From 3d767613cec16a0148f9ee21be354081853a3b26 Mon Sep 17 00:00:00 2001
From: Ayush Singh <81796368+ayush714@users.noreply.github.com>
Date: Sun, 22 Aug 2021 20:13:45 +0530
Subject: [PATCH] Notebook_Julia_Editing_Linear_Regression.ipynb

Notebook_Julia_Editing_Linear_Regression.ipynb
---
 ...book_Julia_Editing_Linear_Regression.ipynb | 2500 +++++++++++++++++
 1 file changed, 2500 insertions(+)
 create mode 100644 2-Regression/3-Linear/solution/Notebook_Julia_Editing_Linear_Regression.ipynb

diff --git a/2-Regression/3-Linear/solution/Notebook_Julia_Editing_Linear_Regression.ipynb b/2-Regression/3-Linear/solution/Notebook_Julia_Editing_Linear_Regression.ipynb
new file mode 100644
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--- /dev/null
+++ b/2-Regression/3-Linear/solution/Notebook_Julia_Editing_Linear_Regression.ipynb
@@ -0,0 +1,2500 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Linear Regression using Julia  \n",
+    "\n",
+    "In this notebook, I presented Julia version of the solutions, Here I have used Linear Regression on Boston dataset, This notebook does not contain polynomial regression part, because It is still in progress. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# import Pkg\n",
+    "# Pkg.add(\"Plots\")\n",
+    "# Pkg.add(\"Lathe\")\n",
+    "# Pkg.add(\"GLM\")\n",
+    "# Pkg.add(\"StatsPlots\")\n",
+    "# Pkg.add(\"MLBase\")\n",
+    "# Pkg.add(\"Metrics\")  \n",
+    "\n",
+    "# Uncomment this if you haven't installed the above libraries "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# packages we will use \n",
+    "using Plots\n",
+    "using Lathe\n",
+    "using GLM\n",
+    "using Statistics\n",
+    "using StatsPlots\n",
+    "using MLBase  \n",
+    "using Metrics  \n",
+    "using DataFrames, CSV\n",
+    "using Polynomials"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div class=\"data-frame\"><p>5 rows × 14 columns (omitted printing of 5 columns)</p><table class=\"data-frame\"><thead><tr><th></th><th>CRIM</th><th>ZN</th><th>INDUS</th><th>CHAS</th><th>NOX</th><th>RM</th><th>AGE</th><th>DIS</th><th>RAD</th></tr><tr><th></th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>0.00632</td><td>18.0</td><td>2.31</td><td>0.0</td><td>0.538</td><td>6.575</td><td>65.2</td><td>4.09</td><td>1.0</td></tr><tr><th>2</th><td>0.02731</td><td>0.0</td><td>7.07</td><td>0.0</td><td>0.469</td><td>6.421</td><td>78.9</td><td>4.9671</td><td>2.0</td></tr><tr><th>3</th><td>0.02729</td><td>0.0</td><td>7.07</td><td>0.0</td><td>0.469</td><td>7.185</td><td>61.1</td><td>4.9671</td><td>2.0</td></tr><tr><th>4</th><td>0.03237</td><td>0.0</td><td>2.18</td><td>0.0</td><td>0.458</td><td>6.998</td><td>45.8</td><td>6.0622</td><td>3.0</td></tr><tr><th>5</th><td>0.06905</td><td>0.0</td><td>2.18</td><td>0.0</td><td>0.458</td><td>7.147</td><td>54.2</td><td>6.0622</td><td>3.0</td></tr></tbody></table></div>"
+      ],
+      "text/latex": [
+       "\\begin{tabular}{r|cccccccccc}\n",
+       "\t& CRIM & ZN & INDUS & CHAS & NOX & RM & AGE & DIS & RAD & \\\\\n",
+       "\t\\hline\n",
+       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
+       "\t\\hline\n",
+       "\t1 & 0.00632 & 18.0 & 2.31 & 0.0 & 0.538 & 6.575 & 65.2 & 4.09 & 1.0 & $\\dots$ \\\\\n",
+       "\t2 & 0.02731 & 0.0 & 7.07 & 0.0 & 0.469 & 6.421 & 78.9 & 4.9671 & 2.0 & $\\dots$ \\\\\n",
+       "\t3 & 0.02729 & 0.0 & 7.07 & 0.0 & 0.469 & 7.185 & 61.1 & 4.9671 & 2.0 & $\\dots$ \\\\\n",
+       "\t4 & 0.03237 & 0.0 & 2.18 & 0.0 & 0.458 & 6.998 & 45.8 & 6.0622 & 3.0 & $\\dots$ \\\\\n",
+       "\t5 & 0.06905 & 0.0 & 2.18 & 0.0 & 0.458 & 7.147 & 54.2 & 6.0622 & 3.0 & $\\dots$ \\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/plain": [
+       "\u001b[1m5×14 DataFrame\u001b[0m\n",
+       "\u001b[1m Row \u001b[0m│\u001b[1m CRIM    \u001b[0m\u001b[1m ZN      \u001b[0m\u001b[1m INDUS   \u001b[0m\u001b[1m CHAS    \u001b[0m\u001b[1m NOX     \u001b[0m\u001b[1m RM      \u001b[0m\u001b[1m AGE     \u001b[0m\u001b[1m DIS     \u001b[0m\u001b[1m\u001b[0m ⋯\n",
+       "\u001b[1m     \u001b[0m│\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m\u001b[0m ⋯\n",
+       "─────┼──────────────────────────────────────────────────────────────────────────\n",
+       "   1 │ 0.00632     18.0     2.31      0.0    0.538    6.575     65.2   4.09    ⋯\n",
+       "   2 │ 0.02731      0.0     7.07      0.0    0.469    6.421     78.9   4.9671\n",
+       "   3 │ 0.02729      0.0     7.07      0.0    0.469    7.185     61.1   4.9671\n",
+       "   4 │ 0.03237      0.0     2.18      0.0    0.458    6.998     45.8   6.0622\n",
+       "   5 │ 0.06905      0.0     2.18      0.0    0.458    7.147     54.2   6.0622  ⋯\n",
+       "\u001b[36m                                                               6 columns omitted\u001b[0m"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# loading the data  \n",
+    "\n",
+    "df = CSV.read(\"data\\\\out.csv\", DataFrame)\n",
+    "first(df,5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(506, 14)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# printing the size of the data \n",
+    "\n",
+    "println(size(df))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div class=\"data-frame\"><p>14 rows × 7 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>variable</th><th>mean</th><th>min</th><th>median</th><th>max</th><th>nmissing</th><th>eltype</th></tr><tr><th></th><th title=\"Symbol\">Symbol</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th><th title=\"DataType\">DataType</th></tr></thead><tbody><tr><th>1</th><td>CRIM</td><td>3.61352</td><td>0.00632</td><td>0.25651</td><td>88.9762</td><td>0</td><td>Float64</td></tr><tr><th>2</th><td>ZN</td><td>11.3636</td><td>0.0</td><td>0.0</td><td>100.0</td><td>0</td><td>Float64</td></tr><tr><th>3</th><td>INDUS</td><td>11.1368</td><td>0.46</td><td>9.69</td><td>27.74</td><td>0</td><td>Float64</td></tr><tr><th>4</th><td>CHAS</td><td>0.06917</td><td>0.0</td><td>0.0</td><td>1.0</td><td>0</td><td>Float64</td></tr><tr><th>5</th><td>NOX</td><td>0.554695</td><td>0.385</td><td>0.538</td><td>0.871</td><td>0</td><td>Float64</td></tr><tr><th>6</th><td>RM</td><td>6.28463</td><td>3.561</td><td>6.2085</td><td>8.78</td><td>0</td><td>Float64</td></tr><tr><th>7</th><td>AGE</td><td>68.5749</td><td>2.9</td><td>77.5</td><td>100.0</td><td>0</td><td>Float64</td></tr><tr><th>8</th><td>DIS</td><td>3.79504</td><td>1.1296</td><td>3.20745</td><td>12.1265</td><td>0</td><td>Float64</td></tr><tr><th>9</th><td>RAD</td><td>9.54941</td><td>1.0</td><td>5.0</td><td>24.0</td><td>0</td><td>Float64</td></tr><tr><th>10</th><td>TAX</td><td>408.237</td><td>187.0</td><td>330.0</td><td>711.0</td><td>0</td><td>Float64</td></tr><tr><th>11</th><td>PTRATIO</td><td>18.4555</td><td>12.6</td><td>19.05</td><td>22.0</td><td>0</td><td>Float64</td></tr><tr><th>12</th><td>B</td><td>356.674</td><td>0.32</td><td>391.44</td><td>396.9</td><td>0</td><td>Float64</td></tr><tr><th>13</th><td>LSTAT</td><td>12.6531</td><td>1.73</td><td>11.36</td><td>37.97</td><td>0</td><td>Float64</td></tr><tr><th>14</th><td>SalePrice</td><td>22.5328</td><td>5.0</td><td>21.2</td><td>50.0</td><td>0</td><td>Float64</td></tr></tbody></table></div>"
+      ],
+      "text/latex": [
+       "\\begin{tabular}{r|ccccccc}\n",
+       "\t& variable & mean & min & median & max & nmissing & eltype\\\\\n",
+       "\t\\hline\n",
+       "\t& Symbol & Float64 & Float64 & Float64 & Float64 & Int64 & DataType\\\\\n",
+       "\t\\hline\n",
+       "\t1 & CRIM & 3.61352 & 0.00632 & 0.25651 & 88.9762 & 0 & Float64 \\\\\n",
+       "\t2 & ZN & 11.3636 & 0.0 & 0.0 & 100.0 & 0 & Float64 \\\\\n",
+       "\t3 & INDUS & 11.1368 & 0.46 & 9.69 & 27.74 & 0 & Float64 \\\\\n",
+       "\t4 & CHAS & 0.06917 & 0.0 & 0.0 & 1.0 & 0 & Float64 \\\\\n",
+       "\t5 & NOX & 0.554695 & 0.385 & 0.538 & 0.871 & 0 & Float64 \\\\\n",
+       "\t6 & RM & 6.28463 & 3.561 & 6.2085 & 8.78 & 0 & Float64 \\\\\n",
+       "\t7 & AGE & 68.5749 & 2.9 & 77.5 & 100.0 & 0 & Float64 \\\\\n",
+       "\t8 & DIS & 3.79504 & 1.1296 & 3.20745 & 12.1265 & 0 & Float64 \\\\\n",
+       "\t9 & RAD & 9.54941 & 1.0 & 5.0 & 24.0 & 0 & Float64 \\\\\n",
+       "\t10 & TAX & 408.237 & 187.0 & 330.0 & 711.0 & 0 & Float64 \\\\\n",
+       "\t11 & PTRATIO & 18.4555 & 12.6 & 19.05 & 22.0 & 0 & Float64 \\\\\n",
+       "\t12 & B & 356.674 & 0.32 & 391.44 & 396.9 & 0 & Float64 \\\\\n",
+       "\t13 & LSTAT & 12.6531 & 1.73 & 11.36 & 37.97 & 0 & Float64 \\\\\n",
+       "\t14 & SalePrice & 22.5328 & 5.0 & 21.2 & 50.0 & 0 & Float64 \\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/plain": [
+       "\u001b[1m14×7 DataFrame\u001b[0m\n",
+       "\u001b[1m Row \u001b[0m│\u001b[1m variable  \u001b[0m\u001b[1m mean       \u001b[0m\u001b[1m min       \u001b[0m\u001b[1m median    \u001b[0m\u001b[1m max      \u001b[0m\u001b[1m nmissing \u001b[0m\u001b[1m eltype\u001b[0m ⋯\n",
+       "\u001b[1m     \u001b[0m│\u001b[90m Symbol    \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Int64    \u001b[0m\u001b[90m DataTy\u001b[0m ⋯\n",
+       "─────┼──────────────────────────────────────────────────────────────────────────\n",
+       "   1 │ CRIM         3.61352     0.00632    0.25651   88.9762         0  Float6 ⋯\n",
+       "   2 │ ZN          11.3636      0.0        0.0      100.0            0  Float6\n",
+       "   3 │ INDUS       11.1368      0.46       9.69      27.74           0  Float6\n",
+       "   4 │ CHAS         0.06917     0.0        0.0        1.0            0  Float6\n",
+       "   5 │ NOX          0.554695    0.385      0.538      0.871          0  Float6 ⋯\n",
+       "   6 │ RM           6.28463     3.561      6.2085     8.78           0  Float6\n",
+       "   7 │ AGE         68.5749      2.9       77.5      100.0            0  Float6\n",
+       "   8 │ DIS          3.79504     1.1296     3.20745   12.1265         0  Float6\n",
+       "   9 │ RAD          9.54941     1.0        5.0       24.0            0  Float6 ⋯\n",
+       "  10 │ TAX        408.237     187.0      330.0      711.0            0  Float6\n",
+       "  11 │ PTRATIO     18.4555     12.6       19.05      22.0            0  Float6\n",
+       "  12 │ B          356.674       0.32     391.44     396.9            0  Float6\n",
+       "  13 │ LSTAT       12.6531      1.73      11.36      37.97           0  Float6 ⋯\n",
+       "  14 │ SalePrice   22.5328      5.0       21.2       50.0            0  Float6\n",
+       "\u001b[36m                                                                1 column omitted\u001b[0m"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# describing the data \n",
+    "\n",
+    "describe(df)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "14-element Vector{String}:\n",
+       " \"CRIM\"\n",
+       " \"ZN\"\n",
+       " \"INDUS\"\n",
+       " \"CHAS\"\n",
+       " \"NOX\"\n",
+       " \"RM\"\n",
+       " \"AGE\"\n",
+       " \"DIS\"\n",
+       " \"RAD\"\n",
+       " \"TAX\"\n",
+       " \"PTRATIO\"\n",
+       " \"B\"\n",
+       " \"LSTAT\"\n",
+       " \"SalePrice\""
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# printing the names of the dataframe \n",
+    "\n",
+    "names(df)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
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+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# boxplot for out target variable \n",
+    "\n",
+    "boxplot(df.SalePrice, title = \"Box Plot - SalePrice\", ylabel = \"CRIM\", legend = false)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
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+       "</svg>\n"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# correlation plot \n",
+    "\n",
+    "train_plot = scatter(df.CRIM,df.SalePrice, title = \"Scatter Plot CRIM vs SalePrice\", ylabel = \"CRIM\", xlabel = \"SalePrice\",legend = false)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
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+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "train_plot = scatter(df.INDUS,df.SalePrice, title = \"Scatter Plot INDUS vs SalePrice\", ylabel = \"INDUS\", xlabel = \"SalePrice\",legend = false)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
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+       "</svg>\n"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "train_plot = scatter(df.TAX,df.SalePrice, title = \"Scatter Plot TAX vs SalePrice\", ylabel = \"TAX\", xlabel = \"SalePrice\",legend = false)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div class=\"data-frame\"><p>5 rows × 14 columns (omitted printing of 5 columns)</p><table class=\"data-frame\"><thead><tr><th></th><th>CRIM</th><th>ZN</th><th>INDUS</th><th>CHAS</th><th>NOX</th><th>RM</th><th>AGE</th><th>DIS</th><th>RAD</th></tr><tr><th></th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>0.02731</td><td>0.0</td><td>7.07</td><td>0.0</td><td>0.469</td><td>6.421</td><td>78.9</td><td>4.9671</td><td>2.0</td></tr><tr><th>2</th><td>0.02729</td><td>0.0</td><td>7.07</td><td>0.0</td><td>0.469</td><td>7.185</td><td>61.1</td><td>4.9671</td><td>2.0</td></tr><tr><th>3</th><td>0.03237</td><td>0.0</td><td>2.18</td><td>0.0</td><td>0.458</td><td>6.998</td><td>45.8</td><td>6.0622</td><td>3.0</td></tr><tr><th>4</th><td>0.06905</td><td>0.0</td><td>2.18</td><td>0.0</td><td>0.458</td><td>7.147</td><td>54.2</td><td>6.0622</td><td>3.0</td></tr><tr><th>5</th><td>0.08829</td><td>12.5</td><td>7.87</td><td>0.0</td><td>0.524</td><td>6.012</td><td>66.6</td><td>5.5605</td><td>5.0</td></tr></tbody></table></div>"
+      ],
+      "text/latex": [
+       "\\begin{tabular}{r|cccccccccc}\n",
+       "\t& CRIM & ZN & INDUS & CHAS & NOX & RM & AGE & DIS & RAD & \\\\\n",
+       "\t\\hline\n",
+       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
+       "\t\\hline\n",
+       "\t1 & 0.02731 & 0.0 & 7.07 & 0.0 & 0.469 & 6.421 & 78.9 & 4.9671 & 2.0 & $\\dots$ \\\\\n",
+       "\t2 & 0.02729 & 0.0 & 7.07 & 0.0 & 0.469 & 7.185 & 61.1 & 4.9671 & 2.0 & $\\dots$ \\\\\n",
+       "\t3 & 0.03237 & 0.0 & 2.18 & 0.0 & 0.458 & 6.998 & 45.8 & 6.0622 & 3.0 & $\\dots$ \\\\\n",
+       "\t4 & 0.06905 & 0.0 & 2.18 & 0.0 & 0.458 & 7.147 & 54.2 & 6.0622 & 3.0 & $\\dots$ \\\\\n",
+       "\t5 & 0.08829 & 12.5 & 7.87 & 0.0 & 0.524 & 6.012 & 66.6 & 5.5605 & 5.0 & $\\dots$ \\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/plain": [
+       "\u001b[1m5×14 DataFrame\u001b[0m\n",
+       "\u001b[1m Row \u001b[0m│\u001b[1m CRIM    \u001b[0m\u001b[1m ZN      \u001b[0m\u001b[1m INDUS   \u001b[0m\u001b[1m CHAS    \u001b[0m\u001b[1m NOX     \u001b[0m\u001b[1m RM      \u001b[0m\u001b[1m AGE     \u001b[0m\u001b[1m DIS     \u001b[0m\u001b[1m\u001b[0m ⋯\n",
+       "\u001b[1m     \u001b[0m│\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m\u001b[0m ⋯\n",
+       "─────┼──────────────────────────────────────────────────────────────────────────\n",
+       "   1 │ 0.02731      0.0     7.07      0.0    0.469    6.421     78.9   4.9671  ⋯\n",
+       "   2 │ 0.02729      0.0     7.07      0.0    0.469    7.185     61.1   4.9671\n",
+       "   3 │ 0.03237      0.0     2.18      0.0    0.458    6.998     45.8   6.0622\n",
+       "   4 │ 0.06905      0.0     2.18      0.0    0.458    7.147     54.2   6.0622\n",
+       "   5 │ 0.08829     12.5     7.87      0.0    0.524    6.012     66.6   5.5605  ⋯\n",
+       "\u001b[36m                                                               6 columns omitted\u001b[0m"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Train test split for diving our data \n",
+    "\n",
+    "using Lathe.preprocess: TrainTestSplit\n",
+    "train, test = TrainTestSplit(df,.75) \n",
+    "first(train, 5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(388, 14)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# taking a look at the size of training data \n",
+    "\n",
+    "println(size(train))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(118, 14)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# taking a look at the size of testing data \n",
+    "\n",
+    "println(size(test))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
+       "\n",
+       "SalePrice ~ 1 + CRIM + ZN + INDUS + CHAS + NOX + RM + AGE + DIS + RAD + TAX + PTRATIO + B + LSTAT\n",
+       "\n",
+       "Coefficients:\n",
+       "────────────────────────────────────────────────────────────────────────────────\n",
+       "                   Coef.  Std. Error      t  Pr(>|t|)     Lower 95%    Upper 95%\n",
+       "────────────────────────────────────────────────────────────────────────────────\n",
+       "(Intercept)   32.2344     6.18734      5.21    <1e-06   20.068       44.4007\n",
+       "CRIM          -0.096813   0.0353805   -2.74    0.0065   -0.166383    -0.0272434\n",
+       "ZN             0.0559225  0.0155536    3.60    0.0004    0.0253389    0.086506\n",
+       "INDUS          0.037159   0.0711401    0.52    0.6017   -0.102726     0.177044\n",
+       "CHAS           2.63139    1.02384      2.57    0.0106    0.618184     4.6446\n",
+       "NOX          -12.7104     4.50354     -2.82    0.0050  -21.5658      -3.85495\n",
+       "RM             3.86041    0.495463     7.79    <1e-13    2.88616      4.83465\n",
+       "AGE           -0.0029226  0.0157267   -0.19    0.8527   -0.0338464    0.0280012\n",
+       "DIS           -1.41053    0.235675    -5.99    <1e-08   -1.87395     -0.947119\n",
+       "RAD            0.285815   0.075898     3.77    0.0002    0.136575     0.435056\n",
+       "TAX           -0.0119566  0.00427923  -2.79    0.0055   -0.0203709   -0.00354219\n",
+       "PTRATIO       -0.919455   0.154836    -5.94    <1e-08   -1.22391     -0.614998\n",
+       "B              0.0114862  0.00308641   3.72    0.0002    0.00541735   0.0175551\n",
+       "LSTAT         -0.580496   0.0639863   -9.07    <1e-17   -0.706314    -0.454678\n",
+       "────────────────────────────────────────────────────────────────────────────────"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# building linear regression model with all the features and one target variable \n",
+    "\n",
+    "fm = @formula(SalePrice ~ CRIM + ZN + INDUS + CHAS + NOX + RM + AGE + DIS + RAD + TAX + PTRATIO + B + LSTAT) \n",
+    "linearregressor = lm(fm, train)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "118-element Vector{Union{Missing, Float64}}:\n",
+       " 30.257569399329533\n",
+       " 25.102897520234006\n",
+       " 10.213362687396213\n",
+       " 18.30609647011218\n",
+       " 15.918702530891178\n",
+       " 18.285305920340207\n",
+       " 11.723530559085212\n",
+       " 17.367774990939857\n",
+       " 15.245581037686078\n",
+       " 19.327415627467538\n",
+       "  7.4161933158744695\n",
+       " 23.451131696858674\n",
+       " 22.92595266546901\n",
+       "  ⋮\n",
+       " 18.773461129422785\n",
+       " 22.759388697901052\n",
+       " 19.0436268251718\n",
+       " 20.536792254149326\n",
+       " 19.82291469224453\n",
+       " 25.6867877444079\n",
+       " 15.067772405729784\n",
+       " 19.393643735031073\n",
+       " 22.371533915466763\n",
+       " 19.451521650198\n",
+       "  2.897763250285564\n",
+       " 21.227743510092843"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# making predictions \n",
+    "\n",
+    "y_predicted = predict(linearregressor, test) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "R2 Score0.7483442644093596\n",
+      "MAE 3.269229661186728\n",
+      "RMSE:- 4.548533879113553\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Evaluating our model using MAE \n",
+    "\n",
+    "println(\"R2 Score\", r2(linearregressor)) \n",
+    "println(\"MAE \", Metrics.mae(y_predicted, test.SalePrice))  \n",
+    "MSE = Metrics.mse(y_predicted, test.SalePrice) \n",
+    "println(\"RMSE:- \", sqrt(MSE)) \n",
+    "\n",
+    "\n",
+    "# here our model is performing bad because linear regression does not works well on non-linear data and with some other assumptions which are:- \n",
+    "# Linear relationship.\n",
+    "# Multivariate normality.\n",
+    "# No or little multicollinearity.\n",
+    "# No auto-correlation.\n",
+    "# Homoscedasticity\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.6.2",
+   "language": "julia",
+   "name": "julia-1.6"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.6.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}