Breast Cancer Prediction Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e8141c9b",
   "metadata": {},
   "source": [
    "# Breast Cancer Prediction Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "817e6b4e",
   "metadata": {},
   "source": [
    "# Problem Statement : \n",
    "\n",
    "Breast cancer is the most common cancer amongst women in the world. It accounts for 25% of all cancer cases, and affected over 2.1 Million people in 2015 alone. It starts when cells in the breast begin to grow out of control. These cells usually form tumors that can be seen via X-ray or felt as lumps in the breast area.The key challenges against it’s detection is how to classify tumors into malignant (cancerous) or benign(non cancerous)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3fed379",
   "metadata": {},
   "source": [
    "# Acknowledgements:\n",
    "\n",
    "The dataset has been referred from Kaggle."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02aec4c9",
   "metadata": {},
   "source": [
    "# Objective : \n",
    "- Build classification model to predict whether the cancer type is Malignant or Benign.\n",
    "- Use of the classification algorithm - Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "88309322",
   "metadata": {},
   "outputs": [],
   "source": [
    "#importing libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "77df63b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('C:/Users/KIIT/Onedrive/Academics and Career/ML/Datasets/Breast Cancer Dataset/archive/breast-cancer.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f0749a8",
   "metadata": {},
   "source": [
    "# Exploring  the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "88787b37",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>diagnosis</th>\n",
       "      <th>radius_mean</th>\n",
       "      <th>texture_mean</th>\n",
       "      <th>perimeter_mean</th>\n",
       "      <th>area_mean</th>\n",
       "      <th>smoothness_mean</th>\n",
       "      <th>compactness_mean</th>\n",
       "      <th>concavity_mean</th>\n",
       "      <th>concave points_mean</th>\n",
       "      <th>...</th>\n",
       "      <th>radius_worst</th>\n",
       "      <th>texture_worst</th>\n",
       "      <th>perimeter_worst</th>\n",
       "      <th>area_worst</th>\n",
       "      <th>smoothness_worst</th>\n",
       "      <th>compactness_worst</th>\n",
       "      <th>concavity_worst</th>\n",
       "      <th>concave points_worst</th>\n",
       "      <th>symmetry_worst</th>\n",
       "      <th>fractal_dimension_worst</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>842302</td>\n",
       "      <td>M</td>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.3001</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>...</td>\n",
       "      <td>25.38</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.1622</td>\n",
       "      <td>0.6656</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>842517</td>\n",
       "      <td>M</td>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.0869</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>...</td>\n",
       "      <td>24.99</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.1238</td>\n",
       "      <td>0.1866</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>84300903</td>\n",
       "      <td>M</td>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.1974</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>...</td>\n",
       "      <td>23.57</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.1444</td>\n",
       "      <td>0.4245</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>84348301</td>\n",
       "      <td>M</td>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.2414</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>...</td>\n",
       "      <td>14.91</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.2098</td>\n",
       "      <td>0.8663</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>84358402</td>\n",
       "      <td>M</td>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.1980</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>...</td>\n",
       "      <td>22.54</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.1374</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 32 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         id diagnosis  radius_mean  texture_mean  perimeter_mean  area_mean  \\\n",
       "0    842302         M        17.99         10.38          122.80     1001.0   \n",
       "1    842517         M        20.57         17.77          132.90     1326.0   \n",
       "2  84300903         M        19.69         21.25          130.00     1203.0   \n",
       "3  84348301         M        11.42         20.38           77.58      386.1   \n",
       "4  84358402         M        20.29         14.34          135.10     1297.0   \n",
       "\n",
       "   smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \\\n",
       "0          0.11840           0.27760          0.3001              0.14710   \n",
       "1          0.08474           0.07864          0.0869              0.07017   \n",
       "2          0.10960           0.15990          0.1974              0.12790   \n",
       "3          0.14250           0.28390          0.2414              0.10520   \n",
       "4          0.10030           0.13280          0.1980              0.10430   \n",
       "\n",
       "   ...  radius_worst  texture_worst  perimeter_worst  area_worst  \\\n",
       "0  ...         25.38          17.33           184.60      2019.0   \n",
       "1  ...         24.99          23.41           158.80      1956.0   \n",
       "2  ...         23.57          25.53           152.50      1709.0   \n",
       "3  ...         14.91          26.50            98.87       567.7   \n",
       "4  ...         22.54          16.67           152.20      1575.0   \n",
       "\n",
       "   smoothness_worst  compactness_worst  concavity_worst  concave points_worst  \\\n",
       "0            0.1622             0.6656           0.7119                0.2654   \n",
       "1            0.1238             0.1866           0.2416                0.1860   \n",
       "2            0.1444             0.4245           0.4504                0.2430   \n",
       "3            0.2098             0.8663           0.6869                0.2575   \n",
       "4            0.1374             0.2050           0.4000                0.1625   \n",
       "\n",
       "   symmetry_worst  fractal_dimension_worst  \n",
       "0          0.4601                  0.11890  \n",
       "1          0.2750                  0.08902  \n",
       "2          0.3613                  0.08758  \n",
       "3          0.6638                  0.17300  \n",
       "4          0.2364                  0.07678  \n",
       "\n",
       "[5 rows x 32 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ea1405ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['id', 'diagnosis', 'radius_mean', 'texture_mean', 'perimeter_mean',\n",
       "       'area_mean', 'smoothness_mean', 'compactness_mean', 'concavity_mean',\n",
       "       'concave points_mean', 'symmetry_mean', 'fractal_dimension_mean',\n",
       "       'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se',\n",
       "       'compactness_se', 'concavity_se', 'concave points_se', 'symmetry_se',\n",
       "       'fractal_dimension_se', 'radius_worst', 'texture_worst',\n",
       "       'perimeter_worst', 'area_worst', 'smoothness_worst',\n",
       "       'compactness_worst', 'concavity_worst', 'concave points_worst',\n",
       "       'symmetry_worst', 'fractal_dimension_worst'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3925bbc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(569, 32)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "582f640d",
   "metadata": {},
   "source": [
    "This shows that the data has 569 records, each with 32 columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "37674d03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 569 entries, 0 to 568\n",
      "Data columns (total 32 columns):\n",
      " #   Column                   Non-Null Count  Dtype  \n",
      "---  ------                   --------------  -----  \n",
      " 0   id                       569 non-null    int64  \n",
      " 1   diagnosis                569 non-null    object \n",
      " 2   radius_mean              569 non-null    float64\n",
      " 3   texture_mean             569 non-null    float64\n",
      " 4   perimeter_mean           569 non-null    float64\n",
      " 5   area_mean                569 non-null    float64\n",
      " 6   smoothness_mean          569 non-null    float64\n",
      " 7   compactness_mean         569 non-null    float64\n",
      " 8   concavity_mean           569 non-null    float64\n",
      " 9   concave points_mean      569 non-null    float64\n",
      " 10  symmetry_mean            569 non-null    float64\n",
      " 11  fractal_dimension_mean   569 non-null    float64\n",
      " 12  radius_se                569 non-null    float64\n",
      " 13  texture_se               569 non-null    float64\n",
      " 14  perimeter_se             569 non-null    float64\n",
      " 15  area_se                  569 non-null    float64\n",
      " 16  smoothness_se            569 non-null    float64\n",
      " 17  compactness_se           569 non-null    float64\n",
      " 18  concavity_se             569 non-null    float64\n",
      " 19  concave points_se        569 non-null    float64\n",
      " 20  symmetry_se              569 non-null    float64\n",
      " 21  fractal_dimension_se     569 non-null    float64\n",
      " 22  radius_worst             569 non-null    float64\n",
      " 23  texture_worst            569 non-null    float64\n",
      " 24  perimeter_worst          569 non-null    float64\n",
      " 25  area_worst               569 non-null    float64\n",
      " 26  smoothness_worst         569 non-null    float64\n",
      " 27  compactness_worst        569 non-null    float64\n",
      " 28  concavity_worst          569 non-null    float64\n",
      " 29  concave points_worst     569 non-null    float64\n",
      " 30  symmetry_worst           569 non-null    float64\n",
      " 31  fractal_dimension_worst  569 non-null    float64\n",
      "dtypes: float64(30), int64(1), object(1)\n",
      "memory usage: 142.4+ KB\n"
     ]
    }
   ],
   "source": [
    "#Reviewing datatypes\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "da8a2904",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>radius_mean</th>\n",
       "      <th>texture_mean</th>\n",
       "      <th>perimeter_mean</th>\n",
       "      <th>area_mean</th>\n",
       "      <th>smoothness_mean</th>\n",
       "      <th>compactness_mean</th>\n",
       "      <th>concavity_mean</th>\n",
       "      <th>concave points_mean</th>\n",
       "      <th>symmetry_mean</th>\n",
       "      <th>...</th>\n",
       "      <th>radius_worst</th>\n",
       "      <th>texture_worst</th>\n",
       "      <th>perimeter_worst</th>\n",
       "      <th>area_worst</th>\n",
       "      <th>smoothness_worst</th>\n",
       "      <th>compactness_worst</th>\n",
       "      <th>concavity_worst</th>\n",
       "      <th>concave points_worst</th>\n",
       "      <th>symmetry_worst</th>\n",
       "      <th>fractal_dimension_worst</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5.690000e+02</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.037183e+07</td>\n",
       "      <td>14.127292</td>\n",
       "      <td>19.289649</td>\n",
       "      <td>91.969033</td>\n",
       "      <td>654.889104</td>\n",
       "      <td>0.096360</td>\n",
       "      <td>0.104341</td>\n",
       "      <td>0.088799</td>\n",
       "      <td>0.048919</td>\n",
       "      <td>0.181162</td>\n",
       "      <td>...</td>\n",
       "      <td>16.269190</td>\n",
       "      <td>25.677223</td>\n",
       "      <td>107.261213</td>\n",
       "      <td>880.583128</td>\n",
       "      <td>0.132369</td>\n",
       "      <td>0.254265</td>\n",
       "      <td>0.272188</td>\n",
       "      <td>0.114606</td>\n",
       "      <td>0.290076</td>\n",
       "      <td>0.083946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.250206e+08</td>\n",
       "      <td>3.524049</td>\n",
       "      <td>4.301036</td>\n",
       "      <td>24.298981</td>\n",
       "      <td>351.914129</td>\n",
       "      <td>0.014064</td>\n",
       "      <td>0.052813</td>\n",
       "      <td>0.079720</td>\n",
       "      <td>0.038803</td>\n",
       "      <td>0.027414</td>\n",
       "      <td>...</td>\n",
       "      <td>4.833242</td>\n",
       "      <td>6.146258</td>\n",
       "      <td>33.602542</td>\n",
       "      <td>569.356993</td>\n",
       "      <td>0.022832</td>\n",
       "      <td>0.157336</td>\n",
       "      <td>0.208624</td>\n",
       "      <td>0.065732</td>\n",
       "      <td>0.061867</td>\n",
       "      <td>0.018061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>8.670000e+03</td>\n",
       "      <td>6.981000</td>\n",
       "      <td>9.710000</td>\n",
       "      <td>43.790000</td>\n",
       "      <td>143.500000</td>\n",
       "      <td>0.052630</td>\n",
       "      <td>0.019380</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.106000</td>\n",
       "      <td>...</td>\n",
       "      <td>7.930000</td>\n",
       "      <td>12.020000</td>\n",
       "      <td>50.410000</td>\n",
       "      <td>185.200000</td>\n",
       "      <td>0.071170</td>\n",
       "      <td>0.027290</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.156500</td>\n",
       "      <td>0.055040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>8.692180e+05</td>\n",
       "      <td>11.700000</td>\n",
       "      <td>16.170000</td>\n",
       "      <td>75.170000</td>\n",
       "      <td>420.300000</td>\n",
       "      <td>0.086370</td>\n",
       "      <td>0.064920</td>\n",
       "      <td>0.029560</td>\n",
       "      <td>0.020310</td>\n",
       "      <td>0.161900</td>\n",
       "      <td>...</td>\n",
       "      <td>13.010000</td>\n",
       "      <td>21.080000</td>\n",
       "      <td>84.110000</td>\n",
       "      <td>515.300000</td>\n",
       "      <td>0.116600</td>\n",
       "      <td>0.147200</td>\n",
       "      <td>0.114500</td>\n",
       "      <td>0.064930</td>\n",
       "      <td>0.250400</td>\n",
       "      <td>0.071460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>9.060240e+05</td>\n",
       "      <td>13.370000</td>\n",
       "      <td>18.840000</td>\n",
       "      <td>86.240000</td>\n",
       "      <td>551.100000</td>\n",
       "      <td>0.095870</td>\n",
       "      <td>0.092630</td>\n",
       "      <td>0.061540</td>\n",
       "      <td>0.033500</td>\n",
       "      <td>0.179200</td>\n",
       "      <td>...</td>\n",
       "      <td>14.970000</td>\n",
       "      <td>25.410000</td>\n",
       "      <td>97.660000</td>\n",
       "      <td>686.500000</td>\n",
       "      <td>0.131300</td>\n",
       "      <td>0.211900</td>\n",
       "      <td>0.226700</td>\n",
       "      <td>0.099930</td>\n",
       "      <td>0.282200</td>\n",
       "      <td>0.080040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.813129e+06</td>\n",
       "      <td>15.780000</td>\n",
       "      <td>21.800000</td>\n",
       "      <td>104.100000</td>\n",
       "      <td>782.700000</td>\n",
       "      <td>0.105300</td>\n",
       "      <td>0.130400</td>\n",
       "      <td>0.130700</td>\n",
       "      <td>0.074000</td>\n",
       "      <td>0.195700</td>\n",
       "      <td>...</td>\n",
       "      <td>18.790000</td>\n",
       "      <td>29.720000</td>\n",
       "      <td>125.400000</td>\n",
       "      <td>1084.000000</td>\n",
       "      <td>0.146000</td>\n",
       "      <td>0.339100</td>\n",
       "      <td>0.382900</td>\n",
       "      <td>0.161400</td>\n",
       "      <td>0.317900</td>\n",
       "      <td>0.092080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.113205e+08</td>\n",
       "      <td>28.110000</td>\n",
       "      <td>39.280000</td>\n",
       "      <td>188.500000</td>\n",
       "      <td>2501.000000</td>\n",
       "      <td>0.163400</td>\n",
       "      <td>0.345400</td>\n",
       "      <td>0.426800</td>\n",
       "      <td>0.201200</td>\n",
       "      <td>0.304000</td>\n",
       "      <td>...</td>\n",
       "      <td>36.040000</td>\n",
       "      <td>49.540000</td>\n",
       "      <td>251.200000</td>\n",
       "      <td>4254.000000</td>\n",
       "      <td>0.222600</td>\n",
       "      <td>1.058000</td>\n",
       "      <td>1.252000</td>\n",
       "      <td>0.291000</td>\n",
       "      <td>0.663800</td>\n",
       "      <td>0.207500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 id  radius_mean  texture_mean  perimeter_mean    area_mean  \\\n",
       "count  5.690000e+02   569.000000    569.000000      569.000000   569.000000   \n",
       "mean   3.037183e+07    14.127292     19.289649       91.969033   654.889104   \n",
       "std    1.250206e+08     3.524049      4.301036       24.298981   351.914129   \n",
       "min    8.670000e+03     6.981000      9.710000       43.790000   143.500000   \n",
       "25%    8.692180e+05    11.700000     16.170000       75.170000   420.300000   \n",
       "50%    9.060240e+05    13.370000     18.840000       86.240000   551.100000   \n",
       "75%    8.813129e+06    15.780000     21.800000      104.100000   782.700000   \n",
       "max    9.113205e+08    28.110000     39.280000      188.500000  2501.000000   \n",
       "\n",
       "       smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \\\n",
       "count       569.000000        569.000000      569.000000           569.000000   \n",
       "mean          0.096360          0.104341        0.088799             0.048919   \n",
       "std           0.014064          0.052813        0.079720             0.038803   \n",
       "min           0.052630          0.019380        0.000000             0.000000   \n",
       "25%           0.086370          0.064920        0.029560             0.020310   \n",
       "50%           0.095870          0.092630        0.061540             0.033500   \n",
       "75%           0.105300          0.130400        0.130700             0.074000   \n",
       "max           0.163400          0.345400        0.426800             0.201200   \n",
       "\n",
       "       symmetry_mean  ...  radius_worst  texture_worst  perimeter_worst  \\\n",
       "count     569.000000  ...    569.000000     569.000000       569.000000   \n",
       "mean        0.181162  ...     16.269190      25.677223       107.261213   \n",
       "std         0.027414  ...      4.833242       6.146258        33.602542   \n",
       "min         0.106000  ...      7.930000      12.020000        50.410000   \n",
       "25%         0.161900  ...     13.010000      21.080000        84.110000   \n",
       "50%         0.179200  ...     14.970000      25.410000        97.660000   \n",
       "75%         0.195700  ...     18.790000      29.720000       125.400000   \n",
       "max         0.304000  ...     36.040000      49.540000       251.200000   \n",
       "\n",
       "        area_worst  smoothness_worst  compactness_worst  concavity_worst  \\\n",
       "count   569.000000        569.000000         569.000000       569.000000   \n",
       "mean    880.583128          0.132369           0.254265         0.272188   \n",
       "std     569.356993          0.022832           0.157336         0.208624   \n",
       "min     185.200000          0.071170           0.027290         0.000000   \n",
       "25%     515.300000          0.116600           0.147200         0.114500   \n",
       "50%     686.500000          0.131300           0.211900         0.226700   \n",
       "75%    1084.000000          0.146000           0.339100         0.382900   \n",
       "max    4254.000000          0.222600           1.058000         1.252000   \n",
       "\n",
       "       concave points_worst  symmetry_worst  fractal_dimension_worst  \n",
       "count            569.000000      569.000000               569.000000  \n",
       "mean               0.114606        0.290076                 0.083946  \n",
       "std                0.065732        0.061867                 0.018061  \n",
       "min                0.000000        0.156500                 0.055040  \n",
       "25%                0.064930        0.250400                 0.071460  \n",
       "50%                0.099930        0.282200                 0.080040  \n",
       "75%                0.161400        0.317900                 0.092080  \n",
       "max                0.291000        0.663800                 0.207500  \n",
       "\n",
       "[8 rows x 31 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#numerical distribution of data\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57442da5",
   "metadata": {},
   "source": [
    "# Cleaning the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9c86549e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "id                         0\n",
       "diagnosis                  0\n",
       "radius_mean                0\n",
       "texture_mean               0\n",
       "perimeter_mean             0\n",
       "area_mean                  0\n",
       "smoothness_mean            0\n",
       "compactness_mean           0\n",
       "concavity_mean             0\n",
       "concave points_mean        0\n",
       "symmetry_mean              0\n",
       "fractal_dimension_mean     0\n",
       "radius_se                  0\n",
       "texture_se                 0\n",
       "perimeter_se               0\n",
       "area_se                    0\n",
       "smoothness_se              0\n",
       "compactness_se             0\n",
       "concavity_se               0\n",
       "concave points_se          0\n",
       "symmetry_se                0\n",
       "fractal_dimension_se       0\n",
       "radius_worst               0\n",
       "texture_worst              0\n",
       "perimeter_worst            0\n",
       "area_worst                 0\n",
       "smoothness_worst           0\n",
       "compactness_worst          0\n",
       "concavity_worst            0\n",
       "concave points_worst       0\n",
       "symmetry_worst             0\n",
       "fractal_dimension_worst    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "af7b3185",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "B    357\n",
       "M    212\n",
       "Name: diagnosis, dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['diagnosis'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "850a85e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "id                           int64\n",
       "diagnosis                   object\n",
       "radius_mean                float64\n",
       "texture_mean               float64\n",
       "perimeter_mean             float64\n",
       "area_mean                  float64\n",
       "smoothness_mean            float64\n",
       "compactness_mean           float64\n",
       "concavity_mean             float64\n",
       "concave points_mean        float64\n",
       "symmetry_mean              float64\n",
       "fractal_dimension_mean     float64\n",
       "radius_se                  float64\n",
       "texture_se                 float64\n",
       "perimeter_se               float64\n",
       "area_se                    float64\n",
       "smoothness_se              float64\n",
       "compactness_se             float64\n",
       "concavity_se               float64\n",
       "concave points_se          float64\n",
       "symmetry_se                float64\n",
       "fractal_dimension_se       float64\n",
       "radius_worst               float64\n",
       "texture_worst              float64\n",
       "perimeter_worst            float64\n",
       "area_worst                 float64\n",
       "smoothness_worst           float64\n",
       "compactness_worst          float64\n",
       "concavity_worst            float64\n",
       "concave points_worst       float64\n",
       "symmetry_worst             float64\n",
       "fractal_dimension_worst    float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1a0c847d",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='diagnosis', ylabel='count'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#To check whether the dataset is balanced or imbalanced\n",
    "sns.countplot(x = 'diagnosis', data = df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b60c1a2",
   "metadata": {},
   "source": [
    "This plot shows that the dataset has balanced values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0e0c0964",
   "metadata": {},
   "outputs": [],
   "source": [
    "#encoding string values into integer values\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "labelencoder = LabelEncoder()\n",
    "df[df.columns[1]]=labelencoder.fit_transform(df.iloc[:,1].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8908bf1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>diagnosis</th>\n",
       "      <th>radius_mean</th>\n",
       "      <th>texture_mean</th>\n",
       "      <th>perimeter_mean</th>\n",
       "      <th>area_mean</th>\n",
       "      <th>smoothness_mean</th>\n",
       "      <th>compactness_mean</th>\n",
       "      <th>concavity_mean</th>\n",
       "      <th>concave points_mean</th>\n",
       "      <th>...</th>\n",
       "      <th>radius_worst</th>\n",
       "      <th>texture_worst</th>\n",
       "      <th>perimeter_worst</th>\n",
       "      <th>area_worst</th>\n",
       "      <th>smoothness_worst</th>\n",
       "      <th>compactness_worst</th>\n",
       "      <th>concavity_worst</th>\n",
       "      <th>concave points_worst</th>\n",
       "      <th>symmetry_worst</th>\n",
       "      <th>fractal_dimension_worst</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>842302</td>\n",
       "      <td>1</td>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.30010</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>...</td>\n",
       "      <td>25.380</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.16220</td>\n",
       "      <td>0.66560</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>842517</td>\n",
       "      <td>1</td>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.08690</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>...</td>\n",
       "      <td>24.990</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.12380</td>\n",
       "      <td>0.18660</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>84300903</td>\n",
       "      <td>1</td>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.19740</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>...</td>\n",
       "      <td>23.570</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.14440</td>\n",
       "      <td>0.42450</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>84348301</td>\n",
       "      <td>1</td>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.24140</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>...</td>\n",
       "      <td>14.910</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.20980</td>\n",
       "      <td>0.86630</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>84358402</td>\n",
       "      <td>1</td>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.19800</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>...</td>\n",
       "      <td>22.540</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.13740</td>\n",
       "      <td>0.20500</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>564</th>\n",
       "      <td>926424</td>\n",
       "      <td>1</td>\n",
       "      <td>21.56</td>\n",
       "      <td>22.39</td>\n",
       "      <td>142.00</td>\n",
       "      <td>1479.0</td>\n",
       "      <td>0.11100</td>\n",
       "      <td>0.11590</td>\n",
       "      <td>0.24390</td>\n",
       "      <td>0.13890</td>\n",
       "      <td>...</td>\n",
       "      <td>25.450</td>\n",
       "      <td>26.40</td>\n",
       "      <td>166.10</td>\n",
       "      <td>2027.0</td>\n",
       "      <td>0.14100</td>\n",
       "      <td>0.21130</td>\n",
       "      <td>0.4107</td>\n",
       "      <td>0.2216</td>\n",
       "      <td>0.2060</td>\n",
       "      <td>0.07115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>565</th>\n",
       "      <td>926682</td>\n",
       "      <td>1</td>\n",
       "      <td>20.13</td>\n",
       "      <td>28.25</td>\n",
       "      <td>131.20</td>\n",
       "      <td>1261.0</td>\n",
       "      <td>0.09780</td>\n",
       "      <td>0.10340</td>\n",
       "      <td>0.14400</td>\n",
       "      <td>0.09791</td>\n",
       "      <td>...</td>\n",
       "      <td>23.690</td>\n",
       "      <td>38.25</td>\n",
       "      <td>155.00</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>0.11660</td>\n",
       "      <td>0.19220</td>\n",
       "      <td>0.3215</td>\n",
       "      <td>0.1628</td>\n",
       "      <td>0.2572</td>\n",
       "      <td>0.06637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>566</th>\n",
       "      <td>926954</td>\n",
       "      <td>1</td>\n",
       "      <td>16.60</td>\n",
       "      <td>28.08</td>\n",
       "      <td>108.30</td>\n",
       "      <td>858.1</td>\n",
       "      <td>0.08455</td>\n",
       "      <td>0.10230</td>\n",
       "      <td>0.09251</td>\n",
       "      <td>0.05302</td>\n",
       "      <td>...</td>\n",
       "      <td>18.980</td>\n",
       "      <td>34.12</td>\n",
       "      <td>126.70</td>\n",
       "      <td>1124.0</td>\n",
       "      <td>0.11390</td>\n",
       "      <td>0.30940</td>\n",
       "      <td>0.3403</td>\n",
       "      <td>0.1418</td>\n",
       "      <td>0.2218</td>\n",
       "      <td>0.07820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>567</th>\n",
       "      <td>927241</td>\n",
       "      <td>1</td>\n",
       "      <td>20.60</td>\n",
       "      <td>29.33</td>\n",
       "      <td>140.10</td>\n",
       "      <td>1265.0</td>\n",
       "      <td>0.11780</td>\n",
       "      <td>0.27700</td>\n",
       "      <td>0.35140</td>\n",
       "      <td>0.15200</td>\n",
       "      <td>...</td>\n",
       "      <td>25.740</td>\n",
       "      <td>39.42</td>\n",
       "      <td>184.60</td>\n",
       "      <td>1821.0</td>\n",
       "      <td>0.16500</td>\n",
       "      <td>0.86810</td>\n",
       "      <td>0.9387</td>\n",
       "      <td>0.2650</td>\n",
       "      <td>0.4087</td>\n",
       "      <td>0.12400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>568</th>\n",
       "      <td>92751</td>\n",
       "      <td>0</td>\n",
       "      <td>7.76</td>\n",
       "      <td>24.54</td>\n",
       "      <td>47.92</td>\n",
       "      <td>181.0</td>\n",
       "      <td>0.05263</td>\n",
       "      <td>0.04362</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>...</td>\n",
       "      <td>9.456</td>\n",
       "      <td>30.37</td>\n",
       "      <td>59.16</td>\n",
       "      <td>268.6</td>\n",
       "      <td>0.08996</td>\n",
       "      <td>0.06444</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.2871</td>\n",
       "      <td>0.07039</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>569 rows × 32 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           id  diagnosis  radius_mean  texture_mean  perimeter_mean  \\\n",
       "0      842302          1        17.99         10.38          122.80   \n",
       "1      842517          1        20.57         17.77          132.90   \n",
       "2    84300903          1        19.69         21.25          130.00   \n",
       "3    84348301          1        11.42         20.38           77.58   \n",
       "4    84358402          1        20.29         14.34          135.10   \n",
       "..        ...        ...          ...           ...             ...   \n",
       "564    926424          1        21.56         22.39          142.00   \n",
       "565    926682          1        20.13         28.25          131.20   \n",
       "566    926954          1        16.60         28.08          108.30   \n",
       "567    927241          1        20.60         29.33          140.10   \n",
       "568     92751          0         7.76         24.54           47.92   \n",
       "\n",
       "     area_mean  smoothness_mean  compactness_mean  concavity_mean  \\\n",
       "0       1001.0          0.11840           0.27760         0.30010   \n",
       "1       1326.0          0.08474           0.07864         0.08690   \n",
       "2       1203.0          0.10960           0.15990         0.19740   \n",
       "3        386.1          0.14250           0.28390         0.24140   \n",
       "4       1297.0          0.10030           0.13280         0.19800   \n",
       "..         ...              ...               ...             ...   \n",
       "564     1479.0          0.11100           0.11590         0.24390   \n",
       "565     1261.0          0.09780           0.10340         0.14400   \n",
       "566      858.1          0.08455           0.10230         0.09251   \n",
       "567     1265.0          0.11780           0.27700         0.35140   \n",
       "568      181.0          0.05263           0.04362         0.00000   \n",
       "\n",
       "     concave points_mean  ...  radius_worst  texture_worst  perimeter_worst  \\\n",
       "0                0.14710  ...        25.380          17.33           184.60   \n",
       "1                0.07017  ...        24.990          23.41           158.80   \n",
       "2                0.12790  ...        23.570          25.53           152.50   \n",
       "3                0.10520  ...        14.910          26.50            98.87   \n",
       "4                0.10430  ...        22.540          16.67           152.20   \n",
       "..                   ...  ...           ...            ...              ...   \n",
       "564              0.13890  ...        25.450          26.40           166.10   \n",
       "565              0.09791  ...        23.690          38.25           155.00   \n",
       "566              0.05302  ...        18.980          34.12           126.70   \n",
       "567              0.15200  ...        25.740          39.42           184.60   \n",
       "568              0.00000  ...         9.456          30.37            59.16   \n",
       "\n",
       "     area_worst  smoothness_worst  compactness_worst  concavity_worst  \\\n",
       "0        2019.0           0.16220            0.66560           0.7119   \n",
       "1        1956.0           0.12380            0.18660           0.2416   \n",
       "2        1709.0           0.14440            0.42450           0.4504   \n",
       "3         567.7           0.20980            0.86630           0.6869   \n",
       "4        1575.0           0.13740            0.20500           0.4000   \n",
       "..          ...               ...                ...              ...   \n",
       "564      2027.0           0.14100            0.21130           0.4107   \n",
       "565      1731.0           0.11660            0.19220           0.3215   \n",
       "566      1124.0           0.11390            0.30940           0.3403   \n",
       "567      1821.0           0.16500            0.86810           0.9387   \n",
       "568       268.6           0.08996            0.06444           0.0000   \n",
       "\n",
       "     concave points_worst  symmetry_worst  fractal_dimension_worst  \n",
       "0                  0.2654          0.4601                  0.11890  \n",
       "1                  0.1860          0.2750                  0.08902  \n",
       "2                  0.2430          0.3613                  0.08758  \n",
       "3                  0.2575          0.6638                  0.17300  \n",
       "4                  0.1625          0.2364                  0.07678  \n",
       "..                    ...             ...                      ...  \n",
       "564                0.2216          0.2060                  0.07115  \n",
       "565                0.1628          0.2572                  0.06637  \n",
       "566                0.1418          0.2218                  0.07820  \n",
       "567                0.2650          0.4087                  0.12400  \n",
       "568                0.0000          0.2871                  0.07039  \n",
       "\n",
       "[569 rows x 32 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "06143bee",
   "metadata": {},
   "outputs": [],
   "source": [
    "X=df.iloc[:,2:].values\n",
    "Y=df.iloc[:,1].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9996561e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X,Y,test_size=0.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fbadaf0",
   "metadata": {},
   "source": [
    "# Feature Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5e2a06a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "sc = StandardScaler()\n",
    "X_train = sc.fit_transform(X_train)\n",
    "X_test = sc.fit_transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "40e69a43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.09150078, -0.39912069, -1.08524296, ..., -1.17917541,\n",
       "        -0.01569402, -0.31508016],\n",
       "       [ 1.42881641, -0.07445406,  1.34098076, ...,  0.15368402,\n",
       "        -0.0587347 , -0.99243491],\n",
       "       [-0.73922917, -0.87363344, -0.75218294, ..., -0.4197753 ,\n",
       "        -0.32176107, -0.87277603],\n",
       "       ...,\n",
       "       [ 1.75244805,  2.04609576,  1.66530887, ...,  0.78845271,\n",
       "        -0.48754739, -0.94115253],\n",
       "       [ 0.1801138 , -0.90768938,  0.19211082, ...,  0.43081474,\n",
       "         0.43543607,  0.03962296],\n",
       "       [-0.84519706, -0.48085494, -0.82744369, ..., -0.25907045,\n",
       "        -0.15597475,  1.75277492]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "742e8f1e",
   "metadata": {},
   "source": [
    "# Building Logistic Regression Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "09414581",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "classifier = LogisticRegression()\n",
    "classifier.fit(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e5c74cd",
   "metadata": {},
   "source": [
    "# Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0187bd1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = classifier.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "04106f8c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[88  0]\n",
      " [ 3 52]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "cm = confusion_matrix(Y_test, predictions)\n",
    "print(cm)\n",
    "sns.heatmap(cm, annot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3d3015b5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9790209790209791\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "print(accuracy_score(Y_test, predictions))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5e3a3f3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1\n",
      " 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0\n",
      " 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1\n",
      " 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "print(Y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3ef836ae",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1\n",
      " 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0\n",
      " 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1\n",
      " 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "print(predictions)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}