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CPSC 375 Examples - Linear Regression
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regression-examples.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
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"source": [
"<a href=\"https://colab.research.google.com/gist/ProfAvery/114e7d50a8c3a546b7413981370777e1/regression-examples.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "h6SOxm7V2meC"
},
"source": [
"# CPSC 375 Examples - Linear Regression"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "TiGPqnCW2meQ",
"outputId": "0effc0de-dac4-40e2-a5db-e127e34f202a"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Collecting lets-plot\n",
" Downloading lets_plot-4.5.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (11 kB)\n",
"Collecting ucimlrepo\n",
" Downloading ucimlrepo-0.0.7-py3-none-any.whl.metadata (5.5 kB)\n",
"Collecting pypng (from lets-plot)\n",
" Downloading pypng-0.20220715.0-py3-none-any.whl.metadata (13 kB)\n",
"Collecting palettable (from lets-plot)\n",
" Downloading palettable-3.3.3-py2.py3-none-any.whl.metadata (3.3 kB)\n",
"Requirement already satisfied: pandas>=1.0.0 in /usr/local/lib/python3.10/dist-packages (from ucimlrepo) (2.2.2)\n",
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"Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=1.0.0->ucimlrepo) (2024.2)\n",
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"Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.2->pandas>=1.0.0->ucimlrepo) (1.16.0)\n",
"Downloading lets_plot-4.5.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (3.4 MB)\n",
"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.4/3.4 MB\u001b[0m \u001b[31m15.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
"\u001b[?25hDownloading ucimlrepo-0.0.7-py3-none-any.whl (8.0 kB)\n",
"Downloading palettable-3.3.3-py2.py3-none-any.whl (332 kB)\n",
"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m332.3/332.3 kB\u001b[0m \u001b[31m6.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
"\u001b[?25hDownloading pypng-0.20220715.0-py3-none-any.whl (58 kB)\n",
"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m58.1/58.1 kB\u001b[0m \u001b[31m2.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
"\u001b[?25hInstalling collected packages: pypng, palettable, lets-plot, ucimlrepo\n",
"Successfully installed lets-plot-4.5.0 palettable-3.3.3 pypng-0.20220715.0 ucimlrepo-0.0.7\n"
]
}
],
"source": [
"%pip install lets-plot ucimlrepo\n",
"\n",
"from lets_plot import *\n",
"from ucimlrepo import fetch_ucirepo\n",
"\n",
"LetsPlot.setup_html()\n",
"auto_mpg = fetch_ucirepo(id=9)"
]
},
{
"cell_type": "code",
"source": [
"autompg = auto_mpg.data.original\n",
"autompg.cylinders = autompg.cylinders.astype('str').astype('category')"
],
"metadata": {
"id": "TuMlatWJ39-i"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "EavLIivi2mek"
},
"source": [
"## Part 8 - Slide 54"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Weq0YCgy2mel"
},
"source": [
"Consider the `auto_mpg.data.original` dataset.\n",
"\n",
"> The goal is to model mpg given engine displacement (a continuous variable) and number of cylinders (pretend this is a categorical variable).\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 206
},
"id": "tHd2kdIK2mey",
"outputId": "19af6098-0895-44a7-bfc5-254d84434d4b"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" car_name cylinders displacement horsepower weight \\\n",
"0 chevrolet,chevelle,malibu 8 307.0 130.0 3504 \n",
"1 buick,skylark,320 8 350.0 165.0 3693 \n",
"2 plymouth,satellite 8 318.0 150.0 3436 \n",
"3 amc,rebel,sst 8 304.0 150.0 3433 \n",
"4 ford,torino 8 302.0 140.0 3449 \n",
"\n",
" acceleration model_year origin mpg \n",
"0 12.0 70 1 18.0 \n",
"1 11.5 70 1 15.0 \n",
"2 11.0 70 1 18.0 \n",
"3 12.0 70 1 16.0 \n",
"4 10.5 70 1 17.0 "
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"type": "dataframe",
"variable_name": "autompg",
"summary": "{\n \"name\": \"autompg\",\n \"rows\": 398,\n \"fields\": [\n {\n \"column\": \"car_name\",\n \"properties\": {\n \"dtype\": \"string\",\n \"num_unique_values\": 305,\n \"samples\": [\n \"mazda,rx-4\",\n \"ford,f108\",\n \"buick,century,luxus,(sw)\"\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"cylinders\",\n \"properties\": {\n \"dtype\": \"category\",\n \"num_unique_values\": 5,\n \"samples\": [\n \"4\",\n \"5\",\n \"6\"\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"displacement\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 104.26983817119581,\n \"min\": 68.0,\n \"max\": 455.0,\n \"num_unique_values\": 82,\n \"samples\": [\n 122.0,\n 307.0,\n 360.0\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"horsepower\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 38.49115993282855,\n \"min\": 46.0,\n \"max\": 230.0,\n \"num_unique_values\": 93,\n \"samples\": [\n 92.0,\n 100.0,\n 52.0\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"weight\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 846,\n \"min\": 1613,\n \"max\": 5140,\n \"num_unique_values\": 351,\n \"samples\": [\n 3730,\n 1995,\n 2215\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"acceleration\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 2.7576889298126757,\n \"min\": 8.0,\n \"max\": 24.8,\n \"num_unique_values\": 95,\n \"samples\": [\n 14.7,\n 18.0,\n 14.3\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"model_year\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 3,\n \"min\": 70,\n \"max\": 82,\n \"num_unique_values\": 13,\n \"samples\": [\n 81,\n 79,\n 70\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"origin\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0,\n \"min\": 1,\n \"max\": 3,\n \"num_unique_values\": 3,\n \"samples\": [\n 1,\n 3,\n 2\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"mpg\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 7.815984312565782,\n \"min\": 9.0,\n \"max\": 46.6,\n \"num_unique_values\": 129,\n \"samples\": [\n 17.7,\n 30.5,\n 30.0\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n }\n ]\n}"
}
},
"metadata": {},
"execution_count": 3
}
],
"source": [
"autompg = auto_mpg.data.original\n",
"autompg.cylinders = autompg.cylinders.astype('str').astype('category')\n",
"autompg.head()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_F4tnEIn2mey"
},
"source": [
"* Create a linear model called `mod_displ_cyl` of mpg vs. displacement and cylinders.\n",
" - Give `sm.formula.ols` code, output of `mod_displ_cyl.summary()`\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "kG3csppD2mez",
"outputId": "d1b4a3b0-c37f-48c2-cff1-6a3a61c44a9d"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: mpg R-squared: 0.685\n",
"Model: OLS Adj. R-squared: 0.681\n",
"Method: Least Squares F-statistic: 170.7\n",
"Date: Thu, 24 Oct 2024 Prob (F-statistic): 4.61e-96\n",
"Time: 23:34:56 Log-Likelihood: -1152.5\n",
"No. Observations: 398 AIC: 2317.\n",
"Df Residuals: 392 BIC: 2341.\n",
"Df Model: 5 \n",
"Covariance Type: nonrobust \n",
"==================================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"----------------------------------------------------------------------------------\n",
"Intercept 24.4345 2.263 10.799 0.000 19.986 28.883\n",
"cylinders[T.4] 10.7351 2.243 4.787 0.000 6.326 15.144\n",
"cylinders[T.5] 10.7011 3.407 3.141 0.002 4.002 17.400\n",
"cylinders[T.6] 7.2391 2.473 2.927 0.004 2.377 12.101\n",
"cylinders[T.8] 9.0138 2.936 3.070 0.002 3.242 14.785\n",
"displacement -0.0536 0.007 -7.737 0.000 -0.067 -0.040\n",
"==============================================================================\n",
"Omnibus: 54.193 Durbin-Watson: 0.907\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 98.199\n",
"Skew: 0.790 Prob(JB): 4.75e-22\n",
"Kurtosis: 4.851 Cond. No. 5.28e+03\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 5.28e+03. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n"
]
}
],
"source": [
"import statsmodels.api as sm\n",
"\n",
"mod_displ_cyl = sm.formula.ols('mpg ~ displacement + cylinders', autompg)\n",
"\n",
"results = mod_displ_cyl.fit()\n",
"print(results.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jI9d3NqS2me0"
},
"source": [
" * Give the model equations relating mpg with displacement and cylinders.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "1opSbzFy2me0"
},
"source": [
"$$\n",
" mpg = 24.4345\n",
" + 10.7351 * cylinders[T.4]\n",
" + 10.7011 * cylinders[T.5]\n",
" + 7.2391 * cylinders[T.6]\n",
" + 9.0138 * cylinders[T.8]\n",
" - 0.0536 * displacement\n",
"$$\n",
"\n",
"<center>or</center>\n",
"\n",
"$$\n",
" mpg =\n",
" \\begin{cases}\n",
" mpg = 24.4345 - 0.0536 \\times displacement\n",
" & \\text{if (cylinders == 3)} \\\\\n",
" mpg = 35.1696 - 0.0536 \\times displacement\n",
" & \\text{if (cylinders == 4)} \\\\\n",
" mpg = 35.1356 - 0.0536 \\times displacement\n",
" & \\text{if (cylinders == 5)} \\\\\n",
" mpg = 31.6736 - 0.0536 \\times displacement \n",
" & \\text{if (cylinders == 6)} \\\\\n",
" mpg = 33.4483 - 0.0536 \\times displacement\n",
" & \\text{if (cylinders == 8)} \\\\\n",
" \\end{cases}\n",
"$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rHm-MZLq2me0"
},
"source": [
"* Plot mpg vs. displacement and overlay the best fit model. (code, plot)\n",
" - Hint: plot the predictions; use `assign()` and `geom_line()` and use the color aesthetic for cylinders\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 417
},
"id": "rLutfamE2me0",
"outputId": "080df633-0911-41b4-b66c-b9cc8107a834"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<lets_plot.plot.core.PlotSpec at 0x7f16cf18ac80>"
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"text/html": [
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" <head>\n",
" <meta charset=\"UTF-8\">\n",
" <script type=\"text/javascript\" data-lets-plot-script=\"library\" src=\"https://cdn.jsdelivr.net/gh/JetBrains/[email protected]/js-package/distr/lets-plot.min.js\"></script>\n",
" </head>\n",
" <body>\n",
" <div id=\"MzkQgu\"></div>\n",
" <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
" \n",
" (function() {\n",
" // ----------\n",
" \n",
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" var plotSpec={\n",
"\"data\":{\n",
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"},\n",
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"},\n",
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"},{\n",
"\"type\":\"str\",\n",
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"},{\n",
"\"type\":\"float\",\n",
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"},{\n",
"\"type\":\"float\",\n",
"\"column\":\"horsepower\"\n",
"},{\n",
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"},{\n",
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"},{\n",
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"},{\n",
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"},{\n",
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"\"column\":\"mpg\"\n",
"},{\n",
"\"type\":\"float\",\n",
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"}]\n",
"},\n",
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"\"layers\":[{\n",
"\"geom\":\"point\",\n",
"\"mapping\":{\n",
"\"x\":\"displacement\",\n",
"\"y\":\"mpg\",\n",
"\"color\":\"cylinders\"\n",
"},\n",
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"},\n",
"\"data\":{\n",
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"},{\n",
"\"geom\":\"line\",\n",
"\"mapping\":{\n",
"\"x\":\"displacement\",\n",
"\"y\":\"pred\",\n",
"\"color\":\"cylinders\"\n",
"},\n",
"\"data_meta\":{\n",
"},\n",
"\"data\":{\n",
"}\n",
"}],\n",
"\"metainfo_list\":[],\n",
"\"spec_id\":\"4\"\n",
"};\n",
" \n",
" var toolbar = null;\n",
" var plotContainer = containerDiv; \n",
" \n",
" var options = {\n",
" sizing: {\n",
" width_mode: \"min\",\n",
" height_mode: \"scaled\",\n",
" width: width\n",
" }\n",
" };\n",
" var fig = LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer, options);\n",
" if (toolbar) {\n",
" toolbar.bind(fig);\n",
" }\n",
" \n",
" break;\n",
" }\n",
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" \n",
" // ----------\n",
" })();\n",
" \n",
" </script>\n",
" </body>\n",
"</html>"
]
},
"metadata": {},
"execution_count": 10
}
],
"source": [
"(\n",
" ggplot(autompg.assign(pred=results.get_prediction().predicted_mean))\n",
" + geom_point(aes(x='displacement', y='mpg', color='cylinders'))\n",
" + geom_line(aes(x='displacement', y='pred', color='cylinders'))\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "e-B1v5c42me1"
},
"source": [
"# Part 9 - Slide 60"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-vd9N3Iw2me1"
},
"source": [
"Consider the `auto_mpg.data.original` dataset\n",
"* Build a linear model to predict mpg given:\n",
" \n",
" $$\\frac{1}{displacement^2}$$"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "wNE8uqVt2me1",
"outputId": "29d67866-9436-4c54-e812-d96eda18ad61"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(16.502808546271417, 123227.9612325492)"
]
},
"metadata": {},
"execution_count": 15
}
],
"source": [
"from sklearn.linear_model import LinearRegression\n",
"\n",
"autompg = auto_mpg.data.original.copy()\n",
"autompg['d2_recip'] = 1 / (autompg.displacement**2)\n",
"\n",
"X = autompg[['d2_recip']]\n",
"y = autompg['mpg']\n",
"\n",
"lm = LinearRegression()\n",
"lm.fit(X, y)\n",
"\n",
"lm.intercept_, *lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "8GFN9jgD2me1"
},
"source": [
"* What is the regression equation?"
]
},
{
"cell_type": "markdown",
"source": [
"$$\n",
" 16.5028 + \\frac{123227.9612}{displacement^2}\n",
"$$"
],
"metadata": {
"id": "57mJ0WxE9Gs_"
}
},
{
"cell_type": "markdown",
"metadata": {
"id": "8uFmMP9t2me2"
},
"source": [
"* Plot the model predictions"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 417
},
"id": "Vyl4rTFj2me2",
"outputId": "ece501eb-e6aa-44c4-b369-201a82fa2d46"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<lets_plot.plot.core.PlotSpec at 0x7f16cab79000>"
],
"text/html": [
"<html lang=\"en\">\n",
" <head>\n",
" <meta charset=\"UTF-8\">\n",
" <script type=\"text/javascript\" data-lets-plot-script=\"library\" src=\"https://cdn.jsdelivr.net/gh/JetBrains/[email protected]/js-package/distr/lets-plot.min.js\"></script>\n",
" </head>\n",
" <body>\n",
" <div id=\"SFNC7F\"></div>\n",
" <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
" \n",
" (function() {\n",
" // ----------\n",
" \n",
" var containerDiv = document.getElementById(\"SFNC7F\");\n",
" var observer = new ResizeObserver(function(entries) {\n",
" for (let entry of entries) {\n",
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" if (entry.contentBoxSize && width > 0) {\n",
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" // Render plot\n",
" if (observer) {\n",
" observer.disconnect();\n",
" observer = null;\n",
" }\n",
"\n",
" var plotSpec={\n",
"\"data\":{\n",
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"},\n",
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"\"column\":\"acceleration\"\n",
"},{\n",
"\"type\":\"int\",\n",
"\"column\":\"model_year\"\n",
"},{\n",
"\"type\":\"int\",\n",
"\"column\":\"origin\"\n",
"},{\n",
"\"type\":\"float\",\n",
"\"column\":\"mpg\"\n",
"},{\n",
"\"type\":\"float\",\n",
"\"column\":\"d2_recip\"\n",
"},{\n",
"\"type\":\"float\",\n",
"\"column\":\"pred\"\n",
"}]\n",
"},\n",
"\"kind\":\"plot\",\n",
"\"scales\":[],\n",
"\"layers\":[{\n",
"\"geom\":\"point\",\n",
"\"mapping\":{\n",
"\"x\":\"displacement\",\n",
"\"y\":\"mpg\"\n",
"},\n",
"\"data_meta\":{\n",
"},\n",
"\"data\":{\n",
"}\n",
"},{\n",
"\"geom\":\"line\",\n",
"\"mapping\":{\n",
"\"x\":\"displacement\",\n",
"\"y\":\"pred\"\n",
"},\n",
"\"data_meta\":{\n",
"},\n",
"\"color\":\"blue\",\n",
"\"data\":{\n",
"}\n",
"}],\n",
"\"metainfo_list\":[],\n",
"\"spec_id\":\"6\"\n",
"};\n",
" \n",
" var toolbar = null;\n",
" var plotContainer = containerDiv; \n",
" \n",
" var options = {\n",
" sizing: {\n",
" width_mode: \"min\",\n",
" height_mode: \"scaled\",\n",
" width: width\n",
" }\n",
" };\n",
" var fig = LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer, options);\n",
" if (toolbar) {\n",
" toolbar.bind(fig);\n",
" }\n",
" \n",
" break;\n",
" }\n",
" }\n",
" });\n",
" \n",
" observer.observe(containerDiv);\n",
" \n",
" // ----------\n",
" })();\n",
" \n",
" </script>\n",
" </body>\n",
"</html>"
]
},
"metadata": {},
"execution_count": 18
}
],
"source": [
"autompg['pred'] = lm.predict(X)\n",
"\n",
"(\n",
" ggplot(autompg)\n",
" + geom_point(aes(x='displacement', y='mpg'))\n",
" + geom_line(aes(x='displacement', y='pred'), color='blue')\n",
")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "murach",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.7"
},
"colab": {
"provenance": [],
"include_colab_link": true
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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