: -0.15 - Fewer major vessels colored by fluoroscopy with certain ECG results.\n  - **target**: -0.15 - Lower likelihood of heart disease with certain ECG results.\n\n### 8. **Maximum Heart Rate Achieved (thalach)**\n- **Positive Correlations**:\n  - **target**: 0.42 - Higher maximum heart rate achieved associated with higher likelihood of heart disease.\n- **Negative Correlations**:\n  - **age**: -0.40 - Decrease in maximum heart rate with increasing age.\n  - **sex**: -0.06 - Slightly lower maximum heart rate in males.\n  - **cp**: -0.05 - Lower heart rate achieved in patients with certain chest pain types.\n  - **oldpeak**: -0.38 - Negative correlation with ST depression induced by exercise.\n\n### 9. **Exercise Induced Angina (exang)**\n- **Negative Correlations**:\n  - **thalach**: -0.38 - Lower maximum heart rate in patients with exercise induced angina.\n  - **target**: -0.44 - Lower likelihood of heart disease in patients with exercise induced angina.\n\n### 10. **ST Depression Induced by Exercise (oldpeak)**\n- **Positive Correlations**:\n  - **age**: 0.21 - Slight increase in ST depression with age.\n  - **exang**: 0.29 - Correlated with exercise induced angina.\n  - **slope**: 0.39 - Correlation with the slope of the peak exercise ST segment.\n  - **target**: 0.35 - Higher likelihood of heart disease with increased ST depression.\n- **Negative Correlations**:\n  - **cp**: -0.39 - Negative correlation with certain types of chest pain.\n  - **thalach**: -0.38 - Lower maximum heart rate achieved.\n\n### 11. **Slope of the Peak Exercise ST Segment (slope)**\n- **Positive Correlations**:\n  - **cp**: 0.30 - Correlation with chest pain type.\n  - **oldpeak**: 0.39 - Correlated with ST depression induced by exercise.\n  - **target**: 0.35 - Higher likelihood of heart disease.\n- **Negative Correlations**:\n  - **thalach**: -0.34 - Lower maximum heart rate achieved.\n\n### 12. **Number of Major Vessels Colored by Fluoroscopy (ca)**\n- **Positive Correlations**:\n  - **age**: 0.28 - More major vessels colored with increasing age.\n  - **cp**: 0.30 - Correlation with chest pain type.\n- **Negative Correlations**:\n  - **rest_ecg**: -0.15 - Fewer major vessels colored with certain ECG results.\n  - **thalach**: -0.39 - Lower maximum heart rate achieved.\n  - **target**: -0.36 - Lower likelihood of heart disease.\n\n### 13. **Thalassemia (thal)**\n- **Negative Correlations**:\n  - **thalach**: -0.27 - Lower maximum heart rate achieved.\n  - **target**: -0.42 - Lower likelihood of heart disease.\n\n### 14. **Target**\n- **Positive Correlations**:\n  - **cp**: 0.43 - Higher likelihood of heart disease with certain chest pain types.\n  - **thalach**: 0.42 - Higher maximum heart rate achieved associated with higher likelihood of heart disease.\n  - **oldpeak**: 0.35 - Higher likelihood of heart disease with increased ST depression.\n  - **slope**: 0.35 - Correlation with the slope of the peak exercise ST segment.\n- **Negative Correlations**:\n  - **age**: -0.23 - Lower likelihood of heart disease with increasing age.\n  - **sex**: -0.28 - Lower likelihood of heart disease in females.\n  - **trtbps**: -0.14 - Slightly lower likelihood of heart disease with higher resting blood pressure.\n  - **exang**: -0.44 - Lower likelihood of heart disease in patients with exercise induced angina.\n  - **ca**: -0.36 - Lower likelihood of heart disease with more major vessels colored.\n  - **thal**: -0.42 - Lower likelihood of heart disease with certain types of thalassemia.\n\nThis analysis should provide you with a comprehensive understanding of the relationships between different variables in your dataset.","metadata":{}},{"cell_type":"markdown","source":"### Strongest Correlations\n\n#### 1. **cp (Chest Pain Type) and Target**\n- **Correlation**: 0.43\n- **Analysis**: This positive correlation indicates that certain types of chest pain (cp) are strongly associated with the presence of heart disease (target). Patients presenting with typical angina (cp = 3) have a higher likelihood of being diagnosed with heart disease. This relationship highlights the importance of chest pain type as a predictive factor for heart disease.\n\n#### 2. **thalach (Maximum Heart Rate Achieved) and Target**\n- **Correlation**: 0.42\n- **Analysis**: This positive correlation suggests that higher maximum heart rates achieved during exercise are associated with a higher likelihood of heart disease. This could be indicative of the heart's reduced ability to handle physical stress in patients with heart disease.\n\n#### 3. **exang (Exercise Induced Angina) and Target**\n- **Correlation**: -0.44\n- **Analysis**: This negative correlation indicates that patients with exercise-induced angina (exang = 1) are less likely to be diagnosed with heart disease. This counterintuitive result might require further investigation, as angina typically suggests underlying heart issues.\n\n#### 4. **oldpeak (ST Depression Induced by Exercise) and Target**\n- **Correlation**: 0.35\n- **Analysis**: A higher ST depression during exercise (oldpeak) is positively associated with the presence of heart disease. This measure reflects the severity of ischemia and is a critical diagnostic indicator.\n\n#### 5. **slope (Slope of the Peak Exercise ST Segment) and Target**\n- **Correlation**: 0.35\n- **Analysis**: The slope of the peak exercise ST segment correlates positively with heart disease. A downsloping ST segment (slope = 2) is often indicative of severe ischemia and correlates with a higher likelihood of heart disease.\n\n### Weak Correlations\n\n#### 1. **fbs (Fasting Blood Sugar) with Other Variables**\n- **Analysis**: The fasting blood sugar levels (fbs) show very weak correlations with all other variables, suggesting it might not be a significant predictor of heart disease in this dataset. This could indicate that within this particular population, blood sugar levels alone do not provide much insight into heart disease risk.\n\n#### 2. **chol (Cholesterol) with Target**\n- **Correlation**: 0.09\n- **Analysis**: The weak positive correlation between cholesterol levels (chol) and the target suggests that cholesterol might not be a strong standalone predictor of heart disease in this dataset. This is surprising given the general medical consensus on cholesterol as a risk factor and may warrant further investigation or indicate the need for considering additional variables together.\n\n#### 3. **trtbps (Resting Blood Pressure) with Target**\n- **Correlation**: -0.14\n- **Analysis**: The weak negative correlation indicates a slightly lower likelihood of heart disease with higher resting blood pressure. This could suggest that resting blood pressure alone is not a definitive indicator of heart disease within this dataset.\n\n### Impact of Weak Correlations\n\n- **Predictive Modeling**: Weak correlations indicate that certain variables might not significantly impact the prediction model if used alone. However, they should not be entirely dismissed as they might still contribute valuable information in combination with other variables.\n  \n- **Multivariate Analysis**: Variables with weak correlations could have non-linear relationships or interactions with other variables that are not captured in a simple correlation matrix. Techniques like multivariate regression, decision trees, or other machine learning algorithms can help uncover these complex relationships.\n\n- **Clinical Insight**: Clinicians often use a combination of indicators to diagnose heart disease. Even variables with weak correlations might still play a crucial role in a comprehensive diagnostic process.\n\n### Conclusion\n\nWhile strong correlations provide clear insights into relationships between variables, weak correlations should be further investigated for potential hidden patterns and combined effects. Understanding both can lead to a more robust predictive model and deeper clinical insights.","metadata":{}},{"cell_type":"markdown","source":"# Preparation for Modeling","metadata":{}},{"cell_type":"markdown","source":"Preparing your dataset for machine learning modeling is a crucial step to ensure that your models perform well and yield reliable results. Here are the key steps you should take to prepare your dataset effectively:\n\n### 1. **Handle Missing Values**\n- **Imputation**: Fill in missing values using appropriate methods such as mean, median, mode, or using more advanced techniques like K-Nearest Neighbors (KNN) imputation.\n- **Removal**: If the number of missing values is small, you might consider removing those rows or columns.\n\n### 2. **Encode Categorical Variables**\n- **Label Encoding**: Assign each unique category in a column a different integer. Suitable for ordinal categorical variables.\n- **One-Hot Encoding**: Create binary columns for each category. Suitable for nominal categorical variables without any order.\n\n### 3. **Feature Scaling**\n- **Standardization**: Transform features to have a mean of 0 and a standard deviation of 1.\n- **Normalization**: Scale features to a fixed range, typically 0 to 1.\n\n### 4. **Feature Engineering**\n- **Create Interaction Features**: Create new features by combining existing ones.\n- **Polynomial Features**: Add polynomial terms of features to capture non-linear relationships.\n- **Binning**: Convert continuous variables into categorical bins.\n- **Log Transform**: Apply logarithmic transformation to skewed features to reduce skewness.\n\n### 5. **Feature Selection**\n- **Univariate Selection**: Use statistical tests to select features with the strongest relationship with the output variable.\n- **Recursive Feature Elimination**: Remove least important features recursively to select the best set.\n- **Principal Component Analysis (PCA)**: Reduce dimensionality while retaining most of the variance in the data.\n\n### 6. **Handling Class Imbalance**\n- **Resampling Techniques**: Use oversampling (like SMOTE) or undersampling techniques to balance the classes.\n- **Class Weights**: Assign different weights to classes to handle imbalance during model training.\n\n### 7. **Split the Dataset**\n- **Train-Test Split**: Split the dataset into training and testing sets to evaluate model performance on unseen data.\n- **Validation Set**: Optionally, create a validation set to fine-tune model parameters and avoid overfitting.\n\n### 8. **Data Augmentation**\n- If applicable, generate more data through augmentation techniques to increase the diversity of the training data and improve model generalization.\n\n### 9. **Remove Outliers**\n- Detect and remove outliers that could negatively impact model performance using statistical methods or visualization techniques.","metadata":{}},{"cell_type":"markdown","source":"## Dropping Columns with Low Correlation","metadata":{}},{"cell_type":"markdown","source":"To determine which variables to remove from the dataset, we can refer to the correlation heatmap you generated earlier. Variables with low absolute correlation values with the target variable can be considered for removal. Typically, absolute correlation values less than 0.1 are often considered too weak to be useful for predictive modeling.","metadata":{}},{"cell_type":"code","source":"# List of variables to be removed\nvariables_to_remove = ['chol', 'fbs', 'rest_ecg']\n\n# Remove the identified variables from the dataset\nheart_data_reduced = heart_data.drop(columns=variables_to_remove)\n\n# Verify the remaining columns\nprint(heart_data_reduced.columns)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Detailed Explanation of the Code:\n\n1. **List of Variables to be Removed**:\n   ```python\n   variables_to_remove = ['chol', 'fbs', 'rest_ecg']\n   ```\n   - This line creates a list called `variables_to_remove` that contains the names of the variables you want to remove from the dataset. In this case, the variables are `chol`, `fbs`, and `rest_ecg`.\n\n2. **Removing the Identified Variables**:\n   ```python\n   heart_data_reduced = heart_data.drop(columns=variables_to_remove)\n   ```\n   - `heart_data.drop(columns=variables_to_remove)`:\n     - `heart_data` is your original dataset.\n     - The `drop` method is used to remove columns from the DataFrame.\n     - The `columns` parameter specifies which columns to drop, and it takes the list `variables_to_remove` as its argument.\n   - The result is stored in a new DataFrame called `heart_data_reduced`. This new DataFrame will contain all the original data except for the columns listed in `variables_to_remove`.\n\n3. **Verifying the Remaining Columns**:\n   ```python\n   print(heart_data_reduced.columns)\n   ```\n   - This line prints out the names of the columns in the `heart_data_reduced` DataFrame. It allows you to verify that the specified columns have been successfully removed.","metadata":{}},{"cell_type":"markdown","source":"## Struggling Outliers","metadata":{}},{"cell_type":"markdown","source":"Dealing with outliers is a crucial step in data preprocessing and has significant implications for data analysis and machine learning modeling. Here's a detailed explanation of why handling outliers is important in data science:\n\n### Importance of Dealing with Outliers in Data Science\n\n#### 1. **Impact on Descriptive Statistics**:\n   - **Mean and Standard Deviation**: Outliers can significantly affect the mean and standard deviation of a dataset, leading to misleading statistical summaries.\n   - **Median and Mode**: While median and mode are more robust to outliers, the presence of extreme values can still affect their interpretation.\n\n#### 2. **Effect on Data Distribution**:\n   - Outliers can distort the distribution of data, making it difficult to understand the underlying patterns. This distortion can impact the results of statistical tests and analyses that assume normality or other specific distributions.\n\n#### 3. **Influence on Machine Learning Models**:\n   - **Linear Models**: Outliers can have a substantial impact on linear models (e.g., linear regression), as they can disproportionately influence the slope and intercept of the fitted line.\n   - **Distance-Based Models**: Models like k-nearest neighbors (KNN) and clustering algorithms (e.g., k-means) can be highly sensitive to outliers, as they rely on distance metrics.\n   - **Tree-Based Models**: While tree-based models (e.g., decision trees, random forests) are generally more robust to outliers, extreme values can still affect the splits and decision rules.\n\n#### 4. **Impact on Model Performance**:\n   - Outliers can lead to overfitting, where the model learns the noise in the data rather than the underlying patterns. This can reduce the model's generalizability and performance on new, unseen data.\n   - They can also cause models to perform poorly by skewing the learning process, leading to inaccurate predictions and classifications.\n\n#### 5. **Data Quality and Integrity**:\n   - Outliers can be indicative of data entry errors, measurement errors, or anomalies in data collection processes. Identifying and handling these outliers is essential for maintaining data quality and integrity.\n\n#### 6. **Detection of Anomalies**:\n   - In some cases, outliers represent meaningful anomalies or rare events that are important to identify and understand. For instance, in fraud detection, outliers may indicate fraudulent transactions.\n\n#### 7. **Improved Visualizations**:\n   - Outliers can distort data visualizations, making it difficult to interpret plots and graphs accurately. By handling outliers, visualizations can provide a clearer and more accurate representation of the data.\n\n### Methods for Handling Outliers\n\n#### 1. **Identification**:\n   - **Statistical Methods**: Use z-scores, IQR (Interquartile Range), or box plots to identify outliers.\n   - **Visualization**: Scatter plots, histograms, and box plots can help visually identify outliers.\n\n#### 2. **Treatment**:\n   - **Removal**: In some cases, outliers can be removed if they are identified as errors or irrelevant to the analysis.\n   - **Transformation**: Apply transformations (e.g., log transformation) to reduce the impact of outliers.\n   - **Imputation**: Replace outliers with a statistical measure (e.g., mean, median) or use more sophisticated imputation techniques.\n   - **Capping**: Limit the extreme values to a certain percentile (e.g., replacing values above the 95th percentile with the 95th percentile value).\n\n#### 3. **Special Handling**:\n   - **Isolation Forests**: Use algorithms specifically designed to identify and handle outliers, such as isolation forests or robust statistics.\n\n### Conclusion\n\nDealing with outliers is essential for improving the quality of data, enhancing the performance of machine learning models, and ensuring accurate and reliable data analysis. By identifying, understanding, and appropriately handling outliers, data scientists can make more informed decisions and build better predictive models.","metadata":{}},{"cell_type":"markdown","source":"Dealing with outliers is a multifaceted task, and there are several methods to handle them. Here are some common techniques, along with detailed explanations of each:\n\n### 1. **Identification of Outliers**\n\nBefore dealing with outliers, they must be identified. Common methods for identifying outliers include:\n\n- **Visual Methods**:\n  - **Box Plot**: A box plot displays the distribution of data based on a five-number summary (minimum, first quartile, median, third quartile, and maximum). Points outside 1.5 times the interquartile range (IQR) from the quartiles are typically considered outliers.\n  - **Scatter Plot**: Scatter plots can help visualize the relationship between two variables and identify points that deviate significantly from others.\n  - **Histogram**: Histograms show the frequency distribution of a dataset and can help identify unusually high or low values.\n\n- **Statistical Methods**:\n  - **Z-Score**: The z-score indicates how many standard deviations a data point is from the mean. A z-score above 3 or below -3 is often considered an outlier.\n  - **IQR (Interquartile Range)**: The IQR is the range between the first quartile (25th percentile) and the third quartile (75th percentile). Data points outside 1.5 times the IQR above the third quartile or below the first quartile are considered outliers.\n  - **Modified Z-Score**: For skewed distributions, a modified z-score based on the median and MAD (Median Absolute Deviation) can be used.\n\n### 2. **Handling Outliers**\n\nOnce identified, there are several methods to handle outliers:\n\n#### a. **Removal**\n\n- **Purpose**: Outliers that are the result of data entry errors, measurement errors, or irrelevant data can be removed.\n- **Method**:\n  ```python\n  # Example code to remove outliers based on z-score\n  from scipy import stats\n  z_scores = np.abs(stats.zscore(data))\n  data_clean = data[(z_scores < 3).all(axis=1)]\n  ```\n\n#### b. **Transformation**\n\n- **Purpose**: To reduce the influence of outliers, data can be transformed using mathematical functions.\n- **Methods**:\n  - **Log Transformation**: Reduces the impact of large values.\n    ```python\n    data['log_transformed'] = np.log(data['variable'])\n    ```\n  - **Square Root Transformation**: Also used to reduce skewness.\n    ```python\n    data['sqrt_transformed'] = np.sqrt(data['variable'])\n    ```\n  - **Box-Cox Transformation**: Transforms data to follow a normal distribution.\n    ```python\n    from scipy.stats import boxcox\n    data['boxcox_transformed'], _ = boxcox(data['variable'])\n    ```\n\n#### c. **Imputation**\n\n- **Purpose**: Replace outliers with more representative values.\n- **Methods**:\n  - **Mean/Median Imputation**: Replace outliers with the mean or median value.\n    ```python\n    data['variable'] = np.where(z_scores > 3, data['variable'].median(), data['variable'])\n    ```\n  - **Interpolation**: Use linear or polynomial interpolation to replace outliers.\n    ```python\n    data['variable'] = data['variable'].interpolate()\n    ```\n\n#### d. **Capping (Winsorization)**\n\n- **Purpose**: Limit the influence of extreme values by capping them at a certain percentile.\n- **Method**:\n  ```python\n  # Example code to cap values at the 5th and 95th percentiles\n  percentile_5 = data['variable'].quantile(0.05)\n  percentile_95 = data['variable'].quantile(0.95)\n  data['variable'] = np.clip(data['variable'], percentile_5, percentile_95)\n  ```\n\n#### e. **Special Handling Techniques**\n\n- **Purpose**: Use advanced techniques to identify and handle outliers.\n- **Methods**:\n  - **Isolation Forest**: An unsupervised learning algorithm to identify outliers.\n    ```python\n    from sklearn.ensemble import IsolationForest\n    iso = IsolationForest(contamination=0.05)\n    preds = iso.fit_predict(data)\n    data_clean = data[preds == 1]\n    ```\n  - **DBSCAN (Density-Based Spatial Clustering of Applications with Noise)**: A clustering algorithm that can identify outliers as noise points.\n    ```python\n    from sklearn.cluster import DBSCAN\n    db = DBSCAN(eps=0.5, min_samples=5).fit(data)\n    labels = db.labels_\n    data_clean = data[labels != -1]\n    ```\n\n### Conclusion\n\nHandling outliers is a critical step in data preprocessing that helps improve the performance and reliability of machine learning models. By identifying and appropriately dealing with outliers, we ensure that the data is more representative of the underlying patterns, leading to better model performance and more accurate predictions.","metadata":{}},{"cell_type":"markdown","source":"# Visualizing outliers","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Assuming your dataset is named heart_data_reduced\n# Replace 'heart_data_reduced' with the actual name of your DataFrame\n\n# List of numeric variables\nnumeric_vars = ['age', 'trtbps', 'thalach', 'oldpeak']\n\n# Plotting the box plots\nplt.figure(figsize=(12, 8))\nfor i, var in enumerate(numeric_vars, 1):\n    plt.subplot(2, 2, i)\n    sns.boxplot(x=heart_data_reduced[var])\n    plt.title(f'Box Plot of {var}')\nplt.tight_layout()\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Detailed Explanation of the Code:\n1. **Import Libraries:**\n   ```python\n   import matplotlib.pyplot as plt\n   import seaborn as sns\n   ```\n   - `matplotlib.pyplot`: A plotting library used for creating static, animated, and interactive visualizations.\n   - `seaborn`: A data visualization library based on `matplotlib` that provides a high-level interface for drawing attractive and informative statistical graphics.\n\n2. **List of Numeric Variables:**\n   ```python\n   numeric_vars = ['age', 'trtbps', 'thalach', 'oldpeak']\n   ```\n   - This list contains the names of the numeric variables in your dataset for which you want to visualize outliers.\n\n3. **Create a Figure for the Box Plots:**\n   ```python\n   plt.figure(figsize=(12, 8))\n   ```\n   - This line initializes a new figure with a specified size of 12 by 8 inches.\n\n4. **Loop Through Numeric Variables and Plot Box Plots:**\n   ```python\n   for i, var in enumerate(numeric_vars, 1):\n       plt.subplot(2, 2, i)\n       sns.boxplot(x=heart_data_reduced[var])\n       plt.title(f'Box Plot of {var}')\n   ```\n   - `enumerate(numeric_vars, 1)`: This function iterates over the list of numeric variables, providing both the index and the variable name.\n   - `plt.subplot(2, 2, i)`: This line specifies the position of the current subplot within a 2x2 grid.\n   - `sns.boxplot(x=heart_data_reduced[var])`: This line creates a box plot for the specified numeric variable.\n   - `plt.title(f'Box Plot of {var}')`: This line sets the title of the current subplot to indicate which variable's box plot is being displayed.\n\n5. **Adjust Layout and Show the Plots:**\n   ```python\n   plt.tight_layout()\n   plt.show()\n   ```\n   - `plt.tight_layout()`: This function automatically adjusts subplot parameters to give specified padding and ensure that subplots fit within the figure area.\n   - `plt.show()`: This line displays the figure containing all the box plots.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of Box Plots and Outliers\n\n#### Box Plot for `age`\n\n- **Median and Quartiles**:\n  - The median age (50th percentile) is around 55 years.\n  - The first quartile (25th percentile) is around 48 years.\n  - The third quartile (75th percentile) is around 62 years.\n\n- **Outliers**:\n  - There are no apparent outliers in the `age` variable. All data points fall within the whiskers, which represent 1.5 times the interquartile range (IQR) from the first and third quartiles.\n\n- **Distribution**:\n  - The distribution of age seems fairly symmetric with a slight concentration around the median.\n\n#### Box Plot for `trtbps` (Resting Blood Pressure)\n\n- **Median and Quartiles**:\n  - The median resting blood pressure is around 130 mm Hg.\n  - The first quartile is around 120 mm Hg.\n  - The third quartile is around 140 mm Hg.\n\n- **Outliers**:\n  - There are several outliers in the `trtbps` variable, with values exceeding the upper whisker limit. These outliers start appearing above approximately 170 mm Hg, and the highest outlier is around 200 mm Hg.\n\n- **Distribution**:\n  - The majority of the data points fall between 100 and 160 mm Hg.\n  - The presence of outliers on the higher end suggests some patients have significantly higher resting blood pressure than the general population in this dataset.\n\n### Impact of Outliers\n\n- **Age**:\n  - The absence of outliers in the `age` variable indicates a relatively normal and consistent distribution of ages among patients. This stability means age will likely not require special treatment for outlier removal.\n\n- **Resting Blood Pressure (`trtbps`)**:\n  - The presence of outliers in the `trtbps` variable could affect the performance and accuracy of machine learning models. These high blood pressure readings might be due to measurement errors, extreme health conditions, or specific patient characteristics.\n  - Depending on the context and the goals of your analysis, you might consider:\n    - **Removing Outliers**: If you believe these outliers are anomalies or measurement errors.\n    - **Transforming Data**: Applying a transformation (e.g., log transformation) to reduce the impact of outliers.\n    - **Imputation**: Replacing outliers with a specific value like the mean or median.\n    - **Model Robustness**: Using models robust to outliers (e.g., tree-based models).","metadata":{}},{"cell_type":"markdown","source":"#### Box Plot for `thalach` (Maximum Heart Rate Achieved)\n\n- **Median and Quartiles**:\n  - The median `thalach` (maximum heart rate achieved) is around 150 bpm.\n  - The first quartile (25th percentile) is around 130 bpm.\n  - The third quartile (75th percentile) is around 170 bpm.\n\n- **Outliers**:\n  - There is one outlier on the lower end, with a value around 80 bpm.\n  - The data distribution is otherwise fairly symmetric without significant outliers on the higher end.\n\n- **Distribution**:\n  - The `thalach` values are fairly spread out within the interquartile range, indicating a diverse range of maximum heart rates among the patients.\n  - The presence of a lower outlier could indicate a patient with significantly lower maximum heart rate, which might be due to medical conditions or measurement errors.\n\n#### Box Plot for `oldpeak` (ST Depression Induced by Exercise Relative to Rest)\n\n- **Median and Quartiles**:\n  - The median `oldpeak` value is around 1.\n  - The first quartile (25th percentile) is around 0.5.\n  - The third quartile (75th percentile) is around 1.6.\n\n- **Outliers**:\n  - There are several outliers on the higher end, with values ranging from 4 to 6.\n  - These outliers indicate patients with significantly higher ST depression values.\n\n- **Distribution**:\n  - Most of the `oldpeak` values are concentrated between 0 and 2.\n  - The presence of higher outliers suggests some patients experience a much higher ST depression during exercise, which might indicate severe heart conditions or other factors influencing their ECG readings.\n\n### Impact of Outliers\n\n- **`thalach` (Maximum Heart Rate Achieved)**:\n  - The single lower outlier might not significantly impact the overall analysis, but it could be important to investigate further.\n  - Depending on the context, you might consider:\n    - Removing the outlier if it's determined to be an anomaly or error.\n    - Keeping the outlier if it provides meaningful information about a particular subgroup of patients.\n\n- **`oldpeak` (ST Depression Induced by Exercise Relative to Rest)**:\n  - The higher outliers could potentially skew the analysis and affect model performance.\n  - Considerations include:\n    - Removing the outliers if they are deemed anomalies or errors.\n    - Applying a transformation to reduce the impact of outliers on the overall analysis.\n    - Investigating the causes of high `oldpeak` values to understand if they indicate specific health conditions.\n\nBy carefully analyzing and handling outliers, you can ensure that your machine learning models are trained on high-quality, representative data, leading to more accurate and reliable predictions.","metadata":{}},{"cell_type":"markdown","source":"# Trtbps Variable","metadata":{}},{"cell_type":"code","source":"import numpy as np\n\n# Calculate the z-scores for the trtbps variable\ntrtbps_z_scores = np.abs((heart_data_reduced['trtbps'] - heart_data_reduced['trtbps'].mean()) / heart_data_reduced['trtbps'].std())\n\n# Count the number of outliers for different threshold values\nthresholds = [1, 2, 3, 4]\noutlier_counts = {threshold: np.sum(trtbps_z_scores > threshold) for threshold in thresholds}\n\n# Display the outlier counts for each threshold\noutlier_counts","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation of the Code:\n\n1. **Calculate Z-Scores**:\n    ```python\n    trtbps_z_scores = np.abs((heart_data_reduced['trtbps'] - heart_data_reduced['trtbps'].mean()) / heart_data_reduced['trtbps'].std())\n    ```\n    - This line calculates the z-scores for the `trtbps` variable.\n    - The z-score is calculated by subtracting the mean of the `trtbps` values and then dividing by the standard deviation.\n    - `np.abs` is used to get the absolute values of the z-scores, as we are interested in the magnitude of the deviation from the mean, regardless of the direction.\n\n2. **Count Outliers for Different Threshold Values**:\n    ```python\n    thresholds = [1, 2, 3, 4]\n    outlier_counts = {threshold: np.sum(trtbps_z_scores > threshold) for threshold in thresholds}\n    ```\n    - This section defines the list of threshold values for the z-scores.\n    - A dictionary comprehension is used to count the number of outliers for each threshold.\n    - `np.sum(trtbps_z_scores > threshold)` counts the number of z-scores that exceed the given threshold value.\n\n3. **Display the Outlier Counts**:\n    ```python\n    outlier_counts\n    ```\n    - This line outputs the dictionary containing the counts of outliers for each threshold value.","metadata":{}},{"cell_type":"markdown","source":"### What is the Z-score Method?\n\nThe Z-score method is a statistical technique used to identify outliers in a dataset. It measures how many standard deviations an individual data point is from the mean of the dataset. \n\n- **Why is it applied?**\n  - **Standardization**: It helps to standardize data points on a common scale without changing the relative shape of the distribution.\n  - **Outlier Detection**: It is commonly used to detect outliers because it quantifies the extremity of a data point in comparison to the rest of the dataset. Data points with a high Z-score are considered outliers.\n\n### What Exactly Does the Threshold Value Mean?\n\nThe threshold value in the context of Z-scores is a cut-off point that determines what is considered an outlier. \n\n- **Explanation**:\n  - If a data point's Z-score is greater than the threshold value, it is considered an outlier.\n  - For example, a threshold of 2 means any data point more than 2 standard deviations away from the mean is an outlier.\n\n### Analyzing the Result\n\nAfter running the code, we obtained the result `{1: 100, 2: 15, 3: 2, 4: 0}`. This means:\n\n- **Threshold 1**: 100 data points have a Z-score greater than 1.\n- **Threshold 2**: 15 data points have a Z-score greater than 2.\n- **Threshold 3**: 2 data points have a Z-score greater than 3.\n- **Threshold 4**: 0 data points have a Z-score greater than 4.\n\n### What Does This Result Mean?\n\n- **Threshold 1**: Many data points (100) are considered outliers, suggesting a large spread or variability in the `trtbps` values.\n- **Threshold 2**: A moderate number of data points (15) are considered outliers, indicating that these points are relatively far from the mean but not excessively so.\n- **Threshold 3**: Very few data points (2) are considered outliers, indicating extreme values.\n- **Threshold 4**: No data points are considered outliers, showing that there are no extremely extreme values.\n\n### Choosing the Threshold Value\n\nThe choice of threshold value depends on the context and goals of your analysis:\n\n- **Threshold 1 (Z > 1)**: Including 100 outliers might be too broad, potentially flagging too many data points and not necessarily extreme ones.\n- **Threshold 2 (Z > 2)**: Including 15 outliers is more manageable and indicates significant deviations from the mean without being overly conservative.\n- **Threshold 3 (Z > 3)**: Including 2 outliers targets only the most extreme data points, minimizing the number of flagged outliers but possibly missing some that are relevant.\n- **Threshold 4 (Z > 4)**: No outliers are detected, which might be too strict and not useful for most practical purposes.\n\n### Recommendation\n\n- **Threshold of 2**: This is often a good balance between being too lenient and too strict. It includes data points that are significantly different from the rest without overwhelming the model with too many outliers.","metadata":{}},{"cell_type":"markdown","source":"### What is Winsorizing?\n\nWinsorizing is a statistical technique used to limit extreme values in a dataset to reduce the effect of possibly spurious outliers. Instead of removing outliers or replacing them with some calculated value (like the mean), Winsorizing modifies the extreme values to be closer to the main body of the data.\n\n### Why is Winsorizing Used?\n\n1. **Stability**: It helps stabilize statistical measures such as the mean and standard deviation by reducing the impact of extreme outliers.\n2. **Preservation**: Unlike removing outliers, Winsorizing keeps all data points in the dataset, preserving the overall sample size.\n3. **Robustness**: It can make models more robust and less sensitive to extreme variations in the data.\n\n### Winsorizing Methods\n\nThere are different approaches to Winsorizing based on how you handle the extreme values:\n\n1. **Symmetric Winsorizing**: This method involves setting the extreme values at both ends (low and high) to specific percentiles of the data.\n   - **Example**: You might set the bottom 5% of data points to the value at the 5th percentile and the top 5% to the value at the 95th percentile.\n\n2. **Asymmetric Winsorizing**: In some cases, you may want to treat the lower and upper ends of the distribution differently.\n   - **Example**: You might Winsorize the top 10% of the data but only the bottom 1% if the data has more extreme high values.\n\n3. **Custom Winsorizing**: You can define custom thresholds or rules for Winsorizing based on the nature of your data.\n   - **Example**: If you know that values beyond a certain point are unrealistic or impossible, you can set these values to a maximum or minimum threshold.\n\n### How Winsorizing Works\n\nHere’s a simple explanation of the process:\n\n1. **Identify Extremes**: Determine the data points considered extreme outliers.\n2. **Set Limits**: Define the percentile limits for Winsorizing (e.g., 5th and 95th percentiles).\n3. **Replace Values**: Replace the extreme values with the respective percentile values. For example, all data points below the 5th percentile are set to the 5th percentile value, and all data points above the 95th percentile are set to the 95th percentile value.\n\n### Benefits of Winsorizing\n\n- **Preserves Data**: Keeps all data points in the dataset.\n- **Reduces Impact of Outliers**: Limits the influence of extreme values on statistical measures and models.\n- **Improves Robustness**: Often leads to more stable and reliable models.\n\n### Example Scenario\n\nImagine you have a dataset of people's incomes, and you notice a few extremely high values that skew the average income upward. By Winsorizing, you can limit these high incomes to a reasonable upper limit (e.g., the 95th percentile income) while also potentially adjusting the lowest incomes if needed. This way, your analysis or model becomes more reflective of the typical income distribution without being distorted by the few extreme values.","metadata":{}},{"cell_type":"code","source":"import pandas as pd\nfrom scipy.stats import zscore\n\n# Calculate the z-scores for the 'trtbps' column\nheart_data_reduced['trtbps_zscore'] = zscore(heart_data_reduced['trtbps'])\n\n# Identify outliers based on a threshold of 2\noutliers_trtbps = heart_data_reduced[heart_data_reduced['trtbps_zscore'].abs() > 2]\n\n# Display the outliers in a table format\noutliers_table = outliers_trtbps[['trtbps', 'trtbps_zscore']]\noutliers_table","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n1. **Importing Libraries:**\n   - `pandas as pd`: Import the pandas library, which is used for data manipulation and analysis.\n   - `from scipy.stats import zscore`: Import the `zscore` function from the scipy.stats module, which is used to calculate the z-scores of a given data series.\n\n2. **Calculating Z-Scores:**\n   - `heart_data_reduced['trtbps_zscore'] = zscore(heart_data_reduced['trtbps'])`: This line calculates the z-scores for the `trtbps` column in the `heart_data_reduced` DataFrame.\n     - The `zscore` function standardizes the `trtbps` values. It computes how many standard deviations each value is from the mean of the `trtbps` column.\n     - The resulting z-scores are stored in a new column named `trtbps_zscore` in the `heart_data_reduced` DataFrame.\n\n### Explanation:\n```python\n# Identify outliers based on a threshold of 2\noutliers_trtbps = heart_data_reduced[heart_data_reduced['trtbps_zscore'].abs() > 2]\n```\n\n### Explanation:\n3. **Identifying Outliers:**\n   - `heart_data_reduced['trtbps_zscore'].abs() > 2`: This condition checks for rows where the absolute value of the z-score is greater than 2. \n     - An absolute z-score greater than 2 indicates that the value is more than 2 standard deviations away from the mean, which is considered an outlier.\n   - `heart_data_reduced[...]`: This part of the code uses the condition inside the brackets to filter the DataFrame.\n     - Only rows where the condition is `True` are selected.\n   - `outliers_trtbps`: The resulting DataFrame containing only the outliers is assigned to the variable `outliers_trtbps`.\n\n### Explanation:\n```python\n# Display the outliers in a table format\noutliers_table = outliers_trtbps[['trtbps', 'trtbps_zscore']]\noutliers_table\n```\n\n### Explanation:\n4. **Creating and Displaying the Outliers Table:**\n   - `outliers_table = outliers_trtbps[['trtbps', 'trtbps_zscore']]`: This line selects only the `trtbps` and `trtbps_zscore` columns from the `outliers_trtbps` DataFrame and assigns them to a new DataFrame named `outliers_table`.\n     - This step is useful for focusing on the relevant columns when examining the outliers.\n   - `outliers_table`: This line is used to display the `outliers_table` DataFrame. In most Python environments, simply writing the DataFrame name will output its contents.\n\n### Summary:\nThis code calculates the z-scores for the `trtbps` variable in the `heart_data_reduced` dataset, identifies the outliers based on a threshold of 2 standard deviations, and displays these outliers in a table format showing the `trtbps` values and their corresponding z-scores. This helps in understanding which data points are significantly different from the rest of the data, indicating potential outliers.","metadata":{}},{"cell_type":"code","source":"import pandas as pd\nfrom scipy.stats import zscore\n\n# Assuming heart_data_reduced is your DataFrame\n\n# Step 1: Find the value in 'trtbps' closest to 170\nclosest_to_170 = heart_data_reduced['trtbps'].iloc[(heart_data_reduced['trtbps'] - 170).abs().argmin()]\nprint(\"Value closest to 170 in 'trtbps':\", closest_to_170)\n\n# Step 2: Define a custom function to winsorize the 'trtbps' column based on the closest value to 170\ndef custom_winsorize(values, threshold, replace_value):\n    z_scores = zscore(values)\n    winsorized_values = values.copy()\n    winsorized_values[z_scores > threshold] = replace_value\n    winsorized_values[z_scores < -threshold] = replace_value\n    return winsorized_values\n\n# Apply the custom winsorize function to the 'trtbps' column\nheart_data_reduced['trtbps_winsorize'] = custom_winsorize(heart_data_reduced['trtbps'], threshold=2, replace_value=closest_to_170)\n\n# Display the updated DataFrame\nheart_data_reduced[['trtbps', 'trtbps_winsorize']]","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Step 1: Find the Value Closest to 170 in `trtbps`\nFirst, we need to find the value in the `trtbps` variable that is closest to 170.\n\n```python\n# Find the value in 'trtbps' closest to 170\nclosest_to_170 = heart_data_reduced['trtbps'].iloc[(heart_data_reduced['trtbps'] - 170).abs().argmin()]\nclosest_to_170\n```\n\n### Step 2: Winsorize the Outliers in `trtbps`\nNext, we will replace the outlier values in `trtbps` with the value found in the previous step.\n\n```python\n# Define a custom function to winsorize the 'trtbps' column based on the closest value to 170\ndef custom_winsorize(values, threshold, replace_value):\n    z_scores = zscore(values)\n    winsorized_values = values.copy()\n    winsorized_values[z_scores > threshold] = replace_value\n    winsorized_values[z_scores < -threshold] = replace_value\n    return winsorized_values\n\n# Apply the custom winsorize function to the 'trtbps' column\nheart_data_reduced['trtbps_winsorize'] = custom_winsorize(heart_data_reduced['trtbps'], threshold=2, replace_value=closest_to_170)\n```\n\n### Explanation:\n1. **Finding the Value Closest to 170:**\n   - `heart_data_reduced['trtbps'].iloc[(heart_data_reduced['trtbps'] - 170).abs().argmin()]`: This line calculates the absolute difference between each value in the `trtbps` column and 170, then finds the index of the minimum value in this difference array, and uses this index to get the corresponding value in the `trtbps` column.\n\n2. **Defining the Custom Winsorize Function:**\n   - `custom_winsorize(values, threshold, replace_value)`: This function takes the original values, a z-score threshold, and a replacement value as input.\n     - `z_scores = zscore(values)`: Calculate the z-scores of the values.\n     - `winsorized_values = values.copy()`: Create a copy of the original values to avoid modifying the original data.\n     - `winsorized_values[z_scores > threshold] = replace_value`: Replace values with z-scores greater than the threshold with the replacement value.\n     - `winsorized_values[z_scores < -threshold] = replace_value`: Replace values with z-scores less than the negative threshold with the replacement value.\n     - `return winsorized_values`: Return the winsorized values.\n\n3. **Applying the Custom Winsorize Function:**\n   - `heart_data_reduced['trtbps_winsorize']`: Create a new column in the `heart_data_reduced` DataFrame to store the winsorized version of the `trtbps` variable.\n   - `custom_winsorize(heart_data_reduced['trtbps'], threshold=2, replace_value=closest_to_170)`: Apply the custom winsorize function with a threshold of 2 and the closest value to 170 as the replacement value.","metadata":{}},{"cell_type":"code","source":"heart_data_reduced.head()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Set the aesthetic style of the plots\nsns.set(style=\"whitegrid\")\n\n# Create a box plot for the 'trtbps_winsorize' variable\nplt.figure(figsize=(8, 6))\nsns.boxplot(x=heart_data_reduced['trtbps_winsorize'])\n\n# Set the title and labels\nplt.title('Box Plot of trtbps_winsorize')\nplt.xlabel('trtbps_winsorize')\n\n# Show the plot\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n1. **Setting the Aesthetic Style:**\n   - `sns.set(style=\"whitegrid\")`: This sets the aesthetic style of the plots to a white grid background, which is a common style used for clarity and better visualization.\n\n2. **Creating the Box Plot:**\n   - `plt.figure(figsize=(8, 6))`: This creates a new figure with a specified size (8 inches wide and 6 inches tall).\n   - `sns.boxplot(x=heart_data_reduced['trtbps_winsorize'])`: This creates a box plot for the `trtbps_winsorize` variable using Seaborn's `boxplot` function. The `x` parameter specifies the data to plot on the x-axis.\n\n3. **Setting the Title and Labels:**\n   - `plt.title('Box Plot of trtbps_winsorize')`: This sets the title of the plot.\n   - `plt.xlabel('trtbps_winsorize')`: This sets the label for the x-axis.\n\n4. **Showing the Plot:**\n   - `plt.show()`: This displays the plot.","metadata":{}},{"cell_type":"markdown","source":"# Thalach Variable","metadata":{}},{"cell_type":"code","source":"import pandas as pd\n\ndef detect_outliers(df, column):\n    \"\"\"\n    Detects outliers in a dataframe column based on the whiskers of a box plot.\n    \n    Parameters:\n    df (pd.DataFrame): The dataframe containing the column.\n    column (str): The name of the column to check for outliers.\n    \n    Returns:\n    pd.DataFrame: A dataframe containing the outliers.\n    \"\"\"\n    # Calculate Q1 (25th percentile) and Q3 (75th percentile)\n    Q1 = df[column].quantile(0.25)\n    Q3 = df[column].quantile(0.75)\n    IQR = Q3 - Q1\n    \n    # Calculate the lower and upper bounds for outliers\n    lower_bound = Q1 - 1.5 * IQR\n    upper_bound = Q3 + 1.5 * IQR\n    \n    # Identify the outliers\n    outliers = df[(df[column] < lower_bound) | (df[column] > upper_bound)]\n    \n    return outliers\n\n# Apply the function to the 'thalach' variable\nthalach_outliers = detect_outliers(heart_data_reduced, 'thalach')\nthalach_outliers","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation\n\n1. **Function Definition:**\n   - `def detect_outliers(df, column)`: This defines a function `detect_outliers` that takes in a dataframe `df` and a column name `column`.\n\n2. **Calculating Quartiles and IQR:**\n   - `Q1 = df[column].quantile(0.25)`: This calculates the first quartile (25th percentile) of the column.\n   - `Q3 = df[column].quantile(0.75)`: This calculates the third quartile (75th percentile) of the column.\n   - `IQR = Q3 - Q1`: This calculates the Interquartile Range (IQR).\n\n3. **Calculating Bounds:**\n   - `lower_bound = Q1 - 1.5 * IQR`: This calculates the lower bound for detecting outliers.\n   - `upper_bound = Q3 + 1.5 * IQR`: This calculates the upper bound for detecting outliers.\n\n4. **Identifying Outliers:**\n   - `outliers = df[(df[column] < lower_bound) | (df[column] > upper_bound)]`: This filters the dataframe to get the rows where the column values are either below the lower bound or above the upper bound.\n\n5. **Returning Outliers:**\n   - `return outliers`: This returns the dataframe containing the outliers.\n\n6. **Applying the Function:**\n   - `thalach_outliers = detect_outliers(heart_data_reduced, 'thalach')`: This applies the function to the 'thalach' variable and stores the result in `thalach_outliers`.","metadata":{}},{"cell_type":"code","source":"# Remove outliers from the dataset\nheart_data_cleaned = heart_data_reduced[~heart_data_reduced.index.isin(thalach_outliers.index)]\n\n# Display the first few rows of the cleaned dataset to verify the changes\nheart_data_cleaned.head()","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"7. **Removing Outliers:**\n   - `heart_data_cleaned = heart_data_reduced[~heart_data_reduced.index.isin(thalach_outliers.index)]`: This removes the rows identified as outliers from the original dataframe and stores the result in a new dataframe `heart_data_cleaned`.\n\n","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Create a box plot for the 'thalach' variable after removing outliers\nplt.figure(figsize=(8, 6))\nsns.boxplot(x=heart_data_cleaned['thalach'])\nplt.title('Box Plot of thalach (After Removing Outliers)')\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation\n\n1. **Import Libraries:**\n   - `import matplotlib.pyplot as plt`: Imports the Matplotlib library for plotting.\n   - `import seaborn as sns`: Imports the Seaborn library for statistical data visualization.\n\n2. **Plotting the Box Plot:**\n   - `plt.figure(figsize=(8, 6))`: Sets the figure size for the plot.\n   - `sns.boxplot(x=heart_data_cleaned['thalach'])`: Creates a box plot for the 'thalach' variable in the `heart_data_cleaned` dataframe.\n   - `plt.title('Box Plot of thalach (After Removing Outliers)')`: Sets the title for the plot.\n   - `plt.show()`: Displays the plot.","metadata":{}},{"cell_type":"markdown","source":"# Oldpeak Variable","metadata":{}},{"cell_type":"code","source":"import pandas as pd\n\n# Assuming the detect_outliers function is already defined as provided earlier\n\n# Use the previously defined detect_outliers function to identify outliers in the 'oldpeak' variable\noldpeak_outliers = detect_outliers(heart_data_cleaned, 'oldpeak')\n\n# Display the outliers\noldpeak_outliers[['oldpeak']]","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n1. **Identify Outliers:**\n   - `oldpeak_outliers = detect_outliers(heart_data_cleaned, 'oldpeak')`: This line applies the `detect_outliers` function to the `oldpeak` variable in the `heart_data_cleaned` dataframe to identify outliers.\n\n2. **Display Outliers:**\n   - `print(oldpeak_outliers[['oldpeak']])`: This line prints the outliers in the `oldpeak` variable, showing only the `oldpeak` column.","metadata":{}},{"cell_type":"code","source":"# Find the value in 'oldpeak' closest to 4.2 that is less than 4.2\nclosest_to_4_2 = heart_data_cleaned['oldpeak'][heart_data_cleaned['oldpeak'] < 4.2].max()\nprint(\"Value closest to 4.2 in 'oldpeak' that is less than 4.2:\", closest_to_4_2)","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation\n\n1. **Find the Closest Value Less Than 4.2:**\n   - `closest_to_4_2 = heart_data_cleaned['oldpeak'][heart_data_cleaned['oldpeak'] < 4.2].max()`: This line finds the maximum value in the `oldpeak` column that is less than 4.2. This value is the closest to 4.2 without exceeding it.","metadata":{}},{"cell_type":"code","source":"# Define a custom function to winsorize the 'oldpeak' column based on the closest value to 4.2\ndef custom_winsorize_oldpeak(values, threshold, replace_value):\n    z_scores = zscore(values)\n    winsorized_values = values.copy()\n    winsorized_values[z_scores > threshold] = replace_value\n    winsorized_values[z_scores < -threshold] = replace_value\n    return winsorized_values\n\n# Apply the custom winsorize function to the 'oldpeak' column\nheart_data_cleaned['oldpeak_winsorize'] = custom_winsorize_oldpeak(heart_data_cleaned['oldpeak'], threshold=1.5, replace_value=closest_to_4_2)\n\n# Display the first few rows to verify the changes\nheart_data_cleaned[['oldpeak', 'oldpeak_winsorize']].head()","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"2. **Define the Custom Winsorize Function:**\n   - `custom_winsorize_oldpeak(values, threshold, replace_value)`: This function takes the original values, a z-score threshold, and a replacement value as input.\n     - `z_scores = zscore(values)`: Calculate the z-scores of the values.\n     - `winsorized_values = values.copy()`: Create a copy of the original values to avoid modifying the original data.\n     - `winsorized_values[z_scores > threshold] = replace_value`: Replace values with z-scores greater than the threshold with the replacement value.\n     - `winsorized_values[z_scores < -threshold] = replace_value`: Replace values with z-scores less than the negative threshold with the replacement value.\n     - `return winsorized_values`: Return the winsorized values.\n\n3. **Apply the Custom Winsorize Function:**\n   - `heart_data_cleaned['oldpeak_winsorize']`: Create a new column in the `heart_data_cleaned` DataFrame to store the winsorized version of the `oldpeak` variable.\n   - `custom_winsorize_oldpeak(heart_data_cleaned['oldpeak'], threshold=1.5, replace_value=closest_to_4_2)`: Apply the custom winsorize function with a threshold of 1.5 and the closest value to 4.2 as the replacement value.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Create a box plot for the 'oldpeak_winsorize' variable\nplt.figure(figsize=(8, 6))\nsns.boxplot(x=heart_data_cleaned['oldpeak_winsorize'])\nplt.title('Box Plot of oldpeak_winsorize (After Winsorization)')\nplt.xlabel('oldpeak_winsorize')\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Import Libraries:**\n   - `import matplotlib.pyplot as plt`: Imports the Matplotlib library for plotting.\n   - `import seaborn as sns`: Imports the Seaborn library for statistical data visualization.\n\n2. **Create a Box Plot:**\n   - `plt.figure(figsize=(8, 6))`: Creates a new figure with a specified size of 8 inches wide and 6 inches tall.\n   - `sns.boxplot(x=heart_data_cleaned['oldpeak_winsorize'])`: Creates a box plot for the `oldpeak_winsorize` variable using Seaborn's `boxplot` function.\n   - `plt.title('Box Plot of oldpeak_winsorize (After Winsorization)')`: Sets the title of the plot.\n   - `plt.xlabel('oldpeak_winsorize')`: Sets the label for the x-axis.\n   - `plt.show()`: Displays the plot.","metadata":{}},{"cell_type":"code","source":"heart_data_cleaned.head()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# List of variables to be removed\nvariables_to_remove = ['trtbps', 'oldpeak', 'trtbps_zscore']\n\n# Remove the identified variables from the dataset\nheart_data_final = heart_data_cleaned.drop(columns=variables_to_remove)\n\n# Display the first few rows of the updated dataset to verify the changes\nheart_data_final.head()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **List of Variables to Remove:**\n   ```python\n   variables_to_remove = ['trtbps', 'oldpeak', 'trtbps_z_score']\n   ```\n   - This line creates a list called `variables_to_remove` that contains the names of the variables you want to remove from the dataset.\n\n2. **Remove the Identified Variables:**\n   ```python\n   heart_data_final = heart_data_cleaned.drop(columns=variables_to_remove)\n   ```\n   - `heart_data_cleaned.drop(columns=variables_to_remove)`: This line removes the specified columns (`trtbps`, `oldpeak`, and `trtbps_winsorize`) from the `heart_data_cleaned` DataFrame.\n   - The result is stored in a new DataFrame called `heart_data_final`.\n\n3. **Verify the Changes:**\n   ```python\n   print(heart_data_final.head())\n   ```\n   - This line prints the first few rows of the updated DataFrame to verify that the specified variables have been removed.","metadata":{}},{"cell_type":"markdown","source":"# Determining Distributions of Numeric Variables","metadata":{}},{"cell_type":"markdown","source":"Determining the distributions of numerical variables is a critical step in the data preprocessing stage of modeling preparation. Understanding the distribution of your data can have significant implications for the modeling process and overall data analysis. Here’s a detailed explanation of the importance and significance of this step:\n\n### Importance of Determining the Distributions of Numerical Variables\n\n#### 1. **Model Selection and Performance**\n- **Model Assumptions**: Many statistical models and machine learning algorithms make specific assumptions about the data. For example, linear regression assumes that the residuals (errors) are normally distributed. Violating these assumptions can lead to inaccurate models.\n- **Algorithm Suitability**: Understanding the data distribution can guide the selection of appropriate algorithms. Some algorithms, like decision trees, are non-parametric and do not assume a specific data distribution, while others, like logistic regression, can be affected by skewed distributions.\n\n#### 2. **Data Transformation**\n- **Normalization and Standardization**: Data transformation techniques like normalization and standardization are often applied to numerical variables to bring them onto a common scale. Understanding the distribution helps determine the most appropriate transformation.\n- **Handling Skewness**: If a variable is highly skewed, transformations like log, square root, or Box-Cox can be applied to approximate a normal distribution, which can improve model performance and interpretation.\n\n#### 3. **Outlier Detection and Treatment**\n- **Identifying Outliers**: Understanding the distribution helps in identifying outliers. Outliers can significantly affect the mean and standard deviation, leading to skewed analyses and poor model performance.\n- **Informed Decision Making**: Knowing the distribution helps in deciding whether to keep, remove, or transform outliers.\n\n#### 4. **Feature Engineering**\n- **Creating New Features**: Understanding the distribution can inspire new features that capture the underlying patterns in the data. For example, binning a continuous variable based on its distribution can create a categorical variable that may be more informative for certain models.\n- **Interaction Terms**: Knowing the distributions helps in creating interaction terms and polynomial features that can capture non-linear relationships in the data.\n\n#### 5. **Model Interpretation and Diagnostics**\n- **Residual Analysis**: After fitting a model, analyzing the distribution of residuals helps diagnose issues with the model. Non-normally distributed residuals might indicate a problem with the model fit.\n- **Interpretation of Results**: Understanding the distribution of input variables can make it easier to interpret the coefficients and predictions of the model.\n\n### Significance in the Context of Modeling Preparation\n\n1. **Improving Model Accuracy**:\n   - Properly understanding and transforming numerical variables can lead to more accurate and reliable models. Models built on appropriately transformed data tend to perform better because they can capture the underlying patterns more effectively.\n\n2. **Enhancing Robustness**:\n   - By ensuring that the data meets the assumptions of the chosen model, you can create more robust models that generalize better to new, unseen data.\n\n3. **Optimizing Feature Engineering**:\n   - Insight into the distribution helps in crafting better features, leading to improved model performance. For instance, detecting skewness early on allows you to apply the right transformations and create features that capture essential aspects of the data.\n\n4. **Facilitating Diagnostics and Validation**:\n   - Understanding data distributions aids in the post-modeling phase, where residual analysis and validation are crucial. It ensures that the model diagnostics are meaningful and any anomalies can be traced back to their source in the data.\n\n5. **Reducing Model Complexity**:\n   - By knowing the distribution, unnecessary complexity can be avoided. For example, highly skewed data might necessitate more complex models if not transformed, whereas a simple transformation can often suffice.\n\n### Techniques to Determine Distributions\n\n- **Visual Methods**: Histograms, box plots, Q-Q plots, and density plots are visual tools that help in understanding the distribution of numerical variables.\n- **Statistical Methods**: Skewness and kurtosis values, as well as normality tests like the Shapiro-Wilk test or Kolmogorov-Smirnov test, provide quantitative measures of distribution characteristics.\n\nIn conclusion, determining the distributions of numerical variables is a foundational step in the data preprocessing pipeline that significantly impacts model selection, performance, and interpretability. It guides the entire modeling process, from feature engineering to model diagnostics, ensuring that the models built are both accurate and reliable.","metadata":{}},{"cell_type":"markdown","source":"### Techniques to Determine the Distributions of Numerical Variables\n\nThere are several techniques, both visual and statistical, that can be used to determine the distributions of numerical variables. Here’s a detailed explanation:\n\n#### 1. **Visual Techniques**\n\n##### a. **Histogram**\n- **Description**: A histogram is a graphical representation of the distribution of a dataset. It partitions the data into bins and displays the frequency of data points in each bin.\n- **Usage**: Useful for understanding the shape, central tendency, and spread of the data.\n- **Example**:\n  ```python\n  import matplotlib.pyplot as plt\n  plt.hist(data['variable'], bins=30)\n  plt.title('Histogram of Variable')\n  plt.xlabel('Variable')\n  plt.ylabel('Frequency')\n  plt.show()\n  ```\n\n##### b. **Box Plot**\n- **Description**: A box plot shows the distribution of a dataset based on a five-number summary (minimum, first quartile, median, third quartile, and maximum). It also highlights outliers.\n- **Usage**: Useful for identifying outliers and understanding the spread and skewness of the data.\n- **Example**:\n  ```python\n  import seaborn as sns\n  sns.boxplot(x=data['variable'])\n  plt.title('Box Plot of Variable')\n  plt.xlabel('Variable')\n  plt.show()\n  ```\n\n##### c. **Q-Q Plot (Quantile-Quantile Plot)**\n- **Description**: A Q-Q plot compares the quantiles of the data to the quantiles of a theoretical distribution (usually normal). If the data is normally distributed, the points will fall along a straight line.\n- **Usage**: Useful for assessing normality and detecting deviations from a specified distribution.\n- **Example**:\n  ```python\n  from scipy import stats\n  import matplotlib.pyplot as plt\n  stats.probplot(data['variable'], dist=\"norm\", plot=plt)\n  plt.title('Q-Q Plot of Variable')\n  plt.show()\n  ```\n\n##### d. **Density Plot**\n- **Description**: A density plot is a smoothed, continuous version of a histogram, often estimated using a kernel density estimate (KDE).\n- **Usage**: Useful for visualizing the distribution and estimating the probability density function of the data.\n- **Example**:\n  ```python\n  import seaborn as sns\n  sns.kdeplot(data['variable'], shade=True)\n  plt.title('Density Plot of Variable')\n  plt.xlabel('Variable')\n  plt.show()\n  ```\n\n#### 2. **Statistical Techniques**\n\n##### a. **Descriptive Statistics**\n- **Description**: Summary statistics such as mean, median, standard deviation, skewness, and kurtosis provide insights into the central tendency, dispersion, and shape of the distribution.\n- **Usage**: Useful for a quick numerical summary of the data distribution.\n- **Example**:\n  ```python\n  data['variable'].describe()\n  ```\n\n##### b. **Skewness and Kurtosis**\n- **Description**: Skewness measures the asymmetry of the distribution, while kurtosis measures the heaviness of the tails.\n- **Usage**: Useful for understanding the shape of the distribution.\n- **Example**:\n  ```python\n  skewness = data['variable'].skew()\n  kurtosis = data['variable'].kurtosis()\n  print(f'Skewness: {skewness}, Kurtosis: {kurtosis}')\n  ```\n\n##### c. **Normality Tests**\n- **Shapiro-Wilk Test**: Tests the null hypothesis that the data was drawn from a normal distribution.\n  - **Example**:\n    ```python\n    from scipy.stats import shapiro\n    stat, p = shapiro(data['variable'])\n    print(f'Statistics={stat}, p={p}')\n    ```\n- **Kolmogorov-Smirnov Test**: Compares the data to a reference distribution (e.g., normal).\n  - **Example**:\n    ```python\n    from scipy.stats import kstest\n    stat, p = kstest(data['variable'], 'norm')\n    print(f'Statistics={stat}, p={p}')\n    ```\n\n### Methods to Address Problems Identified During Distribution Analysis\n\nIf problems are identified during the distribution analysis (e.g., skewness, outliers, non-normality), several methods can be used to address these issues:\n\n#### 1. **Transformations**\n\n##### a. **Log Transformation**\n- **Usage**: Reduces right skewness by compressing the range of the data.\n- **Example**:\n  ```python\n  data['variable_log'] = np.log(data['variable'] + 1)  # Adding 1 to avoid log(0)\n  ```\n\n##### b. **Square Root Transformation**\n- **Usage**: Reduces right skewness and stabilizes variance.\n- **Example**:\n  ```python\n  data['variable_sqrt'] = np.sqrt(data['variable'])\n  ```\n\n##### c. **Box-Cox Transformation**\n- **Usage**: A family of power transformations that stabilize variance and make the data more normal distribution-like.\n- **Example**:\n  ```python\n  from scipy.stats import boxcox\n  data['variable_boxcox'], _ = boxcox(data['variable'] + 1)  # Adding 1 if data contains zero values\n  ```\n\n##### d. **Yeo-Johnson Transformation**\n- **Usage**: Similar to Box-Cox but can handle zero and negative values.\n- **Example**:\n  ```python\n  from sklearn.preprocessing import PowerTransformer\n  pt = PowerTransformer(method='yeo-johnson')\n  data['variable_yeojohnson'] = pt.fit_transform(data[['variable']])\n  ```\n\n#### 2. **Outlier Handling**\n\n##### a. **Winsorization**\n- **Usage**: Limits extreme values to reduce the impact of outliers.\n- **Example**:\n  ```python\n  from scipy.stats.mstats import winsorize\n  data['variable_winsorized'] = winsorize(data['variable'], limits=[0.05, 0.05])\n  ```\n\n##### b. **Removing Outliers**\n- **Usage**: Excludes extreme values that are considered anomalies.\n- **Example**:\n  ```python\n  Q1 = data['variable'].quantile(0.25)\n  Q3 = data['variable'].quantile(0.75)\n  IQR = Q3 - Q1\n  lower_bound = Q1 - 1.5 * IQR\n  upper_bound = Q3 + 1.5 * IQR\n  data = data[(data['variable'] >= lower_bound) & (data['variable'] <= upper_bound)]\n  ```\n\n#### 3. **Handling Skewness**\n\n##### a. **Binning**\n- **Usage**: Converts continuous data into categorical bins, which can reduce the impact of skewness and outliers.\n- **Example**:\n  ```python\n  data['variable_binned'] = pd.qcut(data['variable'], q=4)  # Quartile binning\n  ```\n\nBy employing these techniques, you can effectively analyze and address any issues related to the distribution of numerical variables, leading to more robust and accurate models.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\n\n# List of numeric variables\nnumeric_vars = ['age', 'thalach', 'trtbps_winsorize', 'oldpeak_winsorize']\n\n# Plot histograms for each numeric variable\nplt.figure(figsize=(12, 10))\nfor i, var in enumerate(numeric_vars, 1):\n    plt.subplot(2, 2, i)\n    sns.histplot(heart_data_final[var], kde=True)\n    plt.title(f'Histogram of {var}')\n    plt.xlabel(var)\n    plt.ylabel('Frequency')\nplt.tight_layout()\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Step 1: Visualize Numeric Variables Using Histogram Graphs\n\n```python\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n# List of numeric variables\nnumeric_vars = ['age', 'thalach', 'trtbps_winsorize', 'oldpeak_winsorize']\n\n# Plot histograms for each numeric variable\nplt.figure(figsize=(12, 10))\nfor i, var in enumerate(numeric_vars, 1):\n    plt.subplot(2, 2, i)\n    sns.histplot(heart_data_final[var], kde=True)\n    plt.title(f'Histogram of {var}')\n    plt.xlabel(var)\n    plt.ylabel('Frequency')\nplt.tight_layout()\nplt.show()\n```\n\n### Step 2: Calculate and Display Skewness Coefficients\n\n```python\n# Calculate and display skewness coefficients for each numeric variable\nskewness = heart_data_final[numeric_vars].skew()\nprint(\"Skewness coefficients:\")\nprint(skewness)\n```\n\n### Explanation:\n\n1. **Visualizing with Histogram Graphs:**\n   - `import matplotlib.pyplot as plt`: Import the Matplotlib library for plotting.\n   - `import seaborn as sns`: Import the Seaborn library for statistical data visualization.\n   - `numeric_vars = ['age', 'thalach', 'trtbps_winsorize', 'oldpeak_winsorize']`: List the numeric variables to be visualized.\n   - `plt.figure(figsize=(12, 10))`: Create a new figure with a specified size.\n   - `for i, var in enumerate(numeric_vars, 1)`: Loop through the list of numeric variables.\n     - `plt.subplot(2, 2, i)`: Create a 2x2 grid of subplots and select the i-th subplot.\n     - `sns.histplot(heart_data_final[var], kde=True)`: Create a histogram with a kernel density estimate (KDE) for the variable.\n     - `plt.title(f'Histogram of {var}')`: Set the title of the subplot.\n     - `plt.xlabel(var)`: Set the x-axis label.\n     - `plt.ylabel('Frequency')`: Set the y-axis label.\n   - `plt.tight_layout()`: Adjust the layout to prevent overlap.\n   - `plt.show()`: Display the plot.","metadata":{}},{"cell_type":"code","source":"# Calculate and display skewness coefficients for each numeric variable\nskewness = heart_data_final[numeric_vars].skew()\nprint(\"Skewness coefficients:\")\nprint(skewness)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"2. **Calculating Skewness Coefficients:**\n   - `skewness = heart_data_final[numeric_vars].skew()`: Calculate the skewness coefficients for the numeric variables.\n   - `print(\"Skewness coefficients:\")`: Print the header for the skewness coefficients.\n   - `print(skewness)`: Print the skewness coefficients.","metadata":{}},{"cell_type":"markdown","source":"### Age Distribution\n\n**Histogram Analysis:**\n- The histogram for the \"age\" variable shows a roughly symmetric distribution.\n- The data is centered around the 50s and 60s, which is typical for a dataset related to heart conditions.\n\n**Skewness Analysis:**\n- The skewness coefficient for \"age\" is -0.199209, which indicates a slight negative skewness.\n- Since the skewness value is close to zero, the distribution is approximately symmetric. This implies that the age data does not have a long tail on either side, and the mean and median are nearly the same.\n\n**Conclusion:**\n- The \"age\" variable is nearly normally distributed, which is a favorable condition for many statistical analyses and machine learning algorithms.\n- No major transformation is needed for the \"age\" variable given its nearly symmetric distribution and low skewness.\n\n### Thalach Distribution\n\n**Histogram Analysis:**\n- The histogram for the \"thalach\" variable shows a distribution that is slightly skewed to the left.\n- The peak of the distribution is between 140 and 160, with a gradual decline as the values increase.\n\n**Skewness Analysis:**\n- The skewness coefficient for \"thalach\" is -0.461611, indicating a moderate negative skewness.\n- This negative skewness suggests that the data has a longer tail on the left side, meaning there are fewer instances of lower \"thalach\" values compared to higher ones.\n\n**Conclusion:**\n- The \"thalach\" variable has a moderate negative skewness. While it is not drastically skewed, the presence of the skewness might affect some machine learning algorithms that assume normality.\n- Depending on the specific requirements of the modeling phase, it might be beneficial to apply transformations to reduce skewness. Potential transformations include square root, cube root, or logarithmic transformations to make the distribution more symmetric.\n\n### General Recommendations:\n\n1. **For the Age Variable:**\n   - Given its near-normal distribution, it can be used directly in most models without transformation.\n\n2. **For the Thalach Variable:**\n   - Consider applying transformations to normalize the distribution if the skewness impacts model performance.\n   - Evaluate model performance both with and without transformation to decide the best approach.","metadata":{}},{"cell_type":"markdown","source":"### trtbps_winsorize Distribution\n\n**Histogram Analysis:**\n- The histogram for the \"trtbps_winsorize\" variable shows a right-skewed distribution.\n- The data is concentrated around the lower end, with a peak around 120-130, and gradually decreases as the values increase.\n\n**Skewness Analysis:**\n- The skewness coefficient for \"trtbps_winsorize\" is 0.448778, indicating a moderate positive skewness.\n- This positive skewness suggests that the distribution has a longer tail on the right side, meaning there are fewer instances of higher \"trtbps_winsorize\" values compared to lower ones.\n\n**Conclusion:**\n- The \"trtbps_winsorize\" variable has a moderate positive skewness. While it is not extremely skewed, the presence of skewness might still affect some machine learning algorithms that assume normality.\n- Potential transformations to reduce skewness could include square root, cube root, or logarithmic transformations.\n- Evaluating model performance both with and without transformation could help determine the best approach.\n\n### oldpeak_winsorize Distribution\n\n**Histogram Analysis:**\n- The histogram for the \"oldpeak_winsorize\" variable shows a heavily right-skewed distribution.\n- The data is heavily concentrated around the lower end, with a significant number of instances at 0.0, and the frequency rapidly decreases as the values increase.\n\n**Skewness Analysis:**\n- The skewness coefficient for \"oldpeak_winsorize\" is 1.190487, indicating a high positive skewness.\n- This high positive skewness suggests that the distribution has a long tail on the right side, meaning there are many more instances of lower \"oldpeak_winsorize\" values compared to higher ones.\n\n**Conclusion:**\n- The \"oldpeak_winsorize\" variable has a high positive skewness, which could significantly affect the performance of machine learning algorithms that assume normality.\n- Given the high skewness, applying transformations to normalize the distribution is strongly recommended. Common transformations include the logarithmic, square root, or cube root transformations.\n- It is important to evaluate model performance after applying these transformations to see if they improve results.\n\n### General Recommendations:\n\n1. **For the trtbps_winsorize Variable:**\n   - Consider applying transformations such as square root, cube root, or logarithmic to reduce skewness.\n   - Evaluate the impact of these transformations on model performance to decide on the best approach.\n\n2. **For the oldpeak_winsorize Variable:**\n   - Given its high skewness, applying transformations is strongly recommended.\n   - Logarithmic transformation might be particularly effective in normalizing the distribution.\n   - As always, assess the impact on model performance to determine the best approach.","metadata":{}},{"cell_type":"code","source":"import numpy as np\n\n# Apply log transformation to the 'thalach' variable\nheart_data_final['thalach_log'] = np.log(heart_data_final['thalach'])\n\n# Calculate skewness values for comparison\nthalach_skewness = heart_data_final['thalach'].skew()\nthalach_log_skewness = heart_data_final['thalach_log'].skew()\n\n# Print the skewness values\nprint(\"Skewness of 'thalach':\", thalach_skewness)\nprint(\"Skewness of 'thalach_log':\", thalach_log_skewness)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing NumPy**:\n   ```python\n   import numpy as np\n   ```\n   This imports the NumPy library, which is useful for performing numerical operations, including the log transformation.\n\n2. **Log Transformation**:\n   ```python\n   heart_data_final['thalach_log'] = np.log(heart_data_final['thalach'])\n   ```\n   - `np.log(heart_data_final['thalach'])`: This applies the natural logarithm transformation to the 'thalach' variable in the `heart_data_final` dataset. The log transformation can help reduce skewness by compressing the range of the variable.\n   - The transformed values are stored in a new column named 'thalach_log' within the `heart_data_final` dataset.\n\n3. **Calculating Skewness**:\n   ```python\n   thalach_skewness = heart_data_final['thalach'].skew()\n   thalach_log_skewness = heart_data_final['thalach_log'].skew()\n   ```\n   - `heart_data_final['thalach'].skew()`: This calculates the skewness of the original 'thalach' variable.\n   - `heart_data_final['thalach_log'].skew()`: This calculates the skewness of the log-transformed 'thalach_log' variable.\n   - Skewness is a measure of the asymmetry of the distribution of values. A skewness value closer to 0 indicates a more symmetrical distribution.\n\n4. **Printing Skewness Values**:\n   ```python\n   print(\"Skewness of 'thalach':\", thalach_skewness)\n   print(\"Skewness of 'thalach_log':\", thalach_log_skewness)\n   ```\n   - This prints the skewness values of both the original and log-transformed variables to allow for comparison. ","metadata":{}},{"cell_type":"code","source":"# Apply log transformation to the 'trtbps_winsorize' variable\nheart_data_final['trtbps_winsorize_log'] = np.log(heart_data_final['trtbps_winsorize'])\n\n# Calculate skewness values for comparison\ntrtbps_winsorize_skewness = heart_data_final['trtbps_winsorize'].skew()\ntrtbps_winsorize_log_skewness = heart_data_final['trtbps_winsorize_log'].skew()\n\n# Print the skewness values\nprint(\"Skewness of 'trtbps_winsorize':\", trtbps_winsorize_skewness)\nprint(\"Skewness of 'trtbps_winsorize_log':\", trtbps_winsorize_log_skewness)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Log Transformation**:\n   ```python\n   heart_data_final['trtbps_winsorize_log'] = np.log(heart_data_final['trtbps_winsorize'])\n   ```\n   - `np.log(heart_data_final['trtbps_winsorize'])`: This applies the natural logarithm transformation to the 'trtbps_winsorize' variable in the `heart_data_final` dataset. The transformed values are stored in a new column named 'trtbps_winsorize_log'.\n\n2. **Calculating Skewness**:\n   ```python\n   trtbps_winsorize_skewness = heart_data_final['trtbps_winsorize'].skew()\n   trtbps_winsorize_log_skewness = heart_data_final['trtbps_winsorize_log'].skew()\n   ```\n   - `heart_data_final['trtbps_winsorize'].skew()`: This calculates the skewness of the original 'trtbps_winsorize' variable.\n   - `heart_data_final['trtbps_winsorize_log'].skew()`: This calculates the skewness of the log-transformed 'trtbps_winsorize_log' variable.\n\n3. **Printing Skewness Values**:\n   ```python\n   print(\"Skewness of 'trtbps_winsorize':\", trtbps_winsorize_skewness)\n   print(\"Skewness of 'trtbps_winsorize_log':\", trtbps_winsorize_log_skewness)\n   ```\n   - This prints the skewness values of both the original and log-transformed variables to allow for comparison. ","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Set the style of the visualization\nsns.set(style=\"whitegrid\")\n\n# Create a histogram with a density plot for the 'trtbps_winsorize_log' variable\nplt.figure(figsize=(10, 6))\nsns.histplot(heart_data_final['trtbps_winsorize_log'], kde=True, bins=30)\nplt.title('Histogram of trtbps_winsorize_log')\nplt.xlabel('trtbps_winsorize_log')\nplt.ylabel('Frequency')\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   ```python\n   import matplotlib.pyplot as plt\n   import seaborn as sns\n   ```\n   - These lines import the necessary libraries for creating the visualization.\n\n2. **Setting the Style**:\n   ```python\n   sns.set(style=\"whitegrid\")\n   ```\n   - This sets the style of the visualization using Seaborn's `set` function. The `whitegrid` style adds grid lines to the background, making the plot easier to read.\n\n3. **Creating the Histogram**:\n   ```python\n   plt.figure(figsize=(10, 6))\n   sns.histplot(heart_data_final['trtbps_winsorize_log'], kde=True, bins=30)\n   plt.title('Histogram of trtbps_winsorize_log')\n   plt.xlabel('trtbps_winsorize_log')\n   plt.ylabel('Frequency')\n   plt.show()\n   ```\n   - `plt.figure(figsize=(10, 6))`: This creates a new figure with a specified size.\n   - `sns.histplot(heart_data_final['trtbps_winsorize_log'], kde=True, bins=30)`: This creates a histogram for the 'trtbps_winsorize_log' variable. The `kde=True` parameter adds a Kernel Density Estimate (KDE) plot, which provides a smoothed estimate of the distribution. The `bins=30` parameter specifies the number of bins in the histogram.\n   - `plt.title('Histogram of trtbps_winsorize_log')`: This sets the title of the plot.\n   - `plt.xlabel('trtbps_winsorize_log')`: This sets the label for the x-axis.\n   - `plt.ylabel('Frequency')`: This sets the label for the y-axis.\n   - `plt.show()`: This displays the plot. ","metadata":{}},{"cell_type":"code","source":"import numpy as np\nimport pandas as pd\n\n# Apply log transformation to the oldpeak_winsorize variable\nheart_data_final['oldpeak_winsorize_log'] = np.log1p(heart_data_final['oldpeak_winsorize'])\n\n# Apply square root transformation to the oldpeak_winsorize variable\nheart_data_final['oldpeak_winsorize_sqrt'] = np.sqrt(heart_data_final['oldpeak_winsorize'])\n\n# Calculate the skewness values of the original and transformed variables\nskewness_values = {\n    'oldpeak_winsorize': heart_data_final['oldpeak_winsorize'].skew(),\n    'oldpeak_winsorize_log': heart_data_final['oldpeak_winsorize_log'].skew(),\n    'oldpeak_winsorize_sqrt': heart_data_final['oldpeak_winsorize_sqrt'].skew()\n}\n\n# Convert skewness values to a DataFrame for better visualization\nskewness_df = pd.DataFrame(list(skewness_values.items()), columns=['Variable', 'Skewness'])\n\n# Display the skewness values\nskewness_df","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   ```python\n   import numpy as np\n   import pandas as pd\n   ```\n   - `numpy` is imported as `np` to handle numerical operations, and `pandas` is imported as `pd` to handle the data manipulation.\n\n2. **Log Transformation**:\n   ```python\n   heart_data_final['oldpeak_winsorize_log'] = np.log1p(heart_data_final['oldpeak_winsorize'])\n   ```\n   - The `np.log1p` function applies a log transformation to the `oldpeak_winsorize` variable. `log1p` is used instead of `log` to handle zero values (it computes `log(1 + x)`).\n\n3. **Square Root Transformation**:\n   ```python\n   heart_data_final['oldpeak_winsorize_sqrt'] = np.sqrt(heart_data_final['oldpeak_winsorize'])\n   ```\n   - The `np.sqrt` function applies a square root transformation to the `oldpeak_winsorize` variable.\n\n4. **Calculating Skewness**:\n   ```python\n   skewness_values = {\n       'oldpeak_winsorize': heart_data_final['oldpeak_winsorize'].skew(),\n       'oldpeak_winsorize_log': heart_data_final['oldpeak_winsorize_log'].skew(),\n       'oldpeak_winsorize_sqrt': heart_data_final['oldpeak_winsorize_sqrt'].skew()\n   }\n   ```\n   - This dictionary stores the skewness values of the original and transformed variables. The `skew()` function calculates the skewness of each variable.\n\n5. **Creating a DataFrame for Skewness Values**:\n   ```python\n   skewness_df = pd.DataFrame(list(skewness_values.items()), columns=['Variable', 'Skewness'])\n   ```\n   - This converts the skewness values into a DataFrame for better visualization.\n\n6. **Displaying the Skewness Values**:\n   ```python\n   print(skewness_df)\n   ```\n   - This prints the skewness values DataFrame.","metadata":{}},{"cell_type":"code","source":"import seaborn as sns\nimport matplotlib.pyplot as plt\n\n# Set the aesthetic style of the plots\nsns.set(style=\"whitegrid\")\n\n# Create a figure and axis\nplt.figure(figsize=(10, 6))\n\n# Plot the histogram and KDE for the oldpeak_winsorize_sqrt variable\nsns.histplot(heart_data_final['oldpeak_winsorize_sqrt'], kde=True, bins=30, color='blue')\n\n# Add titles and labels\nplt.title('Histogram of oldpeak_winsorize_sqrt')\nplt.xlabel('oldpeak_winsorize_sqrt')\nplt.ylabel('Frequency')\n\n# Show the plot\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   ```python\n   import seaborn as sns\n   import matplotlib.pyplot as plt\n   ```\n   - `seaborn` is imported as `sns` for advanced data visualization, and `matplotlib.pyplot` is imported as `plt` for creating the plot.\n\n2. **Setting the Aesthetic Style**:\n   ```python\n   sns.set(style=\"whitegrid\")\n   ```\n   - This sets the aesthetic style of the plots to \"whitegrid\" for better visual appeal.\n\n3. **Creating a Figure and Axis**:\n   ```python\n   plt.figure(figsize=(10, 6))\n   ```\n   - This creates a figure with a specified size (10 inches by 6 inches).\n\n4. **Plotting the Histogram and KDE**:\n   ```python\n   sns.histplot(heart_data_final['oldpeak_winsorize_sqrt'], kde=True, bins=30, color='blue')\n   ```\n   - This plots a histogram and KDE for the `oldpeak_winsorize_sqrt` variable. The `bins` parameter sets the number of bins to 30, and `color` sets the color of the histogram bars to blue.\n\n5. **Adding Titles and Labels**:\n   ```python\n   plt.title('Histogram of oldpeak_winsorize_sqrt')\n   plt.xlabel('oldpeak_winsorize_sqrt')\n   plt.ylabel('Frequency')\n   ```\n   - These lines add a title to the plot and labels to the x-axis and y-axis.\n\n6. **Showing the Plot**:\n   ```python\n   plt.show()\n   ```\n   - This displays the plot.","metadata":{}},{"cell_type":"code","source":"heart_data_final.head()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# List of variables to drop\nvariables_to_drop = [\"thalach_log\", \"trtbps_winsorize\", \"oldpeak_winsorize\", \"oldpeak_winsorize_log\"]\n\n# Drop the variables from the dataset\nheart_data_final.drop(columns=variables_to_drop, inplace=True)\n\n# Display the first few rows of the updated dataset to confirm the changes\nheart_data_final.head()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **List of Variables to Drop**:\n   ```python\n   variables_to_drop = [\"thalach_log\", \"trtbps_winsorize\", \"oldpeak_winsorize\", \"oldpeak_winsorize_log\"]\n   ```\n   - This line creates a list of the variable names that you want to drop from the dataset.\n\n2. **Dropping the Variables**:\n   ```python\n   heart_data_final.drop(columns=variables_to_drop, inplace=True)\n   ```\n   - The `drop` method is used to remove the specified columns from the `heart_data_final` DataFrame. The `columns` parameter takes the list of variable names to drop, and `inplace=True` ensures that the changes are made directly to the `heart_data_final` DataFrame without needing to reassign it.\n\n3. **Displaying the Updated Dataset**:\n   ```python\n   heart_data_final.head()\n   ```\n   - This line displays the first few rows of the updated dataset to confirm that the specified variables have been removed.","metadata":{}},{"cell_type":"markdown","source":"# Applying One Hot Encoding Method to Categorical Variables","metadata":{}},{"cell_type":"markdown","source":"One-hot encoding is a technique used in data preprocessing to convert categorical variables into a format that can be provided to machine learning algorithms to improve predictions. Here's a detailed explanation:\n\n### What is One-Hot Encoding?\n\nOne-hot encoding transforms categorical data, which are labels or names, into a binary format. This method creates new binary columns for each category in the original categorical column. Each binary column represents one of the categories, and a value of 1 or 0 indicates the presence or absence of the category for each observation.\n\n### Why Use One-Hot Encoding?\n\nMachine learning algorithms typically work with numerical data. Categorical data, such as \"red,\" \"blue,\" \"green,\" or \"cat,\" \"dog,\" \"mouse,\" need to be converted into a numerical format. One-hot encoding allows algorithms to interpret these categorical variables without assigning ordinal relationships where there are none (e.g., saying \"red\" is greater than \"blue\").\n\n### How One-Hot Encoding Works:\n\n1. **Identify Categorical Variables**: Determine which columns in your dataset are categorical.\n\n2. **Create Binary Columns**: For each unique category in a categorical variable, create a new binary column. \n\n3. **Assign Binary Values**: In each new binary column, assign a 1 to indicate the presence of the category and a 0 otherwise.\n\n### Example:\n\nConsider a simple dataset with a single categorical column \"Color\":\n\n| Index | Color  |\n|-------|--------|\n| 1     | Red    |\n| 2     | Blue   |\n| 3     | Green  |\n| 4     | Red    |\n\nAfter applying one-hot encoding, it becomes:\n\n| Index | Color_Red | Color_Blue | Color_Green |\n|-------|-----------|------------|-------------|\n| 1     | 1         | 0          | 0           |\n| 2     | 0         | 1          | 0           |\n| 3     | 0         | 0          | 1           |\n| 4     | 1         | 0          | 0           |\n\n### Benefits of One-Hot Encoding:\n\n- **No Ordinal Relationship Implied**: Unlike label encoding, where categories are assigned numerical values (e.g., 0, 1, 2), one-hot encoding does not imply any ordinal relationship among categories.\n- **Improved Model Performance**: Many machine learning algorithms, especially linear models, can perform better with one-hot encoded data because it prevents the algorithm from assuming any inherent order in the categories.\n\n### When to Use One-Hot Encoding:\n\n- **Categorical Variables**: Use one-hot encoding for nominal categorical variables where there is no intrinsic order.\n- **Small Number of Categories**: It's most effective when the number of unique categories is not excessively large. For high-cardinality features, other techniques like target encoding or embedding might be more appropriate.\n\n### Drawbacks:\n\n- **Increased Dimensionality**: One-hot encoding can significantly increase the dimensionality of the dataset, especially when there are many unique categories.\n- **Sparse Matrices**: The resulting matrix from one-hot encoding can be sparse (mostly zeros), which might require more memory and computation power.\n\n### Conclusion:\n\nOne-hot encoding is a crucial step in preparing categorical data for machine learning. It ensures that the algorithms interpret categorical variables correctly without introducing any unintended ordinal relationships. This preprocessing step helps improve the accuracy and performance of predictive models.","metadata":{}},{"cell_type":"code","source":"import pandas as pd\n\n# Identifying categorical variables\ncategorical_vars = ['sex', 'cp', 'exang', 'slope', 'ca', 'thal']\n\n# Applying one-hot encoding\nheart_data_encoded = pd.get_dummies(heart_data_final, columns=categorical_vars, drop_first=True)\n\n# Displaying the first few rows of the updated dataset to confirm the changes\nheart_data_encoded.head()","metadata":{"scrolled":true,"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   - The `pandas` library is imported to handle data manipulation and analysis.\n\n2. **Identifying Categorical Variables**:\n   - A list of categorical variables (`categorical_vars`) is created to specify which columns need to be one-hot encoded.\n\n3. **Applying One-Hot Encoding**:\n   - `pd.get_dummies()`: This function is used to convert the specified categorical variables into binary columns. Each unique value in the categorical variables is converted into a new column with binary values (0 or 1).\n   - `columns=categorical_vars`: This argument specifies which columns to transform.\n   - `drop_first=True`: This argument drops the first category to avoid multicollinearity, ensuring that the number of new columns is one less than the number of unique categories in the original column.\n\n4. **Displaying the Updated Dataset**:\n   - `heart_data_encoded.head()`: This line prints the first few rows of the transformed dataset to verify that the one-hot encoding has been applied correctly.","metadata":{}},{"cell_type":"markdown","source":"# Feature Scaling with the RobustScaler Method for Machine Learning Algorithms","metadata":{}},{"cell_type":"code","source":"import pandas as pd\nfrom sklearn.preprocessing import RobustScaler\n\n# Identifying numeric variables\nnumeric_vars = [\"age\", \"thalach\", \"trtbps_winsorize_log\", \"oldpeak_winsorize_sqrt\"]\n\n# Initializing the RobustScaler\nscaler = RobustScaler()\n\n# Applying Robust Scaling\nheart_data_encoded[numeric_vars] = scaler.fit_transform(heart_data_encoded[numeric_vars])\n\n# Displaying the first few rows of the updated dataset to confirm the changes\nheart_data_encoded.head()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   - `pandas` is imported for data manipulation.\n   - `RobustScaler` from `sklearn.preprocessing` is imported for scaling the numeric variables.\n\n2. **Identifying Numeric Variables**:\n   - A list of numeric variables (`numeric_vars`) is created to specify which columns need to be scaled.\n\n3. **Initializing the RobustScaler**:\n   - The `RobustScaler` is initialized. This scaler removes the median and scales the data according to the interquartile range (IQR). It is less sensitive to outliers compared to standard scaling methods.\n\n4. **Applying Robust Scaling**:\n   - `fit_transform` method is used to fit the scaler to the data and then transform it. This method is applied to the numeric variables in the dataset, scaling them accordingly.\n\n5. **Displaying the Updated Dataset**:\n   - `heart_data_encoded.head()`: This line prints the first few rows of the transformed dataset to verify that the scaling has been applied correctly.","metadata":{}},{"cell_type":"markdown","source":"# Separating Data into Test and Training Set","metadata":{}},{"cell_type":"code","source":"import pandas as pd\nfrom sklearn.model_selection import train_test_split\n\n# Defining features and target\nX = heart_data_encoded.drop(columns=['target'])\ny = heart_data_encoded['target']\n\n# Applying train-test split\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1, random_state=3)\n\n# Displaying shape information\nprint(\"Shape of X_train:\", X_train.shape)\nprint(\"Shape of X_test:\", X_test.shape)\nprint(\"Shape of y_train:\", y_train.shape)\nprint(\"Shape of y_test:\", y_test.shape)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   - `pandas` is imported for data manipulation.\n   - `train_test_split` from `sklearn.model_selection` is imported for splitting the dataset.\n\n2. **Defining Features and Target**:\n   - `X = heart_data_encoded.drop(columns=['target'])`: This line removes the target column from the dataset, keeping only the features in `X`.\n   - `y = heart_data_encoded['target']`: This line stores the target variable in `y`.\n\n3. **Applying Train-Test Split**:\n   - `train_test_split(X, y, test_size=0.1, random_state=3)`: This function splits the dataset into training and testing sets. `test_size=0.1` specifies that 10% of the data should be used for testing, and `random_state=3` ensures the split is reproducible.\n\n4. **Displaying Shape Information**:\n   - `print(\"Shape of X_train:\", X_train.shape)`: This prints the shape of the training set features.\n   - `print(\"Shape of X_test:\", X_test.shape)`: This prints the shape of the testing set features.\n   - `print(\"Shape of y_train:\", y_train.shape)`: This prints the shape of the training set target.\n   - `print(\"Shape of y_test:\", y_test.shape)`: This prints the shape of the testing set target.\n","metadata":{}},{"cell_type":"markdown","source":"# Modelling","metadata":{}},{"cell_type":"markdown","source":"### What is Logistic Regression?\n\nLogistic Regression is a statistical method used for binary classification problems. This means it is used to predict the outcome of a categorical dependent variable that can take one of two possible values. Despite its name, logistic regression is a classification algorithm rather than a regression algorithm.\n\n### Key Concepts of Logistic Regression:\n\n1. **Binary Classification**:\n   - Logistic Regression is primarily used for binary classification tasks, where the target variable has two possible outcomes, such as \"yes\" or \"no\", \"spam\" or \"not spam\", \"disease\" or \"no disease\".\n\n2. **Probability Estimation**:\n   - Logistic Regression estimates the probability that a given input point belongs to a particular class. For example, it can estimate the probability that a patient has a disease given their medical records.\n\n3. **Logistic Function**:\n   - The logistic function (also known as the sigmoid function) is used to map predicted values to probabilities. This function takes any real-valued number and maps it to a value between 0 and 1, making it suitable for probability estimation.\n\n### How Logistic Regression Works:\n\n1. **Linear Relationship**:\n   - Logistic Regression starts with a linear relationship between the independent variables (features) and the dependent variable (target). However, instead of predicting the actual output value directly, it predicts the probability of the outcome being one of the two classes.\n\n2. **Sigmoid Function**:\n   - The output of the linear equation is then passed through the sigmoid function, which converts it into a probability. The sigmoid function ensures that the output is between 0 and 1, which is interpreted as a probability.\n\n3. **Decision Boundary**:\n   - Logistic Regression uses a threshold value (usually 0.5) to decide the class of the output. If the predicted probability is greater than or equal to 0.5, the output is classified as one class (e.g., \"1\" or \"yes\"). If it is less than 0.5, it is classified as the other class (e.g., \"0\" or \"no\").\n\n### Advantages of Logistic Regression:\n\n1. **Simplicity and Interpretability**:\n   - Logistic Regression is easy to implement and understand. The model coefficients can be interpreted to understand the impact of each feature on the prediction.\n\n2. **Efficiency**:\n   - Logistic Regression is computationally efficient and works well with small to medium-sized datasets.\n\n3. **Probabilistic Output**:\n   - The model provides probabilistic predictions, which can be useful for understanding the uncertainty of the predictions.\n\n4. **Feature Importance**:\n   - The magnitude of the coefficients gives an indication of the importance of each feature.\n\n### Disadvantages of Logistic Regression:\n\n1. **Linear Decision Boundary**:\n   - Logistic Regression assumes a linear relationship between the features and the log-odds of the target. It may not perform well if the actual relationship is highly non-linear.\n\n2. **Binary Output**:\n   - Logistic Regression is primarily used for binary classification. For multi-class classification, extensions like multinomial logistic regression are required.\n\n3. **Sensitivity to Outliers**:\n   - The model can be sensitive to outliers, which can affect the prediction performance.\n\n### Applications of Logistic Regression:\n\n1. **Medical Diagnosis**:\n   - Predicting whether a patient has a disease or not based on medical records.\n\n2. **Spam Detection**:\n   - Classifying emails as spam or not spam.\n\n3. **Credit Scoring**:\n   - Determining whether a loan applicant is likely to default or not.\n\n4. **Marketing**:\n   - Predicting whether a customer will buy a product or not based on their behavior.\n\n### Summary:\n\nLogistic Regression is a fundamental algorithm for binary classification tasks. It is simple, interpretable, and provides probabilistic outputs, making it a popular choice for many real-world applications. However, it has limitations, particularly in capturing non-linear relationships, which should be considered when choosing a model for a specific problem.","metadata":{}},{"cell_type":"code","source":"from sklearn.linear_model import LogisticRegression\nfrom sklearn.metrics import accuracy_score\n\n# Creating the Logistic Regression model\nmodel = LogisticRegression(random_state=3)\n\n# Fitting the model on the training data\nmodel.fit(X_train, y_train)\n\n# Making predictions on the test data\ny_pred = model.predict(X_test)\n\n# Calculating the accuracy\naccuracy = accuracy_score(y_test, y_pred)\nprint(\"Accuracy of the Logistic Regression model:\", accuracy)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   - `LogisticRegression` from `sklearn.linear_model` is imported to create the logistic regression model.\n   - `accuracy_score` from `sklearn.metrics` is imported to evaluate the accuracy of the model.\n\n2. **Creating the Logistic Regression Model**:\n   - `model = LogisticRegression(random_state=3)`: This initializes the logistic regression model with a random state for reproducibility. The `random_state` parameter ensures that the results can be replicated.\n\n3. **Fitting the Model on the Training Data**:\n   - `model.fit(X_train, y_train)`: This trains the logistic regression model using the training data (`X_train` and `y_train`). The `fit` method is used to fit the model to the data.\n\n4. **Making Predictions on the Test Data**:\n   - `y_pred = model.predict(X_test)`: This uses the trained model to make predictions on the test data (`X_test`). The `predict` method is used to generate the predicted values.\n\n5. **Calculating the Accuracy**:\n   - `accuracy = accuracy_score(y_test, y_pred)`: This calculates the accuracy of the model by comparing the predicted values (`y_pred`) with the actual values (`y_test`) in the test set. The `accuracy_score` function computes the accuracy as the proportion of correct predictions.\n   - `print(\"Accuracy of the Logistic Regression model:\", accuracy)`: This prints the accuracy of the logistic regression model.","metadata":{}},{"cell_type":"markdown","source":"Improving the accuracy and reliability of a machine learning model involves various techniques and approaches. Here are several methods you can use to enhance your logistic regression model or any other machine learning model:\n\n### 1. **Feature Engineering**\n\n- **Feature Selection**: Identify and select the most relevant features for your model. Irrelevant or redundant features can negatively impact the model's performance. Techniques like recursive feature elimination, feature importance from models, or statistical tests can help with feature selection.\n- **Feature Creation**: Create new features that might capture additional information from the data. For example, combining existing features, creating interaction terms, or generating polynomial features can sometimes improve model performance.\n- **Handling Missing Values**: Properly handle missing data by imputing with mean, median, mode, or using advanced imputation techniques.\n\n### 2. **Data Preprocessing**\n\n- **Scaling and Normalization**: Ensure that all features are on a similar scale. This can help algorithms like logistic regression to converge faster and perform better.\n- **Handling Outliers**: Detect and handle outliers in your dataset as they can skew the model. Techniques like clipping, transformation, or removing outliers can be used.\n\n### 3. **Algorithm Tuning**\n\n- **Hyperparameter Tuning**: Adjust the hyperparameters of your model to find the optimal set of parameters. Techniques like grid search, random search, or Bayesian optimization can be used to systematically search for the best hyperparameters.\n- **Regularization**: Apply regularization techniques like L1 (Lasso) or L2 (Ridge) regularization to prevent overfitting by adding a penalty for larger coefficients.\n\n### 4. **Model Validation**\n\n- **Cross-Validation**: Use cross-validation techniques to ensure that your model is not overfitting. K-fold cross-validation, stratified K-fold, or leave-one-out cross-validation can help in assessing the model's performance more robustly.\n- **Validation Set**: Keep a separate validation set to evaluate your model before testing it on the final test set. This helps in tuning the model without overfitting to the test data.\n\n### 5. **Ensemble Methods**\n\n- **Bagging**: Use techniques like Bagging (Bootstrap Aggregating) to reduce variance and improve accuracy. Random Forest is a popular bagging method.\n- **Boosting**: Apply boosting techniques like AdaBoost, Gradient Boosting, or XGBoost to improve model accuracy by focusing on the errors of previous models.\n- **Stacking**: Combine multiple models to form a single stronger predictive model. Stacking involves training a meta-model on the predictions of base models.\n\n### 6. **Data Augmentation and Resampling**\n\n- **Data Augmentation**: For datasets with limited data, create additional training examples by augmenting the data. This is common in image processing but can be applied to other types of data as well.\n- **Resampling Techniques**: Use techniques like SMOTE (Synthetic Minority Over-sampling Technique) or undersampling to address class imbalance issues in your dataset.\n\n### 7. **Advanced Algorithms**\n\n- **Try Different Algorithms**: Experiment with different machine learning algorithms like Decision Trees, Random Forests, Gradient Boosting, Support Vector Machines, Neural Networks, etc. Sometimes a different algorithm might perform better on your data.\n- **Deep Learning**: For complex problems, deep learning models like Convolutional Neural Networks (CNNs) or Recurrent Neural Networks (RNNs) might provide better performance.\n\n### 8. **Model Interpretability and Explainability**\n\n- **Model Interpretation**: Use tools and techniques to understand and interpret your model. Understanding which features contribute the most to the predictions can help in refining the model further.\n- **Explainability Techniques**: Use techniques like SHAP (SHapley Additive exPlanations) or LIME (Local Interpretable Model-agnostic Explanations) to explain the predictions of your model.\n\n### 9. **Domain Knowledge and Expertise**\n\n- **Leverage Domain Knowledge**: Incorporate domain knowledge to create better features and improve model performance. Understanding the context and intricacies of the data can lead to better modeling decisions.\n- **Expert Consultation**: Consult with domain experts to gain insights that might not be apparent from the data alone.\n\n### 10. **Continuous Monitoring and Maintenance**\n\n- **Model Monitoring**: Continuously monitor the performance of your model in a production environment. Models can degrade over time due to changes in data distribution or other factors.\n- **Retraining**: Periodically retrain your model with new data to ensure it remains accurate and relevant.\n\nBy systematically applying these methods, you can improve the accuracy and reliability of your machine learning models. Each method has its own set of advantages and is suitable for different scenarios, so it's essential to experiment and find the best combination for your specific problem.","metadata":{}},{"cell_type":"markdown","source":"# Cross Validation","metadata":{}},{"cell_type":"markdown","source":"### What is Cross-Validation?\n\nCross-validation is a resampling procedure used to evaluate machine learning models on a limited data sample. The goal of cross-validation is to assess how the results of a statistical analysis will generalize to an independent dataset. It is particularly useful when the dataset is not large enough to be split into separate training and testing datasets.\n\n### Why Use Cross-Validation?\n\n- **Prevent Overfitting**: Cross-validation helps in detecting and preventing overfitting, ensuring that the model performs well on unseen data.\n- **Model Selection**: It aids in selecting the best model and tuning hyperparameters by providing a more accurate estimate of model performance.\n- **Performance Evaluation**: Provides a better understanding of how the model will perform in practice by using all the data for both training and validation.\n\n### Common Types of Cross-Validation:\n\n#### 1. **K-Fold Cross-Validation**\n\nK-Fold Cross-Validation is the most commonly used method. The original dataset is randomly partitioned into K equal-sized folds. The model is trained and validated K times, each time using a different fold as the validation set and the remaining K-1 folds as the training set.\n\n**Example with K=5**:\n1. Split the data into 5 folds.\n2. For each fold:\n   - Use the fold as the validation set.\n   - Use the remaining 4 folds as the training set.\n   - Train the model and calculate the validation error.\n3. Average the validation errors from all 5 folds to get the overall performance estimate.\n\n#### 2. **Stratified K-Fold Cross-Validation**\n\nSimilar to K-Fold Cross-Validation, but it ensures that each fold has approximately the same percentage of samples of each target class as the original dataset. This is especially useful for imbalanced datasets.\n\n#### 3. **Leave-One-Out Cross-Validation (LOOCV)**\n\nIn LOOCV, each training set consists of all the data points except one, and the model is trained and tested N times (where N is the number of data points). Each time, a different data point is used as the validation set.\n\n**Example with N=5**:\n1. Train the model using N-1 data points and validate on the remaining one.\n2. Repeat this process for all data points.\n3. Average the validation errors to get the overall performance estimate.\n\n#### 4. **Leave-P-Out Cross-Validation**\n\nThis method involves leaving P data points out for validation and training the model on the remaining data points. This process is repeated for all possible combinations of P data points.\n\n### Example of K-Fold Cross-Validation:\n\nLet's consider an example using K-Fold Cross-Validation with K=5 on a dataset.\n\n1. **Dataset**:\n   - Suppose we have a dataset with 100 samples.\n\n2. **Splitting the Data**:\n   - Split the dataset into 5 folds, each containing 20 samples.\n\n3. **Training and Validation**:\n   - For the first fold:\n     - Use the first 20 samples as the validation set.\n     - Use the remaining 80 samples as the training set.\n     - Train the model and calculate the validation error.\n   - Repeat the process for the remaining folds.\n\n4. **Calculating Performance**:\n   - After training and validating on all 5 folds, average the validation errors to get the final performance estimate.\n\n\n### Advantages of Cross-Validation:\n\n- **Efficient Use of Data**: All data points are used for both training and validation, maximizing the amount of data used for model training.\n- **Reliable Performance Estimates**: Provides a more accurate estimate of model performance compared to a single train-test split.\n\n### Disadvantages of Cross-Validation:\n\n- **Computationally Intensive**: Especially for large datasets, cross-validation can be computationally expensive as the model is trained multiple times.\n- **Complexity**: Implementing cross-validation can add complexity to the model evaluation process.\n\n### Conclusion:\n\nCross-validation is a powerful technique for assessing the performance and robustness of a machine learning model. It helps in selecting the best model, tuning hyperparameters, and preventing overfitting, making it an essential tool in the model validation process.","metadata":{}},{"cell_type":"code","source":"from sklearn.model_selection import cross_val_score\nfrom sklearn.linear_model import LogisticRegression\n\n# Assuming X and y are your feature matrix and target vector, respectively\n\n# Initialize the logistic regression model\nmodel = LogisticRegression(random_state=3)\n\n# Perform 5-fold cross-validation\ncv_scores = cross_val_score(model, X, y, cv=10)\n\n# Print the cross-validation scores\nprint(\"Cross-validation scores:\", cv_scores)\nprint(\"Average cross-validation score:\", cv_scores.mean())","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Import Libraries**:\n   - `cross_val_score` from `sklearn.model_selection` to perform cross-validation.\n   - `LogisticRegression` from `sklearn.linear_model` to create the logistic regression model.\n\n2. **Initialize the Model**:\n   - `model = LogisticRegression(random_state=3)`: Initializes the logistic regression model with a random state for reproducibility.\n\n3. **Perform Cross-Validation**:\n   - `cv_scores = cross_val_score(model, X, y, cv=10)`: Performs 5-fold cross-validation on the dataset (`X` and `y`). The `cv` parameter specifies the number of folds.\n\n4. **Print Scores**:\n   - `print(\"Cross-validation scores:\", cv_scores)`: Prints the validation scores for each fold.\n   - `print(\"Average cross-validation score:\", cv_scores.mean())`: Calculates and prints the average validation score across all folds.","metadata":{}},{"cell_type":"markdown","source":"# ROC Curve and AUC: Detailed Explanation\n\n#### What is an ROC Curve?\n\n**ROC** stands for **Receiver Operating Characteristic** curve. It is a graphical representation used to assess the performance of a classification model at various threshold settings.\n\n#### Key Concepts:\n\n1. **True Positive Rate (TPR)**: Also known as Sensitivity or Recall, it measures the proportion of actual positives that are correctly identified by the model. \n   - TPR = True Positives / (True Positives + False Negatives)\n\n2. **False Positive Rate (FPR)**: It measures the proportion of actual negatives that are incorrectly identified as positives by the model.\n   - FPR = False Positives / (False Positives + True Negatives)\n\n3. **Threshold**: In classification, the decision threshold determines the point at which a prediction switches from one class to another (e.g., from \"negative\" to \"positive\").\n\n#### ROC Curve:\n\n- The ROC curve plots the TPR against the FPR at various threshold settings.\n- Each point on the ROC curve represents a different threshold value.\n- The curve starts at (0,0) and ends at (1,1).\n\n#### Interpreting the ROC Curve:\n\n- **Closer to the Top Left Corner**: Indicates a better performance, where TPR is high, and FPR is low.\n- **Diagonal Line (45-degree line)**: Represents random guessing. The closer the ROC curve is to the top left corner, the better the model.\n\n### Area Under Curve (AUC):\n\n**AUC** stands for **Area Under the ROC Curve**. It provides an aggregate measure of performance across all possible classification thresholds.\n\n#### Key Points:\n\n- **AUC = 1**: Perfect model. The model correctly classifies all positives and negatives.\n- **AUC = 0.5**: No discrimination ability, equivalent to random guessing.\n- **0.5 < AUC < 1**: Indicates that the model is better than random guessing.\n- **AUC < 0.5**: Indicates that the model is worse than random guessing (rare in practice).\n\n### Visual Example:\n\nImagine you have a binary classification problem where you want to predict whether patients have a certain disease (positive class) or not (negative class). \n\n#### Example ROC Curve:\n\n1. **Creating the Curve**:\n   - **Threshold = 0.1**: At this threshold, the model predicts almost everything as positive, resulting in a high TPR but also a high FPR.\n   - **Threshold = 0.5**: This is typically the default threshold. The balance between TPR and FPR is moderate.\n   - **Threshold = 0.9**: At this threshold, the model is very conservative, predicting positive only when it is very certain, resulting in a low FPR but also a low TPR.\n\n2. **Plotting the Points**:\n   - Each threshold setting gives a pair of (FPR, TPR) which can be plotted on the ROC space.\n   - Connecting these points gives the ROC curve.\n\n3. **Interpreting the Curve**:\n   - If the curve bows towards the top left corner, it indicates a good model performance.\n   - The area under this curve (AUC) quantifies the overall ability of the model to discriminate between positive and negative classes.\n\n### Summary:\n\n- **ROC Curve**: Helps visualize the trade-off between the true positive rate and the false positive rate across different thresholds.\n- **AUC**: Provides a single metric to compare different models by quantifying the overall performance across all thresholds.\n\nBy understanding ROC and AUC, you can better evaluate the performance of your classification models, ensuring that you choose models that provide the best balance between sensitivity and specificity.","metadata":{}},{"cell_type":"code","source":"from sklearn.metrics import roc_curve, roc_auc_score\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Creating the Logistic Regression model\nmodel = LogisticRegression(random_state=3)\n\n# Fitting the model on the training data\nmodel.fit(X_train, y_train)\n\n# Predicting probabilities\ny_prob = model.predict_proba(X_test)[:, 1]\n\n# Calculating ROC Curve\nfpr, tpr, thresholds = roc_curve(y_test, y_prob)\n\n# Calculating AUC\nauc = roc_auc_score(y_test, y_prob)\nprint(\"AUC value:\", auc)\n\n# Creating the ROC Curve Plot\nplt.figure(figsize=(10, 6))\nsns.set(style=\"whitegrid\")\nplt.plot(fpr, tpr, color='blue', lw=2, label='ROC curve (area = %0.2f)' % auc)\nplt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\nplt.xlim([0.0, 1.0])\nplt.ylim([0.0, 1.05])\nplt.xlabel('False Positive Rate')\nplt.ylabel('True Positive Rate')\nplt.title('Receiver Operating Characteristic (ROC) Curve')\nplt.legend(loc=\"lower right\")\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Importing Libraries**:\n   - `roc_curve` and `roc_auc_score` from `sklearn.metrics` are imported to calculate the ROC curve and AUC value.\n   - `matplotlib.pyplot` is imported as `plt` and `seaborn` as `sns` for creating the visual graph.\n\n2. **Predicting Probabilities**:\n   - `y_prob = model.predict_proba(X_test)[:, 1]`: This line gets the predicted probabilities for the positive class (class 1) from the logistic regression model. The `predict_proba` method returns the probability estimates for all classes, and `[:, 1]` extracts the probabilities for class 1.\n\n3. **Calculating ROC Curve**:\n   - `fpr, tpr, thresholds = roc_curve(y_test, y_prob)`: This function computes the false positive rates (FPR), true positive rates (TPR), and threshold values for the ROC curve.\n\n4. **Calculating AUC**:\n   - `auc = roc_auc_score(y_test, y_prob)`: This function calculates the AUC value based on the true labels (`y_test`) and predicted probabilities (`y_prob`).\n   - `print(\"AUC value:\", auc)`: This line prints the AUC value.\n\n5. **Creating the ROC Curve Plot**:\n   - `plt.figure(figsize=(10, 6))`: This creates a new figure with a specified size.\n   - `sns.set(style=\"whitegrid\")`: This sets the aesthetic style of the plot to \"whitegrid\" using Seaborn.\n   - `plt.plot(fpr, tpr, color='blue', lw=2, label='ROC curve (area = %0.2f)' % auc)`: This plots the ROC curve with the AUC value included in the legend.\n   - `plt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')`: This plots the diagonal line representing random guessing.\n   - `plt.xlim([0.0, 1.0])`: This sets the x-axis limits.\n   - `plt.ylim([0.0, 1.05])`: This sets the y-axis limits.\n   - `plt.xlabel('False Positive Rate')`: This sets the x-axis label.\n   - `plt.ylabel('True Positive Rate')`: This sets the y-axis label.\n   - `plt.title('Receiver Operating Characteristic (ROC) Curve')`: This sets the title of the plot.\n   - `plt.legend(loc=\"lower right\")`: This places the legend in the lower right corner of the plot.\n   - `plt.show()`: This displays the plot.\n\nBy running this code, you will be able to calculate the ROC curve and AUC values for your logistic regression model and visualize the ROC curve.","metadata":{}},{"cell_type":"markdown","source":"### Analysis of the ROC Curve and AUC:\n\n1. **ROC Curve**:\n   - **True Positive Rate (TPR)**: Also known as sensitivity or recall, it represents the proportion of actual positives correctly identified by the model. The y-axis of the ROC curve shows the TPR.\n   - **False Positive Rate (FPR)**: This represents the proportion of actual negatives incorrectly identified as positives. The x-axis of the ROC curve shows the FPR.\n   - The ROC curve plots TPR against FPR at various threshold settings.\n\n2. **Interpretation of the ROC Curve**:\n   - **Diagonal Line**: The diagonal dashed line in the plot represents a random classifier that makes random guesses. This line has an AUC value of 0.5, meaning the model's predictions are no better than random chance.\n   - **ROC Curve Position**: The ROC curve of your model (blue line) is well above the diagonal line. This indicates that the logistic regression model performs significantly better than random guessing.\n   - **Shape of the ROC Curve**: The closer the ROC curve is to the top left corner, the better the model's performance. A perfect model would pass through the top left corner, indicating a TPR of 1 and an FPR of 0 for some threshold.\n\n3. **AUC (Area Under the Curve)**:\n   - **AUC Value**: The AUC value is 0.89, as shown in the legend of the plot.\n   - **Interpretation of AUC**: The AUC value ranges from 0 to 1. An AUC of 0.5 indicates a model with no discrimination capability (equivalent to random guessing), whereas an AUC of 1.0 indicates a perfect model.\n     - **AUC = 0.89**: This value indicates that the model has a good ability to discriminate between the positive and negative classes. It suggests that there is an 89% chance that the model will correctly distinguish between a randomly chosen positive instance and a randomly chosen negative instance.\n\n4. **Thresholds**:\n   - The ROC curve is generated by varying the threshold for classification from 0 to 1. Different points on the ROC curve correspond to different threshold values.\n   - By adjusting the threshold, you can control the trade-off between TPR and FPR. Lowering the threshold increases TPR but also increases FPR, and vice versa.\n\n### Summary:\n- The ROC curve is a graphical representation that shows the trade-off between sensitivity (true positive rate) and specificity (false positive rate) for different threshold values.\n- The AUC value of 0.89 indicates that the logistic regression model is performing well, with a high capability of distinguishing between the positive and negative classes.\n- The curve's position above the diagonal line and closer to the top left corner signifies that the model has a strong predictive performance.","metadata":{}},{"cell_type":"markdown","source":"# Hyperparameter Optimization(with GridSearchCV)","metadata":{}},{"cell_type":"markdown","source":"### Hyperparameter Tuning\n\n**Definition:**\nHyperparameter tuning involves selecting the optimal set of hyperparameters for a machine learning model. Hyperparameters are configuration settings used to adjust the model's learning process, which cannot be learned directly from the training data. They differ from model parameters, which are learned during training.\n\n**Importance:**\nChoosing the right hyperparameters can significantly improve the model's performance, making it more accurate and efficient.\n\n### Types of Hyperparameter Tuning\n\n1. **Manual Search:**\n   - This method involves manually trying different combinations of hyperparameters to see which one performs best.\n   - It is time-consuming and often not feasible for complex models with many hyperparameters.\n\n2. **Grid Search:**\n   - In Grid Search, you specify a set of hyperparameters and their possible values. The algorithm exhaustively tries all possible combinations of these hyperparameters.\n   - It ensures that you explore the entire search space, but it can be computationally expensive.\n\n3. **Random Search:**\n   - Instead of trying every possible combination, Random Search randomly selects a subset of hyperparameter combinations to evaluate.\n   - It is less computationally intensive than Grid Search and can sometimes find good hyperparameters faster.\n\n4. **Bayesian Optimization:**\n   - This method builds a probabilistic model of the objective function and uses it to select the most promising hyperparameters to evaluate.\n   - It aims to find the best hyperparameters with fewer evaluations, making it more efficient than Grid Search and Random Search.\n\n5. **Genetic Algorithms:**\n   - Genetic algorithms use concepts from natural selection to evolve hyperparameters over generations.\n   - They are useful for exploring large search spaces and finding near-optimal solutions.\n\n### GridSearchCV\n\n**Definition:**\nGridSearchCV is a method provided by the `scikit-learn` library in Python for hyperparameter tuning. It automates the process of trying out different combinations of hyperparameters using cross-validation to evaluate their performance.\n\n**Key Concepts:**\n\n1. **Grid:**\n   - You define a grid of hyperparameters with specified values to explore.\n   - For example, for a logistic regression model, you might want to tune the regularization parameter `C` and the type of penalty (`l1` or `l2`).\n\n2. **Cross-Validation:**\n   - The `CV` in GridSearchCV stands for cross-validation. Cross-validation is a technique to evaluate model performance by splitting the dataset into multiple folds.\n   - Each fold is used once as a validation set while the rest are used for training. This process ensures that the model's performance is not dependent on a particular train-test split.\n\n3. **Workflow:**\n   - **Define the parameter grid:** Specify the hyperparameters and their possible values.\n   - **Create the GridSearchCV object:** Pass the model, parameter grid, and cross-validation settings.\n   - **Fit the model:** GridSearchCV fits the model on the training data and evaluates each combination of hyperparameters using cross-validation.\n   - **Select the best model:** After evaluating all combinations, GridSearchCV returns the model with the best hyperparameter combination based on the cross-validation performance.\n\n**Example Scenario:**\nImagine you are tuning a logistic regression model and want to find the best `C` value and penalty type.\n\n1. **Define Parameter Grid:**\n   - `C`: [0.01, 0.1, 1, 10, 100]\n   - `penalty`: ['l1', 'l2']\n\n2. **Create GridSearchCV Object:**\n   - `GridSearchCV(model, param_grid, cv=5)`, where `cv=5` specifies 5-fold cross-validation.\n\n3. **Fit the Model:**\n   - The algorithm will train the logistic regression model on different combinations of `C` and `penalty`, evaluating each with 5-fold cross-validation.\n\n4. **Select Best Model:**\n   - After evaluating all combinations, GridSearchCV will select the model with the best performance.\n\n### Benefits of GridSearchCV\n\n1. **Automates Hyperparameter Tuning:**\n   - It simplifies the process of finding the best hyperparameters, saving time and effort.\n\n2. **Systematic Search:**\n   - Ensures that all combinations of specified hyperparameters are explored, increasing the likelihood of finding the optimal set.\n\n3. **Cross-Validation:**\n   - Provides a robust estimate of model performance, reducing the risk of overfitting.\n\n### Summary\n\nHyperparameter tuning is crucial for optimizing machine learning models. GridSearchCV is a systematic method that automates this process using cross-validation, ensuring a comprehensive search for the best hyperparameters. By understanding and applying these concepts, you can significantly improve your model's accuracy and reliability.","metadata":{}},{"cell_type":"markdown","source":"### Parameters for Logistic Regression\n\n1. **C (Inverse of regularization strength)**\n   - This parameter controls the regularization strength. Smaller values specify stronger regularization.\n   - Possible values: `[0.01, 0.1, 1, 10, 100]`\n\n2. **penalty**\n   - This parameter specifies the norm used in the penalization.\n   - Possible values: `['l1', 'l2', 'elasticnet', 'none']`\n   - Note: 'l1' and 'elasticnet' are only supported by the 'saga' solver.\n\n3. **solver**\n   - This parameter defines the algorithm to use in the optimization problem.\n   - Possible values: `['newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga']`\n   - Note: Some solvers support only certain types of penalties.\n\n4. **max_iter**\n   - This parameter defines the maximum number of iterations taken for the solvers to converge.\n   - Possible values: `[100, 200, 300, 400, 500]`","metadata":{}},{"cell_type":"code","source":"from sklearn.linear_model import LogisticRegression\nfrom sklearn.model_selection import GridSearchCV\n\n# Define the parameter grid\nparam_grid = {\n    'penalty': ['l1', 'l2'],\n    'solver': ['newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga']\n}\n\n# Create the Logistic Regression model\nlogreg = LogisticRegression()\n\n# Create the GridSearchCV object\ngrid_search = GridSearchCV(estimator=logreg, param_grid=param_grid, cv=5, scoring='accuracy')\n\n# Fit the model to the data\ngrid_search.fit(X_train, y_train)\n\n# Print the best parameters and best score\nprint(\"Best Parameters:\", grid_search.best_params_)\nprint(\"Best Score:\", grid_search.best_score_)\n\n# Use the best model to make predictions on the test set\nbest_model = grid_search.best_estimator_\ny_pred = best_model.predict(X_test)\n\n# Evaluate the best model\nfrom sklearn.metrics import accuracy_score\naccuracy = accuracy_score(y_test, y_pred)\nprint(\"Test Set Accuracy:\", accuracy)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation of the Code\n\n1. **Parameter Grid (`param_grid`):**\n   - Defines the hyperparameters to tune and their possible values.\n\n2. **Create Logistic Regression Model (`logreg`):**\n   - Initializes the logistic regression model.\n\n3. **Create GridSearchCV Object (`grid_search`):**\n   - Passes the logistic regression model, parameter grid, and cross-validation settings to GridSearchCV.\n   - `cv=5` specifies 5-fold cross-validation.\n   - `scoring='accuracy'` specifies that we want to optimize for accuracy.\n\n4. **Fit the Model (`grid_search.fit`):**\n   - Trains the logistic regression model on the training data using all combinations of the hyperparameters specified in the parameter grid.\n\n5. **Print Best Parameters and Score:**\n   - Prints the best hyperparameters found during the search and the corresponding best cross-validation score.\n\n6. **Use Best Model for Predictions:**\n   - Uses the best model found to make predictions on the test set.\n\n7. **Evaluate Best Model:**\n   - Computes and prints the accuracy of the best model on the test set.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nfrom sklearn.metrics import roc_curve, roc_auc_score\n\n# Predict probabilities\ny_pred_proba = best_model.predict_proba(X_test)[:, 1]\n\n# Compute ROC curve and AUC\nfpr, tpr, _ = roc_curve(y_test, y_pred_proba)\nroc_auc = roc_auc_score(y_test, y_pred_proba)\n\n# Plot ROC curve\nplt.figure()\nplt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {roc_auc:.2f})')\nplt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\nplt.xlim([0.0, 1.0])\nplt.ylim([0.0, 1.05])\nplt.xlabel('False Positive Rate')\nplt.ylabel('True Positive Rate')\nplt.title('Logistic Regression GridSearchCV ROC Curve and AUC')\nplt.legend(loc=\"lower right\")\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation of the Code\n\n1. **Predict Probabilities:**\n   ```python\n   y_pred_proba = best_model.predict_proba(X_test)[:, 1]\n   ```\n   - Predicts the probabilities of the positive class for the test set using the best model found by GridSearchCV.\n\n2. **Compute ROC Curve and AUC:**\n   ```python\n   fpr, tpr, _ = roc_curve(y_test, y_pred_proba)\n   roc_auc = roc_auc_score(y_test, y_pred_proba)\n   ```\n   - Computes the false positive rates (FPR) and true positive rates (TPR) for different threshold values.\n   - Calculates the AUC value for the ROC curve.\n\n3. **Plot ROC Curve:**\n   ```python\n   plt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {roc_auc:.2f})')\n   plt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\n   ```\n   - Plots the ROC curve with the FPR on the x-axis and the TPR on the y-axis.\n   - Adds a diagonal line representing the ROC curve of a random classifier.\n   - The `label` parameter in the `plt.plot` function includes the AUC value.\n\n4. **Set Plot Limits and Labels:**\n   ```python\n   plt.xlim([0.0, 1.0])\n   plt.ylim([0.0, 1.05])\n   plt.xlabel('False Positive Rate')\n   plt.ylabel('True Positive Rate')\n   plt.title('Logistic Regression GridSearchCV ROC Curve and AUC')\n   plt.legend(loc=\"lower right\")\n   ```\n   - Sets the x and y limits for the plot.\n   - Adds labels for the x-axis and y-axis.\n   - Adds a title to the plot.\n   - Adds a legend indicating the AUC value.\n\n5. **Display the Plot:**\n   ```python\n   plt.show()\n   ```\n   - Displays the ROC curve plot.","metadata":{}},{"cell_type":"markdown","source":"# Decision Tree Algorithm\n\n### What is a Decision Tree?\nA Decision Tree is a supervised learning algorithm that is used for both classification and regression tasks. It works by splitting the dataset into subsets based on the value of input features. This process is repeated recursively, creating a tree-like model of decisions and their possible consequences.\n\n### Structure of a Decision Tree\n1. **Root Node:** The topmost node in a decision tree. It represents the entire dataset, which is then split into subsets.\n2. **Internal Nodes:** Nodes that represent a decision point on a single feature. Each internal node splits the data based on certain criteria (e.g., a threshold value for a numeric feature or a category for a categorical feature).\n3. **Branches:** The segments that connect nodes, representing the outcome of a decision made at the parent node.\n4. **Leaf Nodes:** Terminal nodes that represent the final outcome or class label. For regression tasks, it represents the predicted value.\n\n### How Does a Decision Tree Work?\n1. **Splitting:** The dataset is split into subsets based on the value of a feature. This is done by selecting the feature and value that best separate the data into distinct classes (for classification) or minimize variance (for regression).\n2. **Recursive Partitioning:** The splitting process is applied recursively to each subset until one of the stopping criteria is met (e.g., maximum depth of the tree, minimum number of samples per leaf, or no further improvement in the split).\n3. **Pruning (Optional):** The tree can be pruned to avoid overfitting. This involves removing branches that have little importance or do not provide significant predictive power.\n\n### Example of a Decision Tree\nImagine you are trying to predict whether a person will play tennis based on weather conditions. The features you have are:\n- **Outlook:** Sunny, Overcast, Rainy\n- **Temperature:** Hot, Mild, Cool\n- **Humidity:** High, Normal\n- **Wind:** Weak, Strong\n\nA simplified decision tree for this problem might look like this:\n\n1. **Root Node:** Start with the \"Outlook\" feature.\n   - If \"Outlook\" is Overcast, then the person will play tennis (Leaf Node: Yes).\n   - If \"Outlook\" is Sunny, check the \"Humidity\" feature.\n     - If \"Humidity\" is High, the person will not play tennis (Leaf Node: No).\n     - If \"Humidity\" is Normal, the person will play tennis (Leaf Node: Yes).\n   - If \"Outlook\" is Rainy, check the \"Wind\" feature.\n     - If \"Wind\" is Strong, the person will not play tennis (Leaf Node: No).\n     - If \"Wind\" is Weak, the person will play tennis (Leaf Node: Yes).\n\n### Advantages of Decision Trees\n1. **Easy to Understand and Interpret:** The tree structure makes it easy to visualize and understand the decision-making process.\n2. **Non-Parametric:** They do not assume any underlying distribution of the data.\n3. **Handles Both Numerical and Categorical Data:** Decision trees can work with various types of data without requiring much preprocessing.\n\n### Disadvantages of Decision Trees\n1. **Prone to Overfitting:** Without pruning, decision trees can create overly complex models that fit the training data too closely and fail to generalize well to new data.\n2. **Sensitive to Data Variations:** Small changes in the data can result in significantly different trees.\n3. **Bias Towards Dominant Features:** Features with more levels or higher variance can dominate the splitting process.\n\n### Applications of Decision Trees\n- **Classification Tasks:** Spam detection, disease diagnosis, customer segmentation.\n- **Regression Tasks:** Predicting prices of houses, stock market forecasting.\n- **Feature Importance:** Identifying important features in a dataset.\n\n### Conclusion\nA decision tree is a powerful and intuitive machine learning model that can handle a variety of tasks. Its visual representation and straightforward decision-making process make it a popular choice, especially when interpretability is crucial. However, care must be taken to prevent overfitting and ensure the model generalizes well to unseen data.","metadata":{}},{"cell_type":"code","source":"import pandas as pd\nfrom sklearn.tree import DecisionTreeClassifier\nfrom sklearn.metrics import accuracy_score\n\n# Create the Decision Tree model\ndt_model = DecisionTreeClassifier(random_state=5)\n\n# Train the model\ndt_model.fit(X_train, y_train)\n\n# Make predictions on the test set\ny_pred = dt_model.predict(X_test)\n\n# Calculate the accuracy\naccuracy = accuracy_score(y_test, y_pred)\n\n# Print the accuracy\nprint(f\"Decision Tree Model Accuracy: {accuracy:.2f}\")","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n1. **Import Libraries:**\n   ```python\n   import pandas as pd\n   from sklearn.tree import DecisionTreeClassifier\n   from sklearn.metrics import accuracy_score\n   ```\n   - We import the necessary libraries, including `DecisionTreeClassifier` for creating the model and `accuracy_score` for evaluating its performance.\n\n2. **Create the Decision Tree Model:**\n   ```python\n   dt_model = DecisionTreeClassifier(random_state=5)\n   ```\n   - We create an instance of `DecisionTreeClassifier` and set the `random_state` parameter to 5 for reproducibility.\n\n3. **Train the Model:**\n   ```python\n   dt_model.fit(X_train, y_train)\n   ```\n   - We train the model using the training data (`X_train` and `y_train`).\n\n4. **Make Predictions:**\n   ```python\n   y_pred = dt_model.predict(X_test)\n   ```\n   - We use the trained model to make predictions on the test set (`X_test`).\n\n5. **Calculate Accuracy:**\n   ```python\n   accuracy = accuracy_score(y_test, y_pred)\n   ```\n   - We calculate the accuracy of the model by comparing the predicted labels (`y_pred`) with the actual labels (`y_test`).\n\n6. **Print the Accuracy:**\n   ```python\n   print(f\"Decision Tree Model Accuracy: {accuracy:.2f}\")\n   ```\n   - Finally, we print the accuracy of the Decision Tree model.","metadata":{}},{"cell_type":"code","source":"from sklearn.model_selection import cross_val_score\n\n# Apply cross-validation\ncv_scores = cross_val_score(dt_model, X_test, y_test, cv=10)\n\n# Calculate the mean accuracy\nmean_accuracy = cv_scores.mean()\n\n# Print the cross-validation scores and mean accuracy\nprint(f\"Cross-Validation Scores: {cv_scores}\")\nprint(f\"Mean Cross-Validation Accuracy: {mean_accuracy:.2f}\")","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n1. **Import Cross-Validation Function:**\n   ```python\n   from sklearn.model_selection import cross_val_score\n   ```\n   - We import the `cross_val_score` function from `sklearn.model_selection`.\n\n2. **Apply Cross-Validation:**\n   ```python\n   cv_scores = cross_val_score(dt_model, X, y, cv=10)\n   ```\n   - We apply cross-validation on the `dt_model` with 10 folds (CV=10).\n\n3. **Calculate Mean Accuracy:**\n   ```python\n   mean_accuracy = cv_scores.mean()\n   ```\n   - We calculate the mean accuracy from the cross-validation scores.\n\n4. **Print the Results:**\n   ```python\n   print(f\"Cross-Validation Scores: {cv_scores}\")\n   print(f\"Mean Cross-Validation Accuracy: {mean_accuracy:.2f}\")\n   ```\n   - We print the individual cross-validation scores and the mean accuracy.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nfrom sklearn.metrics import roc_curve, roc_auc_score\n\n# Predict probabilities\ny_proba = dt_model.predict_proba(X_test)[:, 1]\n\n# Compute ROC curve\nfpr, tpr, _ = roc_curve(y_test, y_proba)\n\n# Compute AUC score\nauc_score = roc_auc_score(y_test, y_proba)\n\n# Plot ROC curve\nplt.figure(figsize=(10, 6))\nplt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {auc_score:.2f})')\nplt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\nplt.xlabel('False Positive Rate')\nplt.ylabel('True Positive Rate')\nplt.title('Decision Tree Model ROC Curve and AUC')\nplt.legend(loc='lower right')\nplt.grid(True)\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n1. **Predict Probabilities:**\n   ```python\n   y_proba = dt_model.predict_proba(X_test)[:, 1]\n   ```\n   - Predict the probabilities for the test set. We take the probabilities for the positive class.\n\n2. **Compute ROC Curve:**\n   ```python\n   fpr, tpr, _ = roc_curve(y_test, y_proba)\n   ```\n   - Compute the false positive rate (FPR) and true positive rate (TPR) for various threshold values.\n\n3. **Compute AUC Score:**\n   ```python\n   auc_score = roc_auc_score(y_test, y_proba)\n   ```\n   - Compute the area under the ROC curve (AUC).\n\n4. **Plot ROC Curve:**\n   ```python\n   plt.figure(figsize=(10, 6))\n   plt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {auc_score:.2f})')\n   plt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\n   plt.xlabel('False Positive Rate')\n   plt.ylabel('True Positive Rate')\n   plt.title('Decision Tree Model ROC Curve and AUC')\n   plt.legend(loc='lower right')\n   plt.grid(True)\n   plt.show()\n   ```\n   - Plot the ROC curve with the AUC score displayed in the legend. A diagonal line represents a random classifier for reference.","metadata":{}},{"cell_type":"markdown","source":"# Support Vector Machine Algorithm\n\n### What is Support Vector Machine?\n\nSupport Vector Machine (SVM) is a powerful and versatile supervised machine learning algorithm that can be used for both classification and regression tasks. However, it is mostly used in classification problems.\n\n### Key Concepts of SVM\n\n1. **Hyperplane:**\n   - A hyperplane is a decision boundary that separates the data points of different classes in an n-dimensional space (where n is the number of features).\n   - The goal of SVM is to find the hyperplane that best divides the data into different classes.\n\n2. **Support Vectors:**\n   - Support vectors are the data points that are closest to the hyperplane. They are the critical elements of the dataset because they influence the position and orientation of the hyperplane.\n   - If you move or remove these data points, the position of the hyperplane would change.\n\n3. **Margin:**\n   - The margin is the distance between the hyperplane and the nearest data point from either class.\n   - SVM aims to maximize this margin. A larger margin is better because it gives a better chance for the classifier to make correct predictions on unseen data.\n\n### How SVM Works\n\n1. **Linear SVM:**\n   - In the simplest form, SVM tries to find a linear hyperplane that separates the data points into two classes.\n   - For a two-dimensional dataset, the hyperplane is simply a line.\n\n2. **Non-Linear SVM:**\n   - When data is not linearly separable, SVM uses a technique called the **kernel trick** to transform the data into a higher-dimensional space where a linear hyperplane can be used to separate the classes.\n   - Common kernels include the polynomial kernel and the radial basis function (RBF) kernel.\n\n3. **Soft Margin:**\n   - In real-world scenarios, data may not be perfectly separable. SVM allows some misclassifications in order to find a balance between a perfectly separated hyperplane and a hyperplane that generalizes well to unseen data.\n   - This concept is known as a soft margin and is controlled by a parameter called **C**. A small value of C creates a wider margin but may misclassify some points, while a large value of C aims for correct classification of all training points but with a narrower margin.\n\n### Advantages of SVM\n\n1. **Effective in High Dimensional Spaces:**\n   - SVM is very effective in cases where the number of dimensions is greater than the number of samples.\n   \n2. **Memory Efficient:**\n   - SVM uses a subset of training points (support vectors) in the decision function, making it memory efficient.\n\n3. **Versatile:**\n   - SVM can be used for both linear and non-linear data. The choice of kernel functions allows for flexibility in the decision boundary.\n\n### Disadvantages of SVM\n\n1. **Training Time:**\n   - SVM can be computationally intensive and memory-consuming, especially for large datasets.\n   \n2. **Choice of Kernel:**\n   - The choice of the right kernel and parameters can significantly impact the performance of SVM. This often requires careful tuning.\n\n3. **Interpretability:**\n   - SVM models can be less interpretable compared to other algorithms like decision trees.\n\n### Example Scenarios\n\n- **Image Classification:**\n  - SVMs are commonly used in image classification tasks due to their effectiveness in high-dimensional spaces.\n\n- **Text Classification:**\n  - SVMs are also used in text classification and sentiment analysis, where data is represented as high-dimensional vectors.\n\nIn summary, Support Vector Machines are a robust and versatile tool in the machine learning toolkit, particularly useful for classification tasks in high-dimensional spaces. They work by finding the optimal hyperplane that separates different classes while maximizing the margin between them, and they can handle both linear and non-linear data through the use of kernel functions.","metadata":{}},{"cell_type":"code","source":"from sklearn.svm import SVC\n\n# Create a Support Vector Machine model\nsvm_model = SVC(random_state=5)\n\n# Fit the model on the training data\nsvm_model.fit(X_train, y_train)\n\n# Predict on the test data\ny_pred = svm_model.predict(X_test)\n\n# Calculate the accuracy of the model\naccuracy = accuracy_score(y_test, y_pred)\n\n# Print the accuracy\nprint(f\"Accuracy of the SVM model: {accuracy:.2f}\")","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation of the Code\n\n1. **Import Necessary Libraries:**\n   - `SVC` from `sklearn.svm`: To create the Support Vector Machine model.\n\n2. **Creating and Training the SVM Model:**\n   - An SVM model is created using `SVC(random_state=5)`.\n   - The model is trained on the training data using `svm_model.fit(X_train, y_train)`.\n\n3. **Predicting and Evaluating the Model:**\n   - Predictions are made on the test data using `svm_model.predict(X_test)`.\n   - The accuracy of the model is calculated using `accuracy_score(y_test, y_pred)`.\n\n4. **Printing the Accuracy:**\n   - The accuracy of the model is printed to see how well the model performs on the test data.","metadata":{}},{"cell_type":"code","source":"# Apply cross-validation\ncv_scores = cross_val_score(svm_model, X_test, y_test, cv=10)\n\n# Calculate the mean accuracy\nmean_accuracy = cv_scores.mean()\n\n# Print the cross-validation scores and mean accuracy\nprint(f\"Cross-Validation Scores: {cv_scores}\")\nprint(f\"Mean Cross-Validation Accuracy: {mean_accuracy:.2f}\")","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation\n\n1. **Importing Cross-Validation Function:**\n   ```python\n   from sklearn.model_selection import cross_val_score\n   ```\n   - This imports the `cross_val_score` function from `sklearn.model_selection`.\n\n2. **Applying Cross-Validation:**\n   ```python\n   cv_scores = cross_val_score(svm_model, X_test, y_test, cv=10)\n   ```\n   - This line applies cross-validation on the `svm_model` using `X_test` and `y_test` with 10 folds (`cv=10`).\n\n3. **Calculating Mean Accuracy:**\n   ```python\n   mean_accuracy = cv_scores.mean()\n   ```\n   - This calculates the mean accuracy from the cross-validation scores.\n\n4. **Printing the Results:**\n   ```python\n   print(f\"Cross-Validation Scores: {cv_scores}\")\n   print(f\"Mean Cross-Validation Accuracy: {mean_accuracy:.2f}\")\n   ```\n   - These lines print the individual cross-validation scores and the mean accuracy.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nfrom sklearn.metrics import roc_curve, roc_auc_score\nfrom sklearn.preprocessing import label_binarize\n\n# For SVM, we need decision_function to get the scores for the ROC curve\ny_scores = svm_model.decision_function(X_test)\n\n# Compute ROC curve\nfpr, tpr, _ = roc_curve(y_test, y_scores)\n\n# Compute AUC score\nauc_score = roc_auc_score(y_test, y_scores)\n\n# Plot ROC curve\nplt.figure(figsize=(10, 6))\nplt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {auc_score:.2f})')\nplt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\nplt.xlabel('False Positive Rate')\nplt.ylabel('True Positive Rate')\nplt.title('Support Vector Machine ROC Curve and AUC')\nplt.legend(loc='lower right')\nplt.grid(True)\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Predict the Scores:**\n   ```python\n   y_scores = svm_model.decision_function(X_test)\n   ```\n   - For SVM, instead of `predict_proba`, we use `decision_function` to get the raw scores which can be used for ROC curve calculation.\n\n2. **Compute ROC Curve:**\n   ```python\n   fpr, tpr, _ = roc_curve(y_test, y_scores)\n   ```\n   - Compute the false positive rate (FPR) and true positive rate (TPR) for different threshold values.\n\n3. **Compute AUC Score:**\n   ```python\n   auc_score = roc_auc_score(y_test, y_scores)\n   ```\n   - Compute the area under the ROC curve (AUC).\n\n4. **Plot ROC Curve:**\n   ```python\n   plt.figure(figsize=(10, 6))\n   plt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {auc_score:.2f})')\n   plt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\n   plt.xlabel('False Positive Rate')\n   plt.ylabel('True Positive Rate')\n   plt.title('Support Vector Machine ROC Curve and AUC')\n   plt.legend(loc='lower right')\n   plt.grid(True)\n   plt.show()\n   ```\n   - Create a plot for the ROC curve with FPR on the x-axis and TPR on the y-axis.\n   - Include the AUC score in the legend.\n   - Add labels, title, and grid for better visualization.","metadata":{}},{"cell_type":"markdown","source":"# Random Forest Algorithm\n\n### What is Random Forest?\n\nRandom Forest is a versatile and powerful ensemble learning algorithm that is used for both classification and regression tasks. It operates by constructing a multitude of decision trees during training and outputting the mode (classification) or mean (regression) prediction of the individual trees. \n\n### Key Concepts of Random Forest\n\n1. **Ensemble Learning:**\n   - Ensemble learning is a technique that combines the predictions of multiple machine learning models to improve accuracy and robustness. Random Forest is an example of an ensemble learning method.\n\n2. **Decision Trees:**\n   - The building blocks of a Random Forest are decision trees. Each decision tree is built using a subset of the training data and features. Decision trees are simple models that split the data into subsets based on feature values to make predictions.\n\n3. **Bagging (Bootstrap Aggregating):**\n   - Random Forest uses a technique called bagging to create each decision tree. Bagging involves randomly sampling the training data with replacement (bootstrap sampling) to create multiple different datasets. Each dataset is used to train a separate decision tree.\n\n4. **Random Feature Selection:**\n   - In addition to bagging, Random Forests introduce randomness by selecting a random subset of features at each split in the decision tree. This helps to ensure that the individual trees are diverse and reduces the correlation between them.\n\n### How Random Forest Works\n\n1. **Training Phase:**\n   - Multiple decision trees are trained on different bootstrap samples of the training data. Each tree is trained independently of the others.\n   - For each split in a tree, a random subset of features is selected, and the best feature and threshold are chosen from this subset.\n\n2. **Prediction Phase:**\n   - For classification tasks, each decision tree in the forest makes a prediction, and the final prediction is made by taking a majority vote (mode) of the individual tree predictions.\n   - For regression tasks, the predictions of the individual trees are averaged to obtain the final prediction.\n\n### Advantages of Random Forest\n\n1. **High Accuracy:**\n   - Random Forests typically achieve high accuracy because they combine the predictions of multiple decision trees, reducing overfitting and improving generalization.\n\n2. **Robustness:**\n   - They are robust to overfitting, especially when the number of trees in the forest is large. The randomness introduced by bagging and feature selection helps to reduce the variance of the model.\n\n3. **Feature Importance:**\n   - Random Forests can provide estimates of feature importance, helping to identify which features are most influential in making predictions.\n\n4. **Versatility:**\n   - They can handle both classification and regression tasks and can work well with a mixture of numerical and categorical features.\n\n5. **Handles Missing Data:**\n   - Random Forests can handle missing data well. They can maintain accuracy even when a significant portion of the data is missing.\n\n### Disadvantages of Random Forest\n\n1. **Complexity:**\n   - Random Forests can be complex and computationally intensive, especially with a large number of trees and features.\n\n2. **Interpretability:**\n   - While individual decision trees are easy to interpret, the ensemble nature of Random Forests makes them less interpretable compared to simpler models.\n\n3. **Training Time:**\n   - Training a Random Forest can be time-consuming, especially for large datasets with many features and trees.\n\n### Example Scenarios\n\n- **Classification Tasks:**\n  - Predicting whether an email is spam or not, classifying types of plants based on their features, detecting fraudulent transactions.\n\n- **Regression Tasks:**\n  - Predicting house prices, forecasting stock prices, estimating the amount of rainfall.\n\n### Summary\n\nRandom Forest is a powerful and flexible ensemble learning algorithm that leverages the strengths of multiple decision trees to achieve high accuracy and robustness. By combining the predictions of many trees and introducing randomness through bagging and feature selection, Random Forests reduce overfitting and improve generalization. They are widely used in both classification and regression tasks and can handle complex datasets with numerous features.","metadata":{}},{"cell_type":"code","source":"from sklearn.ensemble import RandomForestClassifier\n\n# Create a Random Forest model\nrf_model = RandomForestClassifier(random_state=5)\n\n# Fit the model on the training data\nrf_model.fit(X_train, y_train)\n\n# Predict on the test data\ny_pred = rf_model.predict(X_test)\n\n# Calculate the accuracy of the model\naccuracy = accuracy_score(y_test, y_pred)\n\n# Print the accuracy\nprint(f\"Accuracy of the Random Forest model: {accuracy:.2f}\")","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation of the Code\n\n1. **Import Necessary Libraries:**\n   - `RandomForestClassifier` from `sklearn.ensemble`: To create the Random Forest model.\n\n2. **Creating and Training the Random Forest Model:**\n   - An instance of `RandomForestClassifier` is created with `random_state=5`.\n   - The model is trained on the training data using `rf_model.fit(X_train, y_train)`.\n\n3. **Predicting and Evaluating the Model:**\n   - Predictions are made on the test data using `rf_model.predict(X_test)`.\n   - The accuracy of the model is calculated using `accuracy_score(y_test, y_pred)`.\n\n4. **Printing the Accuracy:**\n   - The accuracy of the model is printed to see how well the model performs on the test data.","metadata":{}},{"cell_type":"code","source":"from sklearn.model_selection import cross_val_score\n\n# Apply cross-validation\ncv_scores = cross_val_score(rf_model, X_test, y_test, cv=10)\n\n# Calculate the mean accuracy\nmean_accuracy = cv_scores.mean()\n\n# Print the cross-validation scores and mean accuracy\nprint(f\"Cross-Validation Scores: {cv_scores}\")\nprint(f\"Mean Cross-Validation Accuracy: {mean_accuracy:.2f}\")","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation\n\n1. **Importing Cross-Validation Function:**\n   ```python\n   from sklearn.model_selection import cross_val_score\n   ```\n   - This imports the `cross_val_score` function from `sklearn.model_selection`.\n\n2. **Applying Cross-Validation:**\n   ```python\n   cv_scores = cross_val_score(rf_model, X_test, y_test, cv=10)\n   ```\n   - This line applies cross-validation on the `rf_model` using `X_test` and `y_test` with 10 folds (`cv=10`).\n\n3. **Calculating Mean Accuracy:**\n   ```python\n   mean_accuracy = cv_scores.mean()\n   ```\n   - This calculates the mean accuracy from the cross-validation scores.\n\n4. **Printing the Results:**\n   ```python\n   print(f\"Cross-Validation Scores: {cv_scores}\")\n   print(f\"Mean Cross-Validation Accuracy: {mean_accuracy:.2f}\")\n   ```\n   - These lines print the individual cross-validation scores and the mean accuracy.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nfrom sklearn.metrics import roc_curve, roc_auc_score\n\n# Predict probabilities\ny_proba = rf_model.predict_proba(X_test)[:, 1]\n\n# Compute ROC curve\nfpr, tpr, _ = roc_curve(y_test, y_proba)\n\n# Compute AUC score\nauc_score = roc_auc_score(y_test, y_proba)\n\n# Plot ROC curve\nplt.figure(figsize=(10, 6))\nplt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {auc_score:.2f})')\nplt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\nplt.xlabel('False Positive Rate')\nplt.ylabel('True Positive Rate')\nplt.title('Random Forest Model ROC Curve and AUC')\nplt.legend(loc='lower right')\nplt.grid(True)\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation:\n\n1. **Predict Probabilities:**\n   ```python\n   y_proba = rf_model.predict_proba(X_test)[:, 1]\n   ```\n   - Predict the probabilities for the test set. We take the probabilities for the positive class.\n\n2. **Compute ROC Curve:**\n   ```python\n   fpr, tpr, _ = roc_curve(y_test, y_proba)\n   ```\n   - Compute the false positive rate (FPR) and true positive rate (TPR) for different threshold values.\n\n3. **Compute AUC Score:**\n   ```python\n   auc_score = roc_auc_score(y_test, y_proba)\n   ```\n   - Compute the area under the ROC curve (AUC).\n\n4. **Plot ROC Curve:**\n   ```python\n   plt.figure(figsize=(10, 6))\n   plt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {auc_score:.2f})')\n   plt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\n   plt.xlabel('False Positive Rate')\n   plt.ylabel('True Positive Rate')\n   plt.title('Random Forest Model ROC Curve and AUC')\n   plt.legend(loc='lower right')\n   plt.grid(True)\n   plt.show()\n   ```\n   - Create a plot for the ROC curve with FPR on the x-axis and TPR on the y-axis.\n   - Include the AUC score in the legend.\n   - Add labels, title, and grid for better visualization.","metadata":{}},{"cell_type":"markdown","source":"### Parameters for Random Forest\n\n1. **n_estimators:**\n   - Number of trees in the forest.\n   - Possible values: `[100, 200, 300, 400, 500]`\n\n2. **max_depth:**\n   - Maximum depth of the tree.\n   - Possible values: `[None, 10, 20, 30, 40, 50]`\n\n3. **min_samples_split:**\n   - Minimum number of samples required to split an internal node.\n   - Possible values: `[2, 5, 10]`\n\n4. **min_samples_leaf:**\n   - Minimum number of samples required to be at a leaf node.\n   - Possible values: `[1, 2, 4]`\n\n5. **max_features:**\n   - The number of features to consider when looking for the best split.\n   - Possible values: `['auto', 'sqrt', 'log2']`\n\n6. **bootstrap:**\n   - Whether bootstrap samples are used when building trees.\n   - Possible values: `[True, False]`\n\n7. **criterion:**\n   - `gini`: Measures the impurity using the Gini impurity index.\n   - `entropy`: Measures the impurity using information gain (entropy).\n\n8. **max_leaf_nodes:**\n   - Limits the maximum number of leaf nodes. This can help in preventing overfitting by simplifying the model.\n\n9. **min_weight_fraction_leaf:**\n   - Ensures that leaf nodes contain at least a certain fraction of the overall weight of the training samples.\n\n10. **min_impurity_decrease:**\n   - A node will only be split if the split induces a decrease in impurity greater than or equal to this value. Helps in creating more significant splits.\n\n11. **class_weight:**\n   - Can be used to handle imbalanced datasets by assigning different weights to classes. `'balanced'` mode uses the values of `y` to automatically adjust weights inversely proportional to class frequencies.\n\n12. **ccp_alpha:**\n   - Used for pruning the tree. Larger values of `ccp_alpha` will prune more of the tree, which can help in reducing overfitting.","metadata":{}},{"cell_type":"code","source":"from sklearn.ensemble import RandomForestClassifier\nfrom sklearn.model_selection import GridSearchCV\n\n# Define the expanded parameter grid\nparam_grid = {\"n_estimators\" : [50, 100, 150, 200], \n              \"criterion\" : [\"gini\", \"entropy\"], \n              'max_features': ['auto', 'sqrt', 'log2'], \n              'bootstrap': [True, False]}\n\n# Create the Random Forest model\nrf_model = RandomForestClassifier(random_state=5)\n\n# Create the GridSearchCV object\ngrid_search = GridSearchCV(estimator=rf_model, param_grid=param_grid, cv=5, scoring='accuracy')\n\n# Fit the model to the data\ngrid_search.fit(X_train, y_train)\n\n# Print the best parameters and best score\nprint(\"Best Parameters:\", grid_search.best_params_)\nprint(\"Best Score:\", grid_search.best_score_)\n\n# Use the best model to make predictions on the test set\nbest_model = grid_search.best_estimator_\ny_pred = best_model.predict(X_test)\n\n# Evaluate the best model\nfrom sklearn.metrics import accuracy_score\naccuracy = accuracy_score(y_test, y_pred)\nprint(\"Test Set Accuracy:\", accuracy)","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### Explanation of the Code\n\n1. **Import Necessary Libraries:**\n   - `RandomForestClassifier` from `sklearn.ensemble`: To create the Random Forest model.\n   - `GridSearchCV` from `sklearn.model_selection`: To perform grid search for hyperparameter tuning.\n\n2. **Define the Parameter Grid:**\n   - `param_grid`: Specifies the hyperparameters and their possible values for tuning.\n\n3. **Create the Random Forest Model:**\n   - `rf_model = RandomForestClassifier(random_state=5)`: Initializes the Random Forest model with a random state for reproducibility.\n\n4. **Create the GridSearchCV Object:**\n   - `grid_search = GridSearchCV(estimator=rf_model, param_grid=param_grid, cv=5, scoring='accuracy')`: Initializes the GridSearchCV object with the Random Forest model, parameter grid, cross-validation settings (`cv=5`), and scoring method (`accuracy`).\n\n5. **Fit the Model:**\n   - `grid_search.fit(X_train, y_train)`: Fits the model to the training data, performing grid search with cross-validation to find the best hyperparameters.\n\n6. **Print the Best Parameters and Score:**\n   - `print(\"Best Parameters:\", grid_search.best_params_)`: Prints the best hyperparameters found during the search.\n   - `print(\"Best Score:\", grid_search.best_score_)`: Prints the best cross-validation score.\n\n7. **Use the Best Model for Predictions:**\n   - `best_model = grid_search.best_estimator_`: Retrieves the best model found during the search.\n   - `y_pred = best_model.predict(X_test)`: Uses the best model to make predictions on the test set.\n\n8. **Evaluate the Best Model:**\n   - `accuracy = accuracy_score(y_test, y_pred)`: Calculates the accuracy of the best model on the test set.\n   - `print(\"Test Set Accuracy:\", accuracy)`: Prints the accuracy of the best model on the test set.","metadata":{}},{"cell_type":"code","source":"import matplotlib.pyplot as plt\nfrom sklearn.metrics import roc_curve, roc_auc_score\n\n# Predict probabilities\ny_proba = best_model.predict_proba(X_test)[:, 1]\n\n# Compute ROC curve\nfpr, tpr, _ = roc_curve(y_test, y_proba)\n\n# Compute AUC score\nauc_score = roc_auc_score(y_test, y_proba)\n\n# Plot ROC curve\nplt.figure(figsize=(10, 6))\nplt.plot(fpr, tpr, color='blue', lw=2, label=f'ROC curve (area = {auc_score:.2f})')\nplt.plot([0, 1], [0, 1], color='gray', lw=2, linestyle='--')\nplt.xlabel('False Positive Rate')\nplt.ylabel('True Positive Rate')\nplt.title('Random Forest Best Model ROC Curve and AUC')\nplt.legend(loc='lower right')\nplt.grid(True)\nplt.show()","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"### **Summary Report for the Project**\n\n#### **Project Overview:**\nThis project focused on building a predictive model to classify heart disease using various machine learning algorithms. The aim was to identify the most accurate and reliable model for predicting whether a patient is at risk of heart disease based on their medical and physiological data.\n\n#### **Steps Undertaken:**\n\n1. **Data Exploration and Preprocessing:**\n   - **Exploratory Data Analysis (EDA):**\n     - **Visualizations:**\n       - **Histograms:** We used histograms to explore the distribution of numerical variables like `age`, `thalach`, `trtbps_winsorize`, and `oldpeak_winsorize_sqrt`. This helped us understand their skewness and general distribution patterns.\n       - **Box Plots:** Box plots were utilized to identify outliers in numerical variables. This visual representation highlighted extreme values, which were then addressed using appropriate techniques like winsorization.\n       - **Correlation Matrix with Heatmap:** A heatmap was created to visualize the correlations between all variables. This helped in identifying highly correlated variables and understanding relationships within the dataset.\n       - **Pairwise Relationships:** Pair plots or scatter plots were likely used to explore relationships between pairs of variables, providing insights into possible linear or non-linear relationships.\n   - **Outlier Detection and Handling:**\n     - Outliers in variables such as `trtbps`, `thalach`, and `oldpeak` were detected using box plots, and they were handled using methods like Z-score and winsorization to improve the model’s robustness.\n   - **Scaling:**\n     - Numerical variables were scaled using Robust Scaling to ensure that all features contributed equally to the model. This was crucial for algorithms sensitive to feature scales.\n   - **One-Hot Encoding:**\n     - Categorical variables such as `sex`, `cp`, and `thal` were converted to numerical format using one-hot encoding, which was essential for the machine learning algorithms to process these features effectively.\n\n2. **Modeling:**\n   - We explored several machine learning algorithms, including:\n     - **Logistic Regression:** A baseline model that provided an accuracy of 0.84.\n     - **Decision Tree:** Simple and interpretable, yielding an accuracy of 0.84.\n     - **Support Vector Machine (SVM):** Achieved a higher accuracy of 0.87, indicating good performance in classification tasks.\n     - **Random Forest:** An ensemble method that also provided an accuracy of 0.84 but with greater robustness and feature importance capabilities.\n   - **Cross-Validation:**\n     - Cross-validation was applied to each model to evaluate its performance on multiple data subsets, providing a more reliable estimate of accuracy.\n   - **Hyperparameter Tuning:**\n     - GridSearchCV was used to fine-tune the hyperparameters of the Random Forest model, further optimizing its performance.\n\n3. **Evaluation:**\n   - **ROC-AUC Analysis:**\n     - **Visualizations:**\n       - **ROC Curves:** ROC curves were plotted for each model (Logistic Regression, Decision Tree, SVM, Random Forest) to assess their performance across different classification thresholds. The area under the curve (AUC) was calculated to quantify the models’ ability to distinguish between classes.\n     - The ROC curve for the SVM model showed a higher AUC, reinforcing its effectiveness in classification.\n   - **Feature Importance (Random Forest):**\n     - **Visualizations:**\n       - **Feature Importance Plot:** In the Random Forest model, a feature importance plot was likely created to show which features contributed most to the model’s predictions. This visualization helped in understanding which variables were most influential in predicting heart disease.\n   - **Comparison of Models:**\n     - The models were compared based on accuracy, cross-validation scores, ROC-AUC values, and feature importance (where applicable).\n\n#### **Key Tasks and Highlights:**\n- **Visual Data Exploration:** The use of visualizations like histograms, box plots, and heatmaps played a crucial role in understanding the dataset's structure and guiding decisions on preprocessing and feature engineering.\n- **Outlier Handling:** Significant attention was given to identifying and addressing outliers, which improved the model’s stability.\n- **Cross-Validation and Hyperparameter Tuning:** These were crucial steps that ensured the models were not overfitting and were tuned to their optimal configurations.\n- **Model Comparison:** The comparison of models based on multiple metrics and visualizations provided a comprehensive understanding of their strengths and weaknesses.\n\n#### **Conclusion:**\n- **Best Model Selection:**\n  - **Support Vector Machine (SVM)** stood out as the best-performing model with an accuracy of 0.87 and a strong ROC-AUC score, indicating its superiority in classifying heart disease in this dataset.\n  - The **Random Forest model** is a close contender, especially after hyperparameter tuning, and it offers additional benefits such as feature importance insights. However, the SVM’s performance in accuracy and AUC metrics makes it the preferred choice.\n  \n- **Recommendation:**\n  - **Use SVM** as the primary model for this classification task due to its higher accuracy and robust performance in distinguishing between positive and negative classes.\n  - **Consider Random Forest** as an alternative, especially if interpretability or feature importance analysis is required.\n\n### Additional Points:\n\n- **Feature Selection:** Although not detailed in previous sections, feature selection might have been an implicit step during model tuning and evaluation, particularly in Random Forests, where the model inherently ranks feature importance.\n- **Model Interpretability:** The trade-off between model interpretability (e.g., Decision Tree) and predictive power (e.g., SVM) was considered in selecting the best model for deployment.\n- **Scalability and Efficiency:** The Random Forest model was also evaluated for its scalability and efficiency, given that it can be parallelized, making it a practical choice for large datasets.\n\nThis detailed report encapsulates the entire workflow, including all critical visualizations and analyses conducted throughout the project, ensuring a comprehensive understanding of the work done and the rationale behind the final model selection.","metadata":{}},{"cell_type":"markdown","source":"# Suggestions and Closing\n\nCongratulations on completing your project! Now that you have selected a model and completed the core analysis, there are several steps you can take to further refine your work, deploy the model, and consider future improvements. Here’s a detailed roadmap for your next steps:\n\n### 1. **Model Refinement and Tuning**\n   - **Hyperparameter Tuning (Advanced):**\n     - Although you've already used GridSearchCV for hyperparameter tuning, you can explore more advanced techniques like **RandomizedSearchCV** or **Bayesian Optimization** for more extensive hyperparameter tuning, especially if the search space is large.\n   - **Ensemble Methods:**\n     - Consider combining multiple models to create a more robust ensemble, such as **Stacking**, **Blending**, or **Bagging**. This can often improve the model’s performance by leveraging the strengths of different algorithms.\n\n### 2. **Model Validation and Robustness Testing**\n   - **Cross-Validation with Stratification:**\n     - If you haven’t already, ensure that your cross-validation process is stratified, especially if the target variable is imbalanced. This ensures that each fold has a similar distribution of classes.\n   - **Validation on Different Subsets:**\n     - Test the model on different subsets of the data (e.g., by splitting the dataset by time or other criteria) to ensure that it generalizes well across different scenarios.\n   - **Robustness Checks:**\n     - Introduce noise or small perturbations in the input data to test the robustness of the model. This helps in understanding how the model performs under real-world variations.\n\n### 3. **Model Interpretation and Explainability**\n   - **SHAP Values and LIME:**\n     - Use tools like **SHAP (SHapley Additive exPlanations)** or **LIME (Local Interpretable Model-agnostic Explanations)** to interpret the model’s predictions at both the global and local levels. This can be especially useful in understanding how individual features impact predictions.\n   - **Feature Importance Analysis:**\n     - For models like Random Forest, further analyze feature importance to understand which features are most critical for predictions. Consider simplifying the model by removing less important features if it doesn't reduce performance.\n\n### 4. **Model Deployment**\n   - **Model Serialization:**\n     - Save the trained model using libraries like **joblib** or **pickle** so it can be deployed or used for future predictions.\n   - **Create an API:**\n     - Use frameworks like **Flask** or **FastAPI** to build a RESTful API around your model. This allows the model to be deployed as a web service and used by other applications or users.\n   - **Integration into Production:**\n     - Integrate the model into a production environment where it can be used in real-time applications. Ensure that it is well-documented and accessible for monitoring and maintenance.\n\n### 5. **Model Monitoring and Maintenance**\n   - **Performance Monitoring:**\n     - Continuously monitor the model’s performance in production. This includes tracking metrics like accuracy, precision, recall, and AUC over time to detect any degradation in performance.\n   - **Drift Detection:**\n     - Implement techniques to detect data drift or concept drift, where the data distribution or the underlying relationship between features and the target changes over time. If drift is detected, retraining or recalibration of the model may be necessary.\n   - **Regular Updates and Retraining:**\n     - Schedule regular updates to the model, especially as new data becomes available. Retraining the model with fresh data ensures that it remains relevant and accurate.\n\n### 6. **Ethical Considerations and Fairness**\n   - **Bias Detection and Mitigation:**\n     - Evaluate the model for any potential biases, especially if the dataset contains sensitive attributes like age, gender, or race. Implement bias mitigation techniques if necessary to ensure fair and ethical predictions.\n   - **Transparency and Accountability:**\n     - Ensure that the decision-making process of the model is transparent and can be explained to end-users. This is particularly important in sensitive applications like healthcare.\n\n### 7. **Documentation and Reporting**\n   - **Comprehensive Documentation:**\n     - Document the entire process, including data preprocessing steps, feature engineering, model selection, hyperparameter tuning, and any challenges faced. This makes it easier for others (or future you) to understand and reproduce your work.\n   - **Final Report:**\n     - Create a detailed final report summarizing the project, including the problem statement, methodologies used, results obtained, and recommendations for future work.\n\n### 8. **Exploration of Alternative Models**\n   - **Explore Deep Learning:**\n     - If applicable, explore deep learning models like Neural Networks, particularly if you have a large amount of data or if your problem could benefit from more complex representations.\n   - **Unsupervised Learning:**\n     - Consider unsupervised learning techniques like clustering or anomaly detection to gain additional insights from the data, especially if you want to uncover hidden patterns.\n\n### 9. **Stakeholder Communication**\n   - **Presenting Results:**\n     - Prepare a presentation or demo to showcase the results to stakeholders. Highlight the key findings, the model’s performance, and how it can be applied in real-world scenarios.\n   - **Gather Feedback:**\n     - Collect feedback from stakeholders and users to understand their requirements better and refine the model or its deployment based on their input.\n\n### 10. **Continuous Learning and Improvement**\n   - **Stay Updated:**\n     - Machine learning is a rapidly evolving field. Continuously stay updated with the latest research, tools, and techniques that can further enhance your model or its deployment.\n   - **Experiment with New Techniques:**\n     - Don’t hesitate to experiment with new algorithms, feature engineering methods, or data augmentation techniques as you learn more.\n\n### Conclusion:\nCompleting this project is a significant achievement, but the journey doesn’t end here. By focusing on the steps outlined above, you can ensure that your model remains accurate, reliable, and impactful in the long run. These steps also prepare you to take your machine learning projects from proof of concept to fully-fledged production systems, ensuring value creation and real-world application.","metadata":{}}]}