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ML-For-Beginners/2-Regression/3-Linear/solution/Notebook_Julia_Editing_Line...

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{
"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>"
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"\\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"
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"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>"
],
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"\\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",
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"─────┼──────────────────────────────────────────────────────────────────────────\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": {},
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}
],
"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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],
"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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]
},
"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
}
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