Assignment(FE5).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "98d97f6e",
   "metadata": {},
   "source": [
    "**Q1. Pearson correlation coefficient is a measure of the linear relationship between two variables. Suppose you have collected data on the amount of time students spend studying for an exam and their final exam scores. Calculate the Pearson correlation coefficient between these two variables and interpret the result.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "452c384f",
   "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>Time_Studied</th>\n",
       "      <th>Marks_Obtained</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Time_Studied  Marks_Obtained\n",
       "0             4              60\n",
       "1             3              45\n",
       "2             5              70\n",
       "3             7              90\n",
       "4             6              83"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.DataFrame({\n",
    "    'Time_Studied': [4,3,5,7,6],\n",
    "    'Marks_Obtained': [60 ,45, 70, 90, 83]\n",
    "})\n",
    "df"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "d775ddcf",
   "metadata": {},
   "source": [
    "The formula for finding Pearson's correlation between both the variables is:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "We can also find the Pearson's correlation using Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e3716f3c",
   "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>Time_Studied</th>\n",
       "      <th>Marks_Obtained</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Time_Studied</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.993678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Marks_Obtained</th>\n",
       "      <td>0.993678</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time_Studied  Marks_Obtained\n",
       "Time_Studied        1.000000        0.993678\n",
       "Marks_Obtained      0.993678        1.000000"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method='pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a3ed46e",
   "metadata": {},
   "source": [
    "**Interpretation:**<br>\n",
    "The Pearson's correlation coefficients in the given results indicate a very strong positive correlation between the variables of \"Time_Studied\" and \"Marks_Obtained\".\n",
    "\n",
    "Both correlation coefficients are close to 1.000, which means that there is a very strong positive relationship between the two variables. This suggests that as \"Time_Studied\" increases, \"Marks_Obtained\" also increases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "237f38df",
   "metadata": {},
   "source": [
    "**Q2. Spearman's rank correlation is a measure of the monotonic relationship between two variables. Suppose you have collected data on the amount of sleep individuals get each night and their overall job satisfaction level on a scale of 1 to 10. Calculate the Spearman's rank correlation between these two variables and interpret the result.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "75424c5d",
   "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>Sleep_Amount</th>\n",
       "      <th>Job_Satisfaction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Sleep_Amount  Job_Satisfaction\n",
       "0             6                 8\n",
       "1             7                 9\n",
       "2             5                 4\n",
       "3             8                 7\n",
       "4             7                 6\n",
       "5             6                 5\n",
       "6             5                 3\n",
       "7             9                10\n",
       "8             8                 9\n",
       "9             7                 8"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({\n",
    "    'Sleep_Amount': [6, 7, 5, 8, 7, 6, 5, 9, 8, 7],\n",
    "    'Job_Satisfaction': [8, 9, 4, 7, 6, 5, 3, 10, 9, 8]\n",
    "})\n",
    "df"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "4e31f702",
   "metadata": {},
   "source": [
    "The formula for calculating Spearman's correlation coefficient between the two variables is:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "We can also find the Pearson's correlation using Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2510821d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7976045521851899"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Sleep_Amount'].corr(df['Job_Satisfaction'], method='spearman')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e4c1048d",
   "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>Sleep_Amount</th>\n",
       "      <th>Job_Satisfaction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Sleep_Amount</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.797605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Job_Satisfaction</th>\n",
       "      <td>0.797605</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Sleep_Amount  Job_Satisfaction\n",
       "Sleep_Amount          1.000000          0.797605\n",
       "Job_Satisfaction      0.797605          1.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method='spearman')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1a49a08",
   "metadata": {},
   "source": [
    "**Interpretation:**<br>\n",
    "The correlation coefficient between Sleep Amount and Job Satisfaction is 0.797605, which is close to +1. This indicates a strong positive monotonic correlation between these two variables.\n",
    "\n",
    "As the amount of sleep individuals get each night increases, their overall job satisfaction level tends to increase as well. Conversely, as the amount of sleep decreases, job satisfaction tends to decrease."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b27595f4",
   "metadata": {},
   "source": [
    "**Q3. Suppose you are conducting a study to examine the relationship between the number of hours of exercise per week and body mass index (BMI) in a sample of adults. You collected data on both variables for 50 participants. Calculate the Pearson correlation coefficient and the Spearman's rank correlation between these two variables and compare the results.**\n",
    "\n",
    "To calculate the Pearson correlation coefficient and the Spearman's rank correlation between the number of hours of exercise per week and body mass index (BMI) in a sample of 50 adults, we need to have data for both variables. \n",
    "\n",
    "We can use Python to generate random data for both variables and then calculate the Pearson and Spearman's rank correlation between them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b7993519",
   "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>num_of_hours</th>\n",
       "      <th>bmi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.850243</td>\n",
       "      <td>26.921540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.927887</td>\n",
       "      <td>26.710031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.714134</td>\n",
       "      <td>22.121598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.485821</td>\n",
       "      <td>26.825400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8.962386</td>\n",
       "      <td>19.065979</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   num_of_hours        bmi\n",
       "0      4.850243  26.921540\n",
       "1      2.927887  26.710031\n",
       "2      5.714134  22.121598\n",
       "3      6.485821  26.825400\n",
       "4      8.962386  19.065979"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "num_of_hours = np.random.normal(5, 2, 50)\n",
    "bmi = np.random.normal(25, 5, 50)\n",
    "df = pd.DataFrame({\n",
    "    'num_of_hours': num_of_hours,\n",
    "    'bmi': bmi\n",
    "})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33578694",
   "metadata": {},
   "source": [
    "**Pearson's Coefficient Correlation:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "78a1321e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_of_hours</th>\n",
       "      <th>bmi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>num_of_hours</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.161281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bmi</th>\n",
       "      <td>-0.161281</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              num_of_hours       bmi\n",
       "num_of_hours      1.000000 -0.161281\n",
       "bmi              -0.161281  1.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method='pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d256b4fb",
   "metadata": {},
   "source": [
    "**Spearman's Rank Correlation:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1bdfdd2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
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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>num_of_hours</th>\n",
       "      <th>bmi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>num_of_hours</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.103481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bmi</th>\n",
       "      <td>-0.103481</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              num_of_hours       bmi\n",
       "num_of_hours      1.000000 -0.103481\n",
       "bmi              -0.103481  1.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method='spearman')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d23798bc",
   "metadata": {},
   "source": [
    "**Results Comparison:**\n",
    "\n",
    "The Pearson correlation coefficient measures the linear relationship between two variables, and it ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no correlation. In this case, the Pearson correlation coefficient between num_of_hours and bmi is 0.138895, which indicates a weak positive correlation between the two variables.\n",
    "\n",
    "On the other hand, the Spearman correlation coefficient measures the monotonic relationship between two variables, which means it assesses the strength and direction of a relationship between two variables, without assuming any particular functional form of the relationship. It also ranges from -1 to +1, with 0 indicating no correlation. In this case, the Spearman correlation coefficient between num_of_hours and bmi is 0.116447, which also indicates a weak positive correlation between the two variables."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ef429dc",
   "metadata": {},
   "source": [
    "**Q4. A researcher is interested in examining the relationship between the number of hours individuals spend watching television per day and their level of physical activity. The researcher collected data on both variables from a sample of 50 participants. Calculate the Pearson correlation coefficient between these two variables.**\n",
    "\n",
    "To calculate the Pearson correlation coefficient between the number of hours individuals spend watching television per day and their level of physical activity of hours of exercise per week in a sample of 50 pariticipants, we need to have data for both variables.\n",
    "\n",
    "We can use Python to generate random data for both variables and then calculate the Pearson correlation coeffiecients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "35d70671",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        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>num_of_hours</th>\n",
       "      <th>physical_activity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.967697</td>\n",
       "      <td>15.074671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.798661</td>\n",
       "      <td>5.715256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.109797</td>\n",
       "      <td>6.470502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.191582</td>\n",
       "      <td>15.256605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8.276066</td>\n",
       "      <td>13.528612</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   num_of_hours  physical_activity\n",
       "0      2.967697          15.074671\n",
       "1      2.798661           5.715256\n",
       "2      5.109797           6.470502\n",
       "3      4.191582          15.256605\n",
       "4      8.276066          13.528612"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_of_hours = np.random.normal(6, 4, 50)\n",
    "amount_of_activity= np.random.normal(10, 6, 50)\n",
    "df = pd.DataFrame({\n",
    "    'num_of_hours': num_of_hours,\n",
    "    'physical_activity': amount_of_activity\n",
    "})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65638345",
   "metadata": {},
   "source": [
    "**Pearson's Coefficient Correlation:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7190df63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        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>num_of_hours</th>\n",
       "      <th>physical_activity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>num_of_hours</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.05195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>physical_activity</th>\n",
       "      <td>0.05195</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   num_of_hours  physical_activity\n",
       "num_of_hours            1.00000            0.05195\n",
       "physical_activity       0.05195            1.00000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method='pearson')"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "eb3455da",
   "metadata": {},
   "source": [
    "**Q5. A survey was conducted to examine the relationship between age and preference for a particular brand of soft drink. The survey results are shown below:**\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ce51c62b",
   "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>Age(Years)</th>\n",
       "      <th>Soft Drink Preference</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25</td>\n",
       "      <td>Coke</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>42</td>\n",
       "      <td>Pepsi</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>37</td>\n",
       "      <td>Mountain Dew</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19</td>\n",
       "      <td>Coke</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>31</td>\n",
       "      <td>Pepsi</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>28</td>\n",
       "      <td>Coke</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age(Years) Soft Drink Preference\n",
       "0          25                  Coke\n",
       "1          42                 Pepsi\n",
       "2          37          Mountain Dew\n",
       "3          19                  Coke\n",
       "4          31                 Pepsi\n",
       "5          28                  Coke"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({\n",
    "    \"Age(Years)\": [25, 42, 37, 19, 31, 28],\n",
    "    \"Soft Drink Preference\": ['Coke', 'Pepsi', 'Mountain Dew', 'Coke', 'Pepsi', 'Coke']\n",
    "})\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3bc5662",
   "metadata": {},
   "source": [
    "For finding Pearson correlation, we first need to convert the categorical variable to numerical variable. We can do so by encoding it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "77c6d4b3",
   "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>Age(Years)</th>\n",
       "      <th>Soft Drink Preference Enc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>42</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>31</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>28</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age(Years)  Soft Drink Preference Enc\n",
       "0          25                          0\n",
       "1          42                          2\n",
       "2          37                          1\n",
       "3          19                          0\n",
       "4          31                          2\n",
       "5          28                          0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import LabelEncoder\n",
    "encoder = LabelEncoder()\n",
    "encoded_col = encoder.fit_transform(df['Soft Drink Preference'])\n",
    "df_encoded = pd.DataFrame(encoded_col, columns=['Soft Drink Preference Enc'])\n",
    "df_new = pd.concat([df, df_encoded], axis=1)\n",
    "df_new = df_new.drop('Soft Drink Preference', axis=1)\n",
    "df_new"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bf584f8",
   "metadata": {},
   "source": [
    "**Pearson's Coefficient Correlation:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e239dc2a",
   "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>Age(Years)</th>\n",
       "      <th>Soft Drink Preference Enc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Age(Years)</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.769175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Soft Drink Preference Enc</th>\n",
       "      <td>0.769175</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Age(Years)  Soft Drink Preference Enc\n",
       "Age(Years)                   1.000000                   0.769175\n",
       "Soft Drink Preference Enc    0.769175                   1.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new.corr(method='pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cb7b04a",
   "metadata": {},
   "source": [
    "**Q6. A company is interested in examining the relationship between the number of sales calls made per day and the number of sales made per week. The company collected data on both variables from a sample of 30 sales representatives. Calculate the Pearson correlation coefficient between these two variables.**\n",
    "\n",
    "Rather than generating 30 random values for both the variables, I'm taking 10 values for each variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b40aaddc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_of_calls</th>\n",
       "      <th>num_of_sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30</td>\n",
       "      <td>3</td>\n",
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       "      <th>2</th>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>40</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>80</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>60</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>50</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>40</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>100</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   num_of_calls  num_of_sales\n",
       "0            20             2\n",
       "1            30             3\n",
       "2            10             2\n",
       "3            40             5\n",
       "4            60             5\n",
       "5            80             6\n",
       "6            60             8\n",
       "7            50             5\n",
       "8            40             7\n",
       "9           100            20"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_of_calls = [20, 30, 10, 40, 60, 80, 60, 50, 40, 100]\n",
    "num_of_sales = [2, 3, 2, 5, 5, 6, 8, 5, 7, 20]\n",
    "df = pd.DataFrame({\n",
    "    'num_of_calls': num_of_calls,\n",
    "    'num_of_sales': num_of_sales\n",
    "})\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc370fc6",
   "metadata": {},
   "source": [
    "**Pearson's Coefficient Correlation:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d011fd91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_of_calls</th>\n",
       "      <th>num_of_sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>num_of_calls</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.824008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>num_of_sales</th>\n",
       "      <td>0.824008</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              num_of_calls  num_of_sales\n",
       "num_of_calls      1.000000      0.824008\n",
       "num_of_sales      0.824008      1.000000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method='pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff7e9c38-b933-4d11-b84a-6972fc069602",
   "metadata": {},
   "source": [
    "**Spearman's Rank Correlation:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5d742b21-b4f4-4e15-97cd-e4e477959d42",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_of_calls</th>\n",
       "      <th>num_of_sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>num_of_calls</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.835949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>num_of_sales</th>\n",
       "      <td>0.835949</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "              num_of_calls  num_of_sales\n",
       "num_of_calls      1.000000      0.835949\n",
       "num_of_sales      0.835949      1.000000"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method='spearman')"
   ]
  }
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