Regression_Analysis_Step_by_step_Guide.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "52b0e08c",
   "metadata": {},
   "source": [
    "# Simple Linear Regression with Boston Housing dataset\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8db94b7",
   "metadata": {},
   "source": [
    "Step 1: Install and Load Necessary R Libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "41c88394",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: ‘dplyr’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:MASS’:\n",
      "\n",
      "    select\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n",
      "\n",
      "Loading required package: carData\n",
      "\n",
      "\n",
      "Attaching package: ‘car’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:dplyr’:\n",
      "\n",
      "    recode\n",
      "\n",
      "\n",
      "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n",
      "\u001b[32m✔\u001b[39m \u001b[34mforcats  \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34mstringr  \u001b[39m 1.5.1\n",
      "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.3     \u001b[32m✔\u001b[39m \u001b[34mtibble   \u001b[39m 3.2.1\n",
      "\u001b[32m✔\u001b[39m \u001b[34mpurrr    \u001b[39m 1.0.2     \u001b[32m✔\u001b[39m \u001b[34mtidyr    \u001b[39m 1.3.1\n",
      "\u001b[32m✔\u001b[39m \u001b[34mreadr    \u001b[39m 2.1.5     \n",
      "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mcar\u001b[39m::\u001b[32mrecode()\u001b[39m   masks \u001b[34mdplyr\u001b[39m::recode()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mselect()\u001b[39m masks \u001b[34mMASS\u001b[39m::select()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mpurrr\u001b[39m::\u001b[32msome()\u001b[39m   masks \u001b[34mcar\u001b[39m::some()\n",
      "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m<http://conflicted.r-lib.org/>\u001b[39m\u001b[23m) to force all conflicts to become errors\n"
     ]
    }
   ],
   "source": [
    "# Install and load necessary libraries\n",
    "#install.packages(\"ggplot2\")\n",
    "#install.packages(\"MASS\")\n",
    "library(ggplot2)\n",
    "library(MASS)  # Contains the Boston dataset\n",
    "library(dplyr)\n",
    "library(car)   # For multicollinearity diagnosis\n",
    "library(tidyverse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2ec8ab8",
   "metadata": {},
   "source": [
    "Step 2: load Explore the Data \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e49c43c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 14</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>crim</th><th scope=col>zn</th><th scope=col>indus</th><th scope=col>chas</th><th scope=col>nox</th><th scope=col>rm</th><th scope=col>age</th><th scope=col>dis</th><th scope=col>rad</th><th scope=col>tax</th><th scope=col>ptratio</th><th scope=col>black</th><th scope=col>lstat</th><th scope=col>medv</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0.00632</td><td>18</td><td>2.31</td><td>0</td><td>0.538</td><td>6.575</td><td>65.2</td><td>4.0900</td><td>1</td><td>296</td><td>15.3</td><td>396.90</td><td>4.98</td><td>24.0</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>0.02731</td><td> 0</td><td>7.07</td><td>0</td><td>0.469</td><td>6.421</td><td>78.9</td><td>4.9671</td><td>2</td><td>242</td><td>17.8</td><td>396.90</td><td>9.14</td><td>21.6</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>0.02729</td><td> 0</td><td>7.07</td><td>0</td><td>0.469</td><td>7.185</td><td>61.1</td><td>4.9671</td><td>2</td><td>242</td><td>17.8</td><td>392.83</td><td>4.03</td><td>34.7</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>0.03237</td><td> 0</td><td>2.18</td><td>0</td><td>0.458</td><td>6.998</td><td>45.8</td><td>6.0622</td><td>3</td><td>222</td><td>18.7</td><td>394.63</td><td>2.94</td><td>33.4</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>0.06905</td><td> 0</td><td>2.18</td><td>0</td><td>0.458</td><td>7.147</td><td>54.2</td><td>6.0622</td><td>3</td><td>222</td><td>18.7</td><td>396.90</td><td>5.33</td><td>36.2</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>0.02985</td><td> 0</td><td>2.18</td><td>0</td><td>0.458</td><td>6.430</td><td>58.7</td><td>6.0622</td><td>3</td><td>222</td><td>18.7</td><td>394.12</td><td>5.21</td><td>28.7</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 14\n",
       "\\begin{tabular}{r|llllllllllllll}\n",
       "  & crim & zn & indus & chas & nox & rm & age & dis & rad & tax & ptratio & black & lstat & medv\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 0.00632 & 18 & 2.31 & 0 & 0.538 & 6.575 & 65.2 & 4.0900 & 1 & 296 & 15.3 & 396.90 & 4.98 & 24.0\\\\\n",
       "\t2 & 0.02731 &  0 & 7.07 & 0 & 0.469 & 6.421 & 78.9 & 4.9671 & 2 & 242 & 17.8 & 396.90 & 9.14 & 21.6\\\\\n",
       "\t3 & 0.02729 &  0 & 7.07 & 0 & 0.469 & 7.185 & 61.1 & 4.9671 & 2 & 242 & 17.8 & 392.83 & 4.03 & 34.7\\\\\n",
       "\t4 & 0.03237 &  0 & 2.18 & 0 & 0.458 & 6.998 & 45.8 & 6.0622 & 3 & 222 & 18.7 & 394.63 & 2.94 & 33.4\\\\\n",
       "\t5 & 0.06905 &  0 & 2.18 & 0 & 0.458 & 7.147 & 54.2 & 6.0622 & 3 & 222 & 18.7 & 396.90 & 5.33 & 36.2\\\\\n",
       "\t6 & 0.02985 &  0 & 2.18 & 0 & 0.458 & 6.430 & 58.7 & 6.0622 & 3 & 222 & 18.7 & 394.12 & 5.21 & 28.7\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 14\n",
       "\n",
       "| <!--/--> | crim &lt;dbl&gt; | zn &lt;dbl&gt; | indus &lt;dbl&gt; | chas &lt;int&gt; | nox &lt;dbl&gt; | rm &lt;dbl&gt; | age &lt;dbl&gt; | dis &lt;dbl&gt; | rad &lt;int&gt; | tax &lt;dbl&gt; | ptratio &lt;dbl&gt; | black &lt;dbl&gt; | lstat &lt;dbl&gt; | medv &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 0.00632 | 18 | 2.31 | 0 | 0.538 | 6.575 | 65.2 | 4.0900 | 1 | 296 | 15.3 | 396.90 | 4.98 | 24.0 |\n",
       "| 2 | 0.02731 |  0 | 7.07 | 0 | 0.469 | 6.421 | 78.9 | 4.9671 | 2 | 242 | 17.8 | 396.90 | 9.14 | 21.6 |\n",
       "| 3 | 0.02729 |  0 | 7.07 | 0 | 0.469 | 7.185 | 61.1 | 4.9671 | 2 | 242 | 17.8 | 392.83 | 4.03 | 34.7 |\n",
       "| 4 | 0.03237 |  0 | 2.18 | 0 | 0.458 | 6.998 | 45.8 | 6.0622 | 3 | 222 | 18.7 | 394.63 | 2.94 | 33.4 |\n",
       "| 5 | 0.06905 |  0 | 2.18 | 0 | 0.458 | 7.147 | 54.2 | 6.0622 | 3 | 222 | 18.7 | 396.90 | 5.33 | 36.2 |\n",
       "| 6 | 0.02985 |  0 | 2.18 | 0 | 0.458 | 6.430 | 58.7 | 6.0622 | 3 | 222 | 18.7 | 394.12 | 5.21 | 28.7 |\n",
       "\n"
      ],
      "text/plain": [
       "  crim    zn indus chas nox   rm    age  dis    rad tax ptratio black  lstat\n",
       "1 0.00632 18 2.31  0    0.538 6.575 65.2 4.0900 1   296 15.3    396.90 4.98 \n",
       "2 0.02731  0 7.07  0    0.469 6.421 78.9 4.9671 2   242 17.8    396.90 9.14 \n",
       "3 0.02729  0 7.07  0    0.469 7.185 61.1 4.9671 2   242 17.8    392.83 4.03 \n",
       "4 0.03237  0 2.18  0    0.458 6.998 45.8 6.0622 3   222 18.7    394.63 2.94 \n",
       "5 0.06905  0 2.18  0    0.458 7.147 54.2 6.0622 3   222 18.7    396.90 5.33 \n",
       "6 0.02985  0 2.18  0    0.458 6.430 58.7 6.0622 3   222 18.7    394.12 5.21 \n",
       "  medv\n",
       "1 24.0\n",
       "2 21.6\n",
       "3 34.7\n",
       "4 33.4\n",
       "5 36.2\n",
       "6 28.7"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load the Boston dataset\n",
    "data(\"Boston\")\n",
    "\n",
    "# View the first few rows of the dataset\n",
    "head(Boston)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fc9be44",
   "metadata": {},
   "source": [
    "Step 3: Identify Outliers\n",
    "\n",
    "Use the interquartile range (IQR) method to identify outliers in the medv variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fc26a6e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       crim   zn indus chas    nox    rm   age    dis rad tax ptratio  black\n",
      "1   0.12083  0.0  2.89    0 0.4450 8.069  76.0 3.4952   2 276    18.0 396.90\n",
      "2   0.08187  0.0  2.89    0 0.4450 7.820  36.9 3.4952   2 276    18.0 393.53\n",
      "3   1.22358  0.0 19.58    0 0.6050 6.943  97.4 1.8773   5 403    14.7 363.43\n",
      "4   1.46336  0.0 19.58    0 0.6050 7.489  90.8 1.9709   5 403    14.7 374.43\n",
      "5   1.83377  0.0 19.58    1 0.6050 7.802  98.2 2.0407   5 403    14.7 389.61\n",
      "6   1.51902  0.0 19.58    1 0.6050 8.375  93.9 2.1620   5 403    14.7 388.45\n",
      "7   2.01019  0.0 19.58    0 0.6050 7.929  96.2 2.0459   5 403    14.7 369.30\n",
      "8   0.05780  0.0  2.46    0 0.4880 6.980  58.4 2.8290   3 193    17.8 396.90\n",
      "9   0.06588  0.0  2.46    0 0.4880 7.765  83.3 2.7410   3 193    17.8 395.56\n",
      "10  0.09103  0.0  2.46    0 0.4880 7.155  92.2 2.7006   3 193    17.8 394.12\n",
      "11  0.05602  0.0  2.46    0 0.4880 7.831  53.6 3.1992   3 193    17.8 392.63\n",
      "12  0.09068 45.0  3.44    0 0.4370 6.951  21.5 6.4798   5 398    15.2 377.68\n",
      "13  0.01381 80.0  0.46    0 0.4220 7.875  32.0 5.6484   4 255    14.4 394.23\n",
      "14  0.02177 82.5  2.03    0 0.4150 7.610  15.7 6.2700   2 348    14.7 395.38\n",
      "15  0.03510 95.0  2.68    0 0.4161 7.853  33.2 5.1180   4 224    14.7 392.78\n",
      "16  0.02009 95.0  2.68    0 0.4161 8.034  31.9 5.1180   4 224    14.7 390.55\n",
      "17  0.31533  0.0  6.20    0 0.5040 8.266  78.3 2.8944   8 307    17.4 385.05\n",
      "18  0.52693  0.0  6.20    0 0.5040 8.725  83.0 2.8944   8 307    17.4 382.00\n",
      "19  0.38214  0.0  6.20    0 0.5040 8.040  86.5 3.2157   8 307    17.4 387.38\n",
      "20  0.29819  0.0  6.20    0 0.5040 7.686  17.0 3.3751   8 307    17.4 377.51\n",
      "21  0.57529  0.0  6.20    0 0.5070 8.337  73.3 3.8384   8 307    17.4 385.91\n",
      "22  0.33147  0.0  6.20    0 0.5070 8.247  70.4 3.6519   8 307    17.4 378.95\n",
      "23  0.36894 22.0  5.86    0 0.4310 8.259   8.4 8.9067   7 330    19.1 396.90\n",
      "24  0.01538 90.0  3.75    0 0.3940 7.454  34.2 6.3361   3 244    15.9 386.34\n",
      "25  0.61154 20.0  3.97    0 0.6470 8.704  86.9 1.8010   5 264    13.0 389.70\n",
      "26  0.53412 20.0  3.97    0 0.6470 7.520  89.4 2.1398   5 264    13.0 388.37\n",
      "27  0.52014 20.0  3.97    0 0.6470 8.398  91.5 2.2885   5 264    13.0 386.86\n",
      "28  0.57834 20.0  3.97    0 0.5750 8.297  67.0 2.4216   5 264    13.0 384.54\n",
      "29  0.54050 20.0  3.97    0 0.5750 7.470  52.6 2.8720   5 264    13.0 390.30\n",
      "30  0.03578 20.0  3.33    0 0.4429 7.820  64.5 4.6947   5 216    14.9 387.31\n",
      "31  0.06129 20.0  3.33    1 0.4429 7.645  49.7 5.2119   5 216    14.9 377.07\n",
      "32  0.01501 90.0  1.21    1 0.4010 7.923  24.8 5.8850   1 198    13.6 395.52\n",
      "33  0.07886 80.0  4.95    0 0.4110 7.148  27.7 5.1167   4 245    19.2 396.90\n",
      "34  4.89822  0.0 18.10    0 0.6310 4.970 100.0 1.3325  24 666    20.2 375.52\n",
      "35  5.66998  0.0 18.10    1 0.6310 6.683  96.8 1.3567  24 666    20.2 375.33\n",
      "36  6.53876  0.0 18.10    1 0.6310 7.016  97.5 1.2024  24 666    20.2 392.05\n",
      "37  9.23230  0.0 18.10    0 0.6310 6.216 100.0 1.1691  24 666    20.2 366.15\n",
      "38  8.26725  0.0 18.10    1 0.6680 5.875  89.6 1.1296  24 666    20.2 347.88\n",
      "39 38.35180  0.0 18.10    0 0.6930 5.453 100.0 1.4896  24 666    20.2 396.90\n",
      "40 67.92080  0.0 18.10    0 0.6930 5.683 100.0 1.4254  24 666    20.2 384.97\n",
      "   lstat medv\n",
      "1   4.21 38.7\n",
      "2   3.57 43.8\n",
      "3   4.59 41.3\n",
      "4   1.73 50.0\n",
      "5   1.92 50.0\n",
      "6   3.32 50.0\n",
      "7   3.70 50.0\n",
      "8   5.04 37.2\n",
      "9   7.56 39.8\n",
      "10  4.82 37.9\n",
      "11  4.45 50.0\n",
      "12  5.10 37.0\n",
      "13  2.97 50.0\n",
      "14  3.11 42.3\n",
      "15  3.81 48.5\n",
      "16  2.88 50.0\n",
      "17  4.14 44.8\n",
      "18  4.63 50.0\n",
      "19  3.13 37.6\n",
      "20  3.92 46.7\n",
      "21  2.47 41.7\n",
      "22  3.95 48.3\n",
      "23  3.54 42.8\n",
      "24  3.11 44.0\n",
      "25  5.12 50.0\n",
      "26  7.26 43.1\n",
      "27  5.91 48.8\n",
      "28  7.44 50.0\n",
      "29  3.16 43.5\n",
      "30  3.76 45.4\n",
      "31  3.01 46.0\n",
      "32  3.16 50.0\n",
      "33  3.56 37.3\n",
      "34  3.26 50.0\n",
      "35  3.73 50.0\n",
      "36  2.96 50.0\n",
      "37  9.53 50.0\n",
      "38  8.88 50.0\n",
      "39 30.59  5.0\n",
      "40 22.98  5.0\n"
     ]
    }
   ],
   "source": [
    "# Calculate the IQR for medv\n",
    "Q1 <- quantile(Boston$medv, 0.25)\n",
    "Q3 <- quantile(Boston$medv, 0.75)\n",
    "IQR <- Q3 - Q1\n",
    "\n",
    "# Define outlier thresholds\n",
    "lower_bound <- Q1 - 1.5 * IQR\n",
    "upper_bound <- Q3 + 1.5 * IQR\n",
    "\n",
    "# Identify outliers\n",
    "outliers <- Boston %>%\n",
    "  filter(medv < lower_bound | medv > upper_bound)\n",
    "\n",
    "# Print outliers\n",
    "print(outliers)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd1fd448",
   "metadata": {},
   "source": [
    "Step 4: Remove Outliers\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "27aade96",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Remove outliers from the dataset\n",
    "Boston_clean <- Boston %>%\n",
    "  filter(medv >= lower_bound & medv <= upper_bound)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8079e01d",
   "metadata": {},
   "source": [
    "Step 5: Perform Linear Regression\n",
    "\n",
    "We will run a linear regression model where  medv (median value of owner-occupied homes in $1000s) is the dependent variable and lstat (percentage of lower status of the population) is the independent variable."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ea93174",
   "metadata": {},
   "source": [
    "**Null Hypothesis (H0):** There is no linear relationship between the percentage of lower status population (`lstat`) and the median value of homes (`medv`).\n",
    "\n",
    "**Alternative Hypothesis (H1):** There is a linear relationship between the percentage of lower status population (`lstat`) and the median value of homes (`medv`).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "db4f7a7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = medv ~ lstat, data = Boston_clean)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-12.6960  -2.6909  -0.7157   1.9776  14.6744 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 30.25803    0.41087   73.64   <2e-16 ***\n",
       "lstat       -0.71853    0.02744  -26.19   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 4.103 on 464 degrees of freedom\n",
       "Multiple R-squared:  0.5964,\tAdjusted R-squared:  0.5956 \n",
       "F-statistic: 685.7 on 1 and 464 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fit a linear model\n",
    "model <- lm(medv ~ lstat, data = Boston_clean)\n",
    "\n",
    "# Summary of the model\n",
    "summary(model)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd67ad34",
   "metadata": {},
   "source": [
    "\n",
    "The above linear regression analysis provides the following results:\n",
    "\n",
    "Coefficients: The slope of the regression line is negative(-0.95), indicating that as the percentage of lower status population (lstat) increases, the median value of homes (medv) decreases.\n",
    "\n",
    "R-squared value: Indicates the proportion of the variance in the dependent variable that is predictable from the independent variable.\n",
    "\n",
    "P-value: Tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value <2e-16 (< 0.05) indicates that we can reject the null hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d674163",
   "metadata": {},
   "source": [
    "Step 6: Visualize the Regression Line\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4372c89b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n"
     ]
    },
    {
     "data": {
      "image/png": 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x0hRCwWT5ky5f3793IL5+bmTp06VWmqI4Rcu3bt//7v/wghOTk5kydPll2Mz+f/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\nkEgkJh8XgxB2A59KcjKflDZ3D3w7gtZRHO5zt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5w5g9zh3bt3W7ZsgfrL8PDwuLu7b9q06Q/2JWaEmpoa82RQHBwcnEHBRoyJY6SaxVLP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\nrDHx+fzCwkLDCqPQ0KAVQd2VlJQUFhbWdy3AsKEVgS4YWLADAAAAgJo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/cavyqqoczanyKldSGM4Kjoy1f5PrGEYcv6obl+J1Xx0vVuO1\nFYr2DTfjhqypoYIAWoYxdgBSFNfau8uIz3/Yd/f+rlHuNCHC++cv5bBbtnKMu3q5wtUYa39f\nFv/h3aci6YvYQYMHNZPehGJyLp+/W+45anJf6zeHNOn6zcUn938fYVeuzqFajx4dxKl4JcvF\nzYXFMBJJ9cFGLL9PD9y5vWW0E0UIYYQFKfdPnn0iYBgJQwgR3Dx/tcSm/+j+Nm9ul9kP/miA\nTcXPuTrvSEYQeekG37rfhGGust8Spu3Hhbaik65eeVmn5RuUH5nTtu+7TsLISzf5hMm9deM5\nr+uE2b3dhZFX75YRSeb1azFUYL/3PGkNr45CtEOnj385dDs5J/P5lUMbv/l0oC//7v7lU3p2\nGLL2YWn1pyv95DVCu/l48cpvb1j469HIpCIxoWz7LNmxa/U4f5YaL67WUNW4Uiy3oZMHOryZ\nPUu7Dp/6obPw3v+uabJcSm3fvjoNSd3Gz5SkpuQSOwc7DSYCa3iV5RWcP/RvHqv18GHNWYQQ\nQnsNHBLMFt45cjxR/XF2XCcXWyY1Sf06A9QFljuBxoyyGbTi3NZ+ildNEGVl5EgEqf83oNf/\nvf0A7VBQxLz5p5NjxdeVJCMlTcTyauZV5cuZtvZoaU0I4V9S41C29nbq/aElyX2wb+26vefv\nPI1NeJVTyrJ1MGOInfSRV6nFlLO7W5UfbK67pwut/jt6gynIyCylXb09q65kwvL08WRJHqRl\nSoh/rf8oVHnkzn17Wm2/cflBef+i63fEbb7q3t27q+WGG1eflXd9eeWe2Hva+y1YRKjZ1VGK\na+8fMtI/ZOTn34myrkdMGPnlua8W/znyzLQm8k+s+ZPXDN1k8qbdMZ8u/P3LkYeWsqw82nR7\nb/DY6TPDOjjUkOyUNVRVn6c3IYTl0dSz6i97bjN/b3Z5RlqW+uGE1PLtq6qeLyEaNH5BaRmh\nzCzMa9H6arzKyo7F5J87dDafYeefXRb6QPpESVY2iwjvHDmeOGdeU/XqQfF4XCIQaF5ngNpA\njx1ADVhm5iaUw8enq61TIH69rf+br1gWS/YzxOFyCCkrUzSZUK1DUer1QpTe+ubd7hPW3bN4\nd+bKvRcfvswuSN0x1OrNsHMOm2L4xSVVUhpTJhAyGlTjDZ4JjzCl/Ldm9jKCUgFDONy6rdOm\n6sgWIX278V5dvfL88fVbhd7durpbvNOzEzvu2vWku1du8p3f6xfM1vzqyBE/+bmHa5MPtqS8\nnWzYTt0WRsxowy59fO+ZfBem0k9eDYxYLJa9ZU7T4SvPx2Um3T2za8WM911ST/40oVuXWWfz\nazO9WI0rxfBL3pppypTySxmKw+UoqP1b9ayitm9frYakZuOnzK0saKYgr0C9QFqbq/wWJv/s\nobP5xNbTmc7NrpBLu/nYU8K7GvTZMfySUmJhqeazAeoIwQ6gBpyANi3ZBfcio6v87hfH7l/y\n6YyNtxXdqPNo6W8pjr5zv8rCGgXHPw3y7frtLaLZoZQR3vxzZxTz/q/n9v/w2cj33wnytjMR\nl/IrFgOh7PxbOJOMx4/SZV85kleRkW++1zR5R5SFf4AnSb11u+rKDvzIG4/Kuf4BvnXp6ld5\nZMq+d98O9NNLh09ce2n5TrcgNuXQLSSAPLj055nrGVa9+3XmafheFKCbNLEtyrhy8kKG/Jez\nuLCgWEI7uznLd54p/eQVE5WXVzYG/otnidI7j0zBvf1rVu+4mmXq3q7/+Pk/bTv14P6699gv\njx29o/RwiqlzpUSx129mVlZFknb1SozYpkXLigWEa6hnXd++2tVTn6lXU1cqOytbvUhVi6v8\nFibv30PnClgtP997+VIV/x2a04YtvHvkbzWTHVOcmppPezVT68kAdYZgB1AD2mfEuBCTqPUL\n1jyouLdX+vT3OXNW7n1BuyjaacH83XEjXAv//r8vT6dKw0bJ/Q2/7o0u8GnTkqfhoRRgJBJJ\n5b/5xfw3C96nXfhpzbkSRsIwhBBO54/G+ouvrvvuVJqYEELKk49+u+5G2Ztbk5pUg9N+zOiW\nTGTE/E2PiwkhhIjS/v3yq32ZtgPHDqrbXgcqj0y793k/UHJj46ZIqkP3jiaEsHxDurvxL23c\n9pjXvV+IucbvpTrKdtCUkW7FpxeFfn06sTIIClPPfzt/Szyv40ejA9985av3ycs/mTIzNyMl\nty/eLJKW599Y8f2hijufFJ144v8Wzlj8x9M3Zy5JTcoqp61trWvzG1mNK8XwL/w4b/cLASGE\nMMWPf5/546Uyz5Fje5gorWc16r99zaqnwXsN6hjMy3j4sFpSU0iDq6wIk/vvoQuFrMBRo9q8\nFUBZLUaMasMW3j36d4Ja1RA9vvdY4tOhnTrPBdAC7c3DADAkNS0P9hZh9JYP3dkUx6Zpp76D\n+7Z3N6XYLgPWRwkYpmLtLt6gHTmVs+AkmadnBplRbNtmXfoN7tve3Yxiu32wLbZc5aFe/NyJ\nU7nUHMMwTOGeD03Yrb99WM4wjOjZTx04tF27kZ99dSBGxL+xtLUpxXPrNGzSlPFDQ3wdPHqP\n7uPBYrv3/mzrnRKGKbr9c28nNtfev3v/fl19HTwHfjrCl23ywe58le+omsIb33W1pSkz1za9\nB/R9p5ktm+L5jtufVLFSnOpZsbSdf9decvp+c7FUxZEZhim/tciPRQin3fdR0rKio2G2FKFM\n+vxWOQtWw6sjT1IYuXKAO4+iWBZNAjp2C+neubWXDYeiTJqO2va8Yh6sJp/8209myu59196M\noix8e4dOGjeko7sp18PX26RitmnJra/bm1OUWZPg3oOHDnm3lTOP4nqH7UtWsBKHWg1Vyecp\nTlrXk8tu2uNdXzOLJsG93g8JdDahKLOgWWeyJAzDKK9n1VmxGr39t9exU3a5VTT+alctbUs/\nc9uwo0VqtjQ1rnKlt2e2Sl7/OdSK4rT/8Wm16bmi6J87cSlu15VxYsWvlX8yz3PmpYa1cwwY\nMVZ4eHh9Z0uA+iBMfXQvy7LzkDFdax49zXJoP3L8gObmopL8fIFZ065jFm/a8eMHXtLpeyVJ\n954U+fQNe8/3TQ8RZe43YPzwtrbiouzsAsap/Yj5a7f++KH06UoPxU95+CjP4/3Q95tXrOFK\nxFlPb72yDBnxQbAdTTu0DLQuSk9Pz+W07DeoQ/C7I9/z5vDz0jNKLP16TFq+9deZA3zL01Ky\nCh3eGRbiZdGke9iod+zEhdnZ5U36fvn7ynZP1u6JCfp48dDmbBXVkMfz6PlRaEgTtiA/J19k\n6f/uxK83/f5lH5eKTg5+8oNH+V59w/r4Khhyx+RE33opsrWo1iHC8uoZ1tvHXOmRCaGdLEoe\nvpT4D/v0s+5NWIQQjh1Jf5Rl2WPSvLDgiq04Nb068ihek65jp47u4mNvRktE5SLasknrPmGz\nf9y0YVGfitknGn3yPq5Vnxzs1CRkeF9vnkiQk/g8Kknc8qPVOxf4JLyy7jm6r78Z171X6NA2\ndnRZUV5+sdjSr/eELzdsXvaei6KWqE5DVXKlmILIXevPW889/+/S5kUpya+F1i3f//i7zZvm\ndZVOLWW5KqknKU68H1Xs2y/s3WZcjkcv9d9+G17i3af8FoPG9vBkqWhIyht/tatm4fX/7d1P\nSJNxHMfx7fEfj0Ki4EXFVvMPIsjwIKHQQGqLYoQMpt0mqJcxQdjhwYsxnagEw4mxwyS7FHVK\nDyG5ivIQiGDIypps4A5CqCM6OA/Pejp4SOzQdDDHz/fr/sCP3/OF3we+v+f7FGzMBWOtg91N\nJRlUWtH/3/Jf2sG3T3GtxdJ7u1HW61Lriy+jUseA0td2eh1SZXVxIpI8KjPetTSV6v999oR0\n/Kni3bH5fdaaTD56BrKm17Tz3NYFkI+0n+EJ90Lynne69/rxKaJ+9d0w+cr931dc/IX8Mvqd\nmO1q8Ogebb9z14lRAKn37hbHj8noC0dFVlcCciP9xdfeEXZ+fuu+Jsb2I/8x7gQQiP5KfdX+\n61FXLLU3bGuuUHfXnk1NRgzOxQe1nCoQg2z2jLR3Buajdk9Gg/8u1K9w4MmhM+Qk1SF3KDZA\nJJJh4Pmbxz1lHyb671us9qH5hEl5FZ6xnmWiK5DXpKt9M4ocGl86yPd+k7oVHFu95X9oZtQJ\ncohWLCCotKpKhYUEussuFfu4vKlrvXPTKF/0UgDkAMEOAABAELRiAQAABEGwAwAAEATBDgAA\nQBAEOwAAAEEQ7AAAAARBsAMAABAEwQ4AAEAQBDsAAABBEOwAAAAE8QeVaN35ZPYgZgAAAABJ\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the data and the regression line\n",
    "ggplot(Boston, aes(x = lstat, y = medv)) +\n",
    "  geom_point() +\n",
    "  geom_smooth(method = \"lm\", col = \"blue\") +\n",
    "  labs(title = \"Linear Regression: MEDV vs LSTAT\",\n",
    "       x = \"Percentage of Lower Status Population (LSTAT)\",\n",
    "       y = \"Median Value of Homes (MEDV)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ce40ce3",
   "metadata": {},
   "source": [
    "Interpretation:\n",
    "\n",
    "Based on the results, we can conclude that there is a statistically significant negative linear relationship between the percentage of lower status population (lstat) and the median value of homes (medv). This means that as the percentage of lower status population increases, the median value of homes tends to decrease.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa628a88",
   "metadata": {},
   "source": [
    "# Multiple regression model and resolving multicollinearity issue"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd1c8501",
   "metadata": {},
   "source": [
    "Step 1: Perform Multiple Regression\n",
    "\n",
    "We will run a multiple regression model with the same Boston Housing dataset. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "785abac0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = medv ~ lstat + age + crim + indus + chas + nox + \n",
       "    rm + dis + rad + tax + ptratio + black + zn, data = Boston_clean)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.7132 -2.0649 -0.3593  1.6672 12.3615 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  39.471164   3.615425  10.917  < 2e-16 ***\n",
       "lstat        -0.376918   0.036654 -10.283  < 2e-16 ***\n",
       "age          -0.019819   0.009319  -2.127 0.033975 *  \n",
       "crim         -0.102528   0.024416  -4.199 3.23e-05 ***\n",
       "indus        -0.036373   0.043042  -0.845 0.398532    \n",
       "chas          1.067257   0.643670   1.658 0.097995 .  \n",
       "nox         -11.905541   2.624466  -4.536 7.34e-06 ***\n",
       "rm            1.883539   0.336569   5.596 3.80e-08 ***\n",
       "dis          -1.016060   0.141478  -7.182 2.85e-12 ***\n",
       "rad           0.228851   0.045792   4.998 8.31e-07 ***\n",
       "tax          -0.012057   0.002593  -4.650 4.36e-06 ***\n",
       "ptratio      -0.698618   0.091872  -7.604 1.67e-13 ***\n",
       "black         0.007295   0.001833   3.979 8.05e-05 ***\n",
       "zn            0.038380   0.010245   3.746 0.000203 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 3.191 on 452 degrees of freedom\n",
       "Multiple R-squared:  0.7622,\tAdjusted R-squared:  0.7553 \n",
       "F-statistic: 111.4 on 13 and 452 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fit a multiple regression model\n",
    "model_multiple <- lm(medv ~ lstat + age + crim + indus + chas + nox + rm + dis + rad + tax + ptratio + black + zn, data = Boston_clean)\n",
    "\n",
    "# Summary of the model\n",
    "summary(model_multiple)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af910b5e",
   "metadata": {},
   "source": [
    "Step 2: Check for Multicollinearity\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d78db489",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>lstat</dt><dd>2.94996212439051</dd><dt>age</dt><dd>3.11938282874547</dd><dt>crim</dt><dd>1.85062937977976</dd><dt>indus</dt><dd>3.90505046987397</dd><dt>chas</dt><dd>1.07081526708928</dd><dt>nox</dt><dd>4.3352133422408</dd><dt>rm</dt><dd>1.71821331466086</dd><dt>dis</dt><dd>4.12712948435875</dd><dt>rad</dt><dd>7.40263283493423</dd><dt>tax</dt><dd>8.72113433876161</dd><dt>ptratio</dt><dd>1.64086552175433</dd><dt>black</dt><dd>1.37567429328257</dd><dt>zn</dt><dd>2.35739368540262</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[lstat] 2.94996212439051\n",
       "\\item[age] 3.11938282874547\n",
       "\\item[crim] 1.85062937977976\n",
       "\\item[indus] 3.90505046987397\n",
       "\\item[chas] 1.07081526708928\n",
       "\\item[nox] 4.3352133422408\n",
       "\\item[rm] 1.71821331466086\n",
       "\\item[dis] 4.12712948435875\n",
       "\\item[rad] 7.40263283493423\n",
       "\\item[tax] 8.72113433876161\n",
       "\\item[ptratio] 1.64086552175433\n",
       "\\item[black] 1.37567429328257\n",
       "\\item[zn] 2.35739368540262\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "lstat\n",
       ":   2.94996212439051age\n",
       ":   3.11938282874547crim\n",
       ":   1.85062937977976indus\n",
       ":   3.90505046987397chas\n",
       ":   1.07081526708928nox\n",
       ":   4.3352133422408rm\n",
       ":   1.71821331466086dis\n",
       ":   4.12712948435875rad\n",
       ":   7.40263283493423tax\n",
       ":   8.72113433876161ptratio\n",
       ":   1.64086552175433black\n",
       ":   1.37567429328257zn\n",
       ":   2.35739368540262\n",
       "\n"
      ],
      "text/plain": [
       "   lstat      age     crim    indus     chas      nox       rm      dis \n",
       "2.949962 3.119383 1.850629 3.905050 1.070815 4.335213 1.718213 4.127129 \n",
       "     rad      tax  ptratio    black       zn \n",
       "7.402633 8.721134 1.640866 1.375674 2.357394 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check for multicollinearity using Variance Inflation Factor (VIF)\n",
    "vif(model_multiple)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b83ec51a",
   "metadata": {},
   "source": [
    "Step 3: Solve Multicollinearity problem in the model\n",
    "\n",
    "Method 1: Remove Highly Correlated Predictors\n",
    "\n",
    "Remove predictors with high VIF values (typically > 10).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cac2cf59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = medv ~ lstat + age + rm + dis + ptratio, data = Boston)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-15.4589  -2.9756  -0.5301   1.7054  27.7711 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 25.33065    4.11134   6.161 1.49e-09 ***\n",
       "lstat       -0.63468    0.05085 -12.481  < 2e-16 ***\n",
       "age         -0.02060    0.01350  -1.526    0.128    \n",
       "rm           4.32360    0.42828  10.095  < 2e-16 ***\n",
       "dis         -0.71106    0.16414  -4.332 1.79e-05 ***\n",
       "ptratio     -0.96601    0.11599  -8.329 7.90e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 5.132 on 500 degrees of freedom\n",
       "Multiple R-squared:  0.6917,\tAdjusted R-squared:  0.6887 \n",
       "F-statistic: 224.4 on 5 and 500 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>lstat</dt><dd>2.52871354674107</dd><dt>age</dt><dd>2.76762633536574</dd><dt>rm</dt><dd>1.73637665499154</dd><dt>dis</dt><dd>2.29088652707565</dd><dt>ptratio</dt><dd>1.20909009771782</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[lstat] 2.52871354674107\n",
       "\\item[age] 2.76762633536574\n",
       "\\item[rm] 1.73637665499154\n",
       "\\item[dis] 2.29088652707565\n",
       "\\item[ptratio] 1.20909009771782\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "lstat\n",
       ":   2.52871354674107age\n",
       ":   2.76762633536574rm\n",
       ":   1.73637665499154dis\n",
       ":   2.29088652707565ptratio\n",
       ":   1.20909009771782\n",
       "\n"
      ],
      "text/plain": [
       "   lstat      age       rm      dis  ptratio \n",
       "2.528714 2.767626 1.736377 2.290887 1.209090 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Refit the model without highly correlated predictors\n",
    "model_reduced <- lm(medv ~ lstat + age + rm + dis + ptratio, data = Boston)\n",
    "\n",
    "# Summary of the reduced model\n",
    "summary(model_reduced)\n",
    "\n",
    "# Check VIF again\n",
    "vif(model_reduced)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f0cb7d9",
   "metadata": {},
   "source": [
    "Method 2: Principal Component Regression (PCR)\n",
    "Use Principal Component Analysis (PCA) to create uncorrelated components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1f667bc1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: ‘pls’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:stats’:\n",
      "\n",
      "    loadings\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data: \tX dimension: 506 13 \n",
      "\tY dimension: 506 1\n",
      "Fit method: svdpc\n",
      "Number of components considered: 13\n",
      "\n",
      "VALIDATION: RMSEP\n",
      "Cross-validated using 10 random segments.\n",
      "       (Intercept)  1 comps  2 comps  3 comps  4 comps  5 comps  6 comps\n",
      "CV           9.206    7.297    6.810    5.574    5.377    5.139    5.125\n",
      "adjCV        9.206    7.295    6.808    5.567    5.444    5.131    5.118\n",
      "       7 comps  8 comps  9 comps  10 comps  11 comps  12 comps  13 comps\n",
      "CV       5.148    5.122    5.133     5.135      5.15     4.927     4.855\n",
      "adjCV    5.142    5.115    5.126     5.127      5.14     4.918     4.846\n",
      "\n",
      "TRAINING: % variance explained\n",
      "      1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps  8 comps\n",
      "X       47.13    58.15    67.71    74.31    80.73    85.79    89.91    92.95\n",
      "medv    37.42    45.59    63.59    64.78    69.70    70.05    70.05    70.56\n",
      "      9 comps  10 comps  11 comps  12 comps  13 comps\n",
      "X       95.08     96.78     98.21     99.51    100.00\n",
      "medv    70.57     70.89     71.30     73.21     74.06\n"
     ]
    },
    {
     "data": {
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BrCTiN8fHx6RsTn7dgjewgAAJCGsNOOXJ21/MQZ2SsAAIA0hJ12VPp5OedzjR0A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",
      "text/plain": [
       "Plot with title “medv”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Install and load necessary library\n",
    "#install.packages(\"pls\")\n",
    "library(pls)\n",
    "\n",
    "# Fit a PCR model\n",
    "pcr_model <- pcr(medv ~ ., data = Boston, scale = TRUE, validation = \"CV\")\n",
    "\n",
    "# Summary of the PCR model\n",
    "summary(pcr_model)\n",
    "\n",
    "# Plot the PCR model\n",
    "validationplot(pcr_model, val.type = \"MSEP\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11782c79",
   "metadata": {},
   "source": [
    "Conclusion\n",
    "\n",
    "The multiple regression analysis with the Boston Housing dataset identifies and addresses multicollinearity issues using two different methods:\n",
    "\n",
    "1. Removing predictors with high VIF 2.Running a reduced model with where PCA is used to consider only unccorrelated components.\n",
    "\n",
    "\n",
    "With the reduced model we have the summary which include, \n",
    "\n",
    "Coefficients: The model coefficients indicate the relationship between each predictor and the median value of homes (medv).\n",
    "\n",
    "R-squared value: Indicates the proportion of the variance in the dependent variable that is predictable from the independent variables.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "981e8796",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b86bcc",
   "metadata": {},
   "source": [
    "Example with Logistic Regression\n",
    "\n",
    "In this example, we'll use a dataset to predict whether a student is admitted to a university based on their GRE scores, GPA, and the rank of the undergraduate school.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f6a3769",
   "metadata": {},
   "source": [
    "Step 1: Install and Load Necessary R Libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "56c19fb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install and load necessary libraries\n",
    "library(ggplot2)\n",
    "library(dplyr)\n",
    "library(broom)\n",
    "library(caTools)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af50c804",
   "metadata": {},
   "source": [
    "Step 2: Create a sample dataset/load a dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ce70b245",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 12</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>PassengerId</th><th scope=col>Survived</th><th scope=col>Pclass</th><th scope=col>Name</th><th scope=col>Sex</th><th scope=col>Age</th><th scope=col>SibSp</th><th scope=col>Parch</th><th scope=col>Ticket</th><th scope=col>Fare</th><th scope=col>Cabin</th><th scope=col>Embarked</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td>0</td><td>3</td><td>Braund, Mr. Owen Harris                            </td><td>male  </td><td>22</td><td>1</td><td>0</td><td>A/5 21171       </td><td> 7.2500</td><td>    </td><td>S</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2</td><td>1</td><td>1</td><td>Cumings, Mrs. John Bradley (Florence Briggs Thayer)</td><td>female</td><td>38</td><td>1</td><td>0</td><td>PC 17599        </td><td>71.2833</td><td>C85 </td><td>C</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>3</td><td>1</td><td>3</td><td>Heikkinen, Miss. Laina                             </td><td>female</td><td>26</td><td>0</td><td>0</td><td>STON/O2. 3101282</td><td> 7.9250</td><td>    </td><td>S</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>4</td><td>1</td><td>1</td><td>Futrelle, Mrs. Jacques Heath (Lily May Peel)       </td><td>female</td><td>35</td><td>1</td><td>0</td><td>113803          </td><td>53.1000</td><td>C123</td><td>S</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>5</td><td>0</td><td>3</td><td>Allen, Mr. William Henry                           </td><td>male  </td><td>35</td><td>0</td><td>0</td><td>373450          </td><td> 8.0500</td><td>    </td><td>S</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>6</td><td>0</td><td>3</td><td>Moran, Mr. James                                   </td><td>male  </td><td>NA</td><td>0</td><td>0</td><td>330877          </td><td> 8.4583</td><td>    </td><td>Q</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 12\n",
       "\\begin{tabular}{r|llllllllllll}\n",
       "  & PassengerId & Survived & Pclass & Name & Sex & Age & SibSp & Parch & Ticket & Fare & Cabin & Embarked\\\\\n",
       "  & <int> & <int> & <int> & <chr> & <chr> & <dbl> & <int> & <int> & <chr> & <dbl> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 & 1 & 0 & 3 & Braund, Mr. Owen Harris                             & male   & 22 & 1 & 0 & A/5 21171        &  7.2500 &      & S\\\\\n",
       "\t2 & 2 & 1 & 1 & Cumings, Mrs. John Bradley (Florence Briggs Thayer) & female & 38 & 1 & 0 & PC 17599         & 71.2833 & C85  & C\\\\\n",
       "\t3 & 3 & 1 & 3 & Heikkinen, Miss. Laina                              & female & 26 & 0 & 0 & STON/O2. 3101282 &  7.9250 &      & S\\\\\n",
       "\t4 & 4 & 1 & 1 & Futrelle, Mrs. Jacques Heath (Lily May Peel)        & female & 35 & 1 & 0 & 113803           & 53.1000 & C123 & S\\\\\n",
       "\t5 & 5 & 0 & 3 & Allen, Mr. William Henry                            & male   & 35 & 0 & 0 & 373450           &  8.0500 &      & S\\\\\n",
       "\t6 & 6 & 0 & 3 & Moran, Mr. James                                    & male   & NA & 0 & 0 & 330877           &  8.4583 &      & Q\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 12\n",
       "\n",
       "| <!--/--> | PassengerId &lt;int&gt; | Survived &lt;int&gt; | Pclass &lt;int&gt; | Name &lt;chr&gt; | Sex &lt;chr&gt; | Age &lt;dbl&gt; | SibSp &lt;int&gt; | Parch &lt;int&gt; | Ticket &lt;chr&gt; | Fare &lt;dbl&gt; | Cabin &lt;chr&gt; | Embarked &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1 | 0 | 3 | Braund, Mr. Owen Harris                             | male   | 22 | 1 | 0 | A/5 21171        |  7.2500 | <!----> | S |\n",
       "| 2 | 2 | 1 | 1 | Cumings, Mrs. John Bradley (Florence Briggs Thayer) | female | 38 | 1 | 0 | PC 17599         | 71.2833 | C85  | C |\n",
       "| 3 | 3 | 1 | 3 | Heikkinen, Miss. Laina                              | female | 26 | 0 | 0 | STON/O2. 3101282 |  7.9250 | <!----> | S |\n",
       "| 4 | 4 | 1 | 1 | Futrelle, Mrs. Jacques Heath (Lily May Peel)        | female | 35 | 1 | 0 | 113803           | 53.1000 | C123 | S |\n",
       "| 5 | 5 | 0 | 3 | Allen, Mr. William Henry                            | male   | 35 | 0 | 0 | 373450           |  8.0500 | <!----> | S |\n",
       "| 6 | 6 | 0 | 3 | Moran, Mr. James                                    | male   | NA | 0 | 0 | 330877           |  8.4583 | <!----> | Q |\n",
       "\n"
      ],
      "text/plain": [
       "  PassengerId Survived Pclass\n",
       "1 1           0        3     \n",
       "2 2           1        1     \n",
       "3 3           1        3     \n",
       "4 4           1        1     \n",
       "5 5           0        3     \n",
       "6 6           0        3     \n",
       "  Name                                                Sex    Age SibSp Parch\n",
       "1 Braund, Mr. Owen Harris                             male   22  1     0    \n",
       "2 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female 38  1     0    \n",
       "3 Heikkinen, Miss. Laina                              female 26  0     0    \n",
       "4 Futrelle, Mrs. Jacques Heath (Lily May Peel)        female 35  1     0    \n",
       "5 Allen, Mr. William Henry                            male   35  0     0    \n",
       "6 Moran, Mr. James                                    male   NA  0     0    \n",
       "  Ticket           Fare    Cabin Embarked\n",
       "1 A/5 21171         7.2500       S       \n",
       "2 PC 17599         71.2833 C85   C       \n",
       "3 STON/O2. 3101282  7.9250       S       \n",
       "4 113803           53.1000 C123  S       \n",
       "5 373450            8.0500       S       \n",
       "6 330877            8.4583       Q       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Install and load the Titanic dataset\n",
    "library(titanic)\n",
    "\n",
    "# Load the Titanic dataset\n",
    "data <- titanic_train\n",
    "\n",
    "# View the first few rows of the dataset\n",
    "head(data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b672ea6d",
   "metadata": {},
   "source": [
    "The dataset contains information about the passengers on the Titanic. Key variables used in this analysis are:\n",
    "\n",
    "\n",
    "Survived: 1 if the passenger survived, 0 otherwise (dependent variable).\n",
    "\n",
    "Pclass: Passenger class (1 = 1st, 2 = 2nd, 3 = 3rd).\n",
    "\n",
    "Sex: Gender of the passenger.\n",
    "\n",
    "Age: Age of the passenger.\n",
    "\n",
    "Fare: Ticket fare.\n",
    "\n",
    "Embarked: Port of embarkation (C = Cherbourg, Q = Queenstown, S = Southampton)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a838c0a",
   "metadata": {},
   "source": [
    "Step 3: Data Preprocessing\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e37daf97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Survived</th><th scope=col>Pclass</th><th scope=col>Sex</th><th scope=col>Age</th><th scope=col>Fare</th><th scope=col>Embarked</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0</td><td>3</td><td>male  </td><td>22</td><td> 7.2500</td><td>S</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>1</td><td>1</td><td>female</td><td>38</td><td>71.2833</td><td>C</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>1</td><td>3</td><td>female</td><td>26</td><td> 7.9250</td><td>S</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>1</td><td>1</td><td>female</td><td>35</td><td>53.1000</td><td>S</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>0</td><td>3</td><td>male  </td><td>35</td><td> 8.0500</td><td>S</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>0</td><td>1</td><td>male  </td><td>54</td><td>51.8625</td><td>S</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 6\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & Survived & Pclass & Sex & Age & Fare & Embarked\\\\\n",
       "  & <int> & <fct> & <fct> & <dbl> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 0 & 3 & male   & 22 &  7.2500 & S\\\\\n",
       "\t2 & 1 & 1 & female & 38 & 71.2833 & C\\\\\n",
       "\t3 & 1 & 3 & female & 26 &  7.9250 & S\\\\\n",
       "\t4 & 1 & 1 & female & 35 & 53.1000 & S\\\\\n",
       "\t5 & 0 & 3 & male   & 35 &  8.0500 & S\\\\\n",
       "\t6 & 0 & 1 & male   & 54 & 51.8625 & S\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 6\n",
       "\n",
       "| <!--/--> | Survived &lt;int&gt; | Pclass &lt;fct&gt; | Sex &lt;fct&gt; | Age &lt;dbl&gt; | Fare &lt;dbl&gt; | Embarked &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 1 | 0 | 3 | male   | 22 |  7.2500 | S |\n",
       "| 2 | 1 | 1 | female | 38 | 71.2833 | C |\n",
       "| 3 | 1 | 3 | female | 26 |  7.9250 | S |\n",
       "| 4 | 1 | 1 | female | 35 | 53.1000 | S |\n",
       "| 5 | 0 | 3 | male   | 35 |  8.0500 | S |\n",
       "| 6 | 0 | 1 | male   | 54 | 51.8625 | S |\n",
       "\n"
      ],
      "text/plain": [
       "  Survived Pclass Sex    Age Fare    Embarked\n",
       "1 0        3      male   22   7.2500 S       \n",
       "2 1        1      female 38  71.2833 C       \n",
       "3 1        3      female 26   7.9250 S       \n",
       "4 1        1      female 35  53.1000 S       \n",
       "5 0        3      male   35   8.0500 S       \n",
       "6 0        1      male   54  51.8625 S       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data preprocessing\n",
    "data <- data %>%\n",
    "  select(Survived, Pclass, Sex, Age, Fare, Embarked) %>%\n",
    "  drop_na() %>%  # Remove rows with missing values\n",
    "  mutate(Sex = as.factor(Sex),\n",
    "         Pclass = as.factor(Pclass),\n",
    "         Embarked = as.factor(Embarked))\n",
    "\n",
    "# View the cleaned data\n",
    "head(data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "705b0806",
   "metadata": {},
   "source": [
    "### Hypothesis\n",
    "\n",
    "Null Hypothesis (H0): The independent variables do not affect the probability of the dependent variable.\n",
    "\n",
    "Alternative Hypothesis (H1): The independent variables affect the probability of the dependent variable."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6ac3350",
   "metadata": {},
   "source": [
    "Step 3: Perform Logistic Regression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1952726e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "glm(formula = Survived ~ Pclass + Sex + Age + Fare + Embarked, \n",
       "    family = binomial, data = data)\n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)  1.644e+01  6.126e+02   0.027 0.978594    \n",
       "Pclass2     -1.152e+00  3.201e-01  -3.600 0.000318 ***\n",
       "Pclass3     -2.419e+00  3.329e-01  -7.265 3.73e-13 ***\n",
       "Sexmale     -2.517e+00  2.102e-01 -11.973  < 2e-16 ***\n",
       "Age         -3.614e-02  7.790e-03  -4.640 3.49e-06 ***\n",
       "Fare        -1.306e-04  2.292e-03  -0.057 0.954563    \n",
       "EmbarkedC   -1.239e+01  6.126e+02  -0.020 0.983870    \n",
       "EmbarkedQ   -1.320e+01  6.126e+02  -0.022 0.982806    \n",
       "EmbarkedS   -1.288e+01  6.126e+02  -0.021 0.983224    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 964.52  on 713  degrees of freedom\n",
       "Residual deviance: 642.67  on 705  degrees of freedom\n",
       "AIC: 660.67\n",
       "\n",
       "Number of Fisher Scoring iterations: 13\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fit a logistic regression model\n",
    "model_logistic <- glm(Survived ~ Pclass + Sex + Age + Fare + Embarked, data = data, family = binomial)\n",
    "\n",
    "# Summary of the model\n",
    "summary(model_logistic)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5daaf1be",
   "metadata": {},
   "source": [
    "Step 4: Interpret the Model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1d47ad51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>13762381.1411689</dd><dt>Pclass2</dt><dd>0.315927659872683</dd><dt>Pclass3</dt><dd>0.0890322623842147</dd><dt>Sexmale</dt><dd>0.0807090448157914</dd><dt>Age</dt><dd>0.964502306798699</dd><dt>Fare</dt><dd>0.999869419649507</dd><dt>EmbarkedC</dt><dd>4.17813690827105e-06</dd><dt>EmbarkedQ</dt><dd>1.84652866237663e-06</dd><dt>EmbarkedS</dt><dd>2.54454491841012e-06</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 13762381.1411689\n",
       "\\item[Pclass2] 0.315927659872683\n",
       "\\item[Pclass3] 0.0890322623842147\n",
       "\\item[Sexmale] 0.0807090448157914\n",
       "\\item[Age] 0.964502306798699\n",
       "\\item[Fare] 0.999869419649507\n",
       "\\item[EmbarkedC] 4.17813690827105e-06\n",
       "\\item[EmbarkedQ] 1.84652866237663e-06\n",
       "\\item[EmbarkedS] 2.54454491841012e-06\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   13762381.1411689Pclass2\n",
       ":   0.315927659872683Pclass3\n",
       ":   0.0890322623842147Sexmale\n",
       ":   0.0807090448157914Age\n",
       ":   0.964502306798699Fare\n",
       ":   0.999869419649507EmbarkedC\n",
       ":   4.17813690827105e-06EmbarkedQ\n",
       ":   1.84652866237663e-06EmbarkedS\n",
       ":   2.54454491841012e-06\n",
       "\n"
      ],
      "text/plain": [
       " (Intercept)      Pclass2      Pclass3      Sexmale          Age         Fare \n",
       "1.376238e+07 3.159277e-01 8.903226e-02 8.070904e-02 9.645023e-01 9.998694e-01 \n",
       "   EmbarkedC    EmbarkedQ    EmbarkedS \n",
       "4.178137e-06 1.846529e-06 2.544545e-06 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exponentiate the coefficients to get the odds ratios\n",
    "exp(coef(model_logistic))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c57da98c",
   "metadata": {},
   "source": [
    "Step 5: Predict and Evaluate the Model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "aa4abd87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   \n",
       "      0   1\n",
       "  0 110  17\n",
       "  1  23  64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Split the data into training and test sets\n",
    "set.seed(123)\n",
    "split <- sample.split(data$Survived, SplitRatio = 0.7)\n",
    "training_set <- subset(data, split == TRUE)\n",
    "test_set <- subset(data, split == FALSE)\n",
    "\n",
    "# Fit the model on the training set\n",
    "model_logistic_train <- glm(Survived ~ Pclass + Sex + Age + Fare + Embarked, data = training_set, family = binomial)\n",
    "\n",
    "# Predict on the test set\n",
    "test_set$predicted_prob <- predict(model_logistic_train, newdata = test_set, type = \"response\")\n",
    "test_set$predicted_class <- ifelse(test_set$predicted_prob > 0.5, 1, 0)\n",
    "\n",
    "# Confusion matrix\n",
    "conf_matrix <- table(test_set$Survived, test_set$predicted_class)\n",
    "conf_matrix\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d448e831",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "\n",
    "#### Passenger Class (Pclass):\n",
    "\n",
    "The coefficients for Pclass indicate that passengers in higher classes (1st class) had higher odds of survival compared to those in lower classes (3rd class).\n",
    "\n",
    "The odds ratios for Pclass suggest that being in 1st class significantly increased the odds of survival, whereas being in 3rd class decreased the odds of survival.\n",
    "\n",
    "#### Sex:\n",
    "\n",
    "The coefficient for Sex (male) is negative, indicating that males had lower odds of survival compared to females.\n",
    "\n",
    "The odds ratio for Sex confirms that being female significantly increased the odds of survival.\n",
    "\n",
    "#### Age:\n",
    "\n",
    "The coefficient for Age is negative, suggesting that older passengers had lower odds of survival.\n",
    "\n",
    "The odds ratio for Age shows that as age increases, the odds of survival decrease.\n",
    "\n",
    "#### Fare:\n",
    "\n",
    "The coefficient for Fare is negative, indicating that passengers who paid lower fares(which is weird!we possibly need some preprocessing of the data) had higher odds of survival.\n",
    "\n",
    "The odds ratio for Fare suggests that lower fares are associated with increased odds of survival.\n",
    "\n",
    "#### Port of Embarkation (Embarked):\n",
    "\n",
    "The coefficients for Embarked indicate differences in survival odds based on the port of embarkation.\n",
    "\n",
    "The odds ratios for Embarked suggest that passengers who embarked from Cherbourg (C) had higher odds of survival \n",
    "\n",
    "compared to those who embarked from Southampton (S).\n",
    "\n",
    "#### Model Evaluation:\n",
    "\n",
    "The confusion matrix indicates that the logistic regression model correctly predicted survival for a significant proportion of the test set.\n",
    "\n",
    "The exact accuracy, sensitivity, and specificity can be calculated from the confusion matrix as needed.\n",
    "\n",
    "\n",
    "### Interpretation\n",
    "\n",
    "Based on the results of the logistic regression analysis, we can conclude that passenger class, sex, age, fare, and port of embarkation significantly affect the probability of survival on the Titanic. The logistic regression model provides valuable insights into the factors that influenced survival during the Titanic disaster.\n",
    "\n",
    "\n",
    "We will dive into deeper in another notebook. However, this is precisely how we run and interpret a logistic regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07f70585",
   "metadata": {},
   "source": [
    "# Polynomial regression model\n",
    "\n",
    "Polynomial regression is a type of regression analysis in which the relationship between the independent variable \n",
    "$x$ and the dependent variable  $𝑦$ is modeled as an nth degree polynomial. It can be useful for capturing non-linear relationships.here is an example of polynomial regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4b91aa6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>x</th><th scope=col>y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>-10.000000</td><td>-766.0476</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> -9.797980</td><td>-695.1216</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> -9.595960</td><td>-479.6997</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> -9.393939</td><td>-593.3245</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> -9.191919</td><td>-553.5649</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> -8.989899</td><td>-362.3941</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & x & y\\\\\n",
       "  & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & -10.000000 & -766.0476\\\\\n",
       "\t2 &  -9.797980 & -695.1216\\\\\n",
       "\t3 &  -9.595960 & -479.6997\\\\\n",
       "\t4 &  -9.393939 & -593.3245\\\\\n",
       "\t5 &  -9.191919 & -553.5649\\\\\n",
       "\t6 &  -8.989899 & -362.3941\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | x &lt;dbl&gt; | y &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 1 | -10.000000 | -766.0476 |\n",
       "| 2 |  -9.797980 | -695.1216 |\n",
       "| 3 |  -9.595960 | -479.6997 |\n",
       "| 4 |  -9.393939 | -593.3245 |\n",
       "| 5 |  -9.191919 | -553.5649 |\n",
       "| 6 |  -8.989899 | -362.3941 |\n",
       "\n"
      ],
      "text/plain": [
       "  x          y        \n",
       "1 -10.000000 -766.0476\n",
       "2  -9.797980 -695.1216\n",
       "3  -9.595960 -479.6997\n",
       "4  -9.393939 -593.3245\n",
       "5  -9.191919 -553.5649\n",
       "6  -8.989899 -362.3941"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load necessary libraries\n",
    "library(ggplot2)\n",
    "\n",
    "# Generate synthetic data\n",
    "set.seed(123)\n",
    "x <- seq(-10, 10, length.out = 100)\n",
    "y <- 0.5 * x^3 - 2 * x^2 + x + rnorm(100, mean = 0, sd = 100)\n",
    "\n",
    "# Combine into a data frame\n",
    "data <- data.frame(x, y)\n",
    "\n",
    "# View the first few rows of the dataset\n",
    "head(data)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4753b8cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ poly(x, 3, raw = TRUE), data = data)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-239.329  -59.982   -2.484   66.930  218.883 \n",
       "\n",
       "Coefficients:\n",
       "                        Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)             -1.46156   13.78543  -0.106    0.916    \n",
       "poly(x, 3, raw = TRUE)1  1.79321    3.94097   0.455    0.650    \n",
       "poly(x, 3, raw = TRUE)2 -1.69117    0.30217  -5.597 2.06e-07 ***\n",
       "poly(x, 3, raw = TRUE)3  0.50735    0.05902   8.596 1.53e-13 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 91.9 on 96 degrees of freedom\n",
       "Multiple R-squared:  0.849,\tAdjusted R-squared:  0.8443 \n",
       "F-statistic: 179.9 on 3 and 96 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FFOASDYAQAAAHwgIyOjQO2WA8EOAAAA4ANVq1bN2SiTycqVK2f+YgoEwQ4AAADg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\nz9+wYcPYsWNnz5594cIFTYcDdISSY+zwJhOXjt8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Dg1m2tvKwsEIDA8jqQL1UaedcfHx8YWEhn89Xf0PvyzwAACAASURBVDwAAM2CW7FA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\nyidlomdB/Vu59J+xdEPwngPnnuXJc64u9Wnu4BFwKb3698uk7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zZu3FitWrWbHhkdLU+ZYg4JUV591XtzJrLUq1fv888/Hz9+fExMjBAi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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fit a polynomial regression model of degree 3\n",
    "model_poly <- lm(y ~ poly(x, 3, raw = TRUE), data = data)\n",
    "\n",
    "# Summary of the model\n",
    "summary(model_poly)\n",
    "\n",
    "# Create a sequence of x values for predictions\n",
    "x_pred <- seq(min(x), max(x), length.out = 100)\n",
    "\n",
    "# Predict y values using the polynomial model\n",
    "y_pred <- predict(model_poly, newdata = data.frame(x = x_pred))\n",
    "\n",
    "# Plot the data and the polynomial regression line\n",
    "ggplot(data, aes(x = x, y = y)) +\n",
    "  geom_point() +\n",
    "  geom_line(aes(x = x_pred, y = y_pred), color = \"blue\") +\n",
    "  labs(title = \"Polynomial Regression of Degree 3\",\n",
    "       x = \"Independent Variable (x)\",\n",
    "       y = \"Dependent Variable (y)\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4cabba30",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.3.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}