2020-03-28 01:06:31 +00:00
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"cells": [
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{
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"cell_type": "code",
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2020-08-01 22:25:45 +00:00
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"execution_count": 1,
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2020-03-28 01:06:31 +00:00
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"metadata": {},
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"outputs": [],
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"source": [
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"library(MASS)"
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]
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},
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2020-08-01 22:25:45 +00:00
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"`symmary(model)` reports basic statistics"
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]
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},
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2020-03-28 01:06:31 +00:00
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{
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"cell_type": "code",
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2020-08-01 22:25:45 +00:00
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"execution_count": 15,
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2020-03-28 01:06:31 +00:00
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"metadata": {},
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"outputs": [
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{
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"data": {
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2020-08-01 22:25:45 +00:00
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"text/plain": [
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"\n",
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2020-08-01 22:25:45 +00:00
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"Call:\n",
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"lm(formula = medv ~ lstat, data = Boston)\n",
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2020-03-28 01:06:31 +00:00
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"\n",
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"Residuals:\n",
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" Min 1Q Median 3Q Max \n",
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"-15.168 -3.990 -1.318 2.034 24.500 \n",
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2020-03-28 01:06:31 +00:00
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"\n",
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2020-08-01 22:25:45 +00:00
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"Coefficients:\n",
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" Estimate Std. Error t value Pr(>|t|) \n",
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"(Intercept) 34.55384 0.56263 61.41 <2e-16 ***\n",
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"lstat -0.95005 0.03873 -24.53 <2e-16 ***\n",
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"---\n",
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"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
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2020-03-28 01:06:31 +00:00
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"\n",
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"Residual standard error: 6.216 on 504 degrees of freedom\n",
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"Multiple R-squared: 0.5441,\tAdjusted R-squared: 0.5432 \n",
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"F-statistic: 601.6 on 1 and 504 DF, p-value: < 2.2e-16\n"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/html": [
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"<style>\n",
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".list-inline {list-style: none; margin:0; padding: 0}\n",
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".list-inline>li {display: inline-block}\n",
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".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
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"</style>\n",
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"<ol class=list-inline><li>'coefficients'</li><li>'residuals'</li><li>'effects'</li><li>'rank'</li><li>'fitted.values'</li><li>'assign'</li><li>'qr'</li><li>'df.residual'</li><li>'xlevels'</li><li>'call'</li><li>'terms'</li><li>'model'</li></ol>\n"
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],
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"text/latex": [
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"\\begin{enumerate*}\n",
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"\\item 'coefficients'\n",
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"\\item 'residuals'\n",
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"\\item 'effects'\n",
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"\\item 'rank'\n",
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"\\item 'fitted.values'\n",
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"\\item 'assign'\n",
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"\\item 'qr'\n",
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"\\item 'df.residual'\n",
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"\\item 'xlevels'\n",
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"\\item 'call'\n",
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"\\item 'terms'\n",
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"\\item 'model'\n",
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"\\end{enumerate*}\n"
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],
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"text/markdown": [
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"1. 'coefficients'\n",
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"2. 'residuals'\n",
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"3. 'effects'\n",
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"4. 'rank'\n",
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"5. 'fitted.values'\n",
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"6. 'assign'\n",
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"7. 'qr'\n",
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"8. 'df.residual'\n",
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"9. 'xlevels'\n",
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"10. 'call'\n",
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"11. 'terms'\n",
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"12. 'model'\n",
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"\n",
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"\n"
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],
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"text/plain": [
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2020-08-01 22:25:45 +00:00
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" [1] \"coefficients\" \"residuals\" \"effects\" \"rank\" \n",
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" [5] \"fitted.values\" \"assign\" \"qr\" \"df.residual\" \n",
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" [9] \"xlevels\" \"call\" \"terms\" \"model\" "
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/html": [
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"<style>\n",
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".dl-inline {width: auto; margin:0; padding: 0}\n",
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".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
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".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
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".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
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"</style><dl class=dl-inline><dt>(Intercept)</dt><dd>34.5538408793831</dd><dt>lstat</dt><dd>-0.950049353757991</dd></dl>\n"
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],
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"text/latex": [
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"\\begin{description*}\n",
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"\\item[(Intercept)] 34.5538408793831\n",
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"\\item[lstat] -0.950049353757991\n",
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"\\end{description*}\n"
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],
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"text/markdown": [
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"(Intercept)\n",
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": 34.5538408793831lstat\n",
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": -0.950049353757991\n",
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"\n"
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],
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"text/plain": [
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"(Intercept) lstat \n",
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" 34.5538409 -0.9500494 "
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"# create linear model and fit with response~predictors\n",
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"lm.fit = lm(medv~lstat, data=Boston)\n",
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"summary(lm.fit)\n",
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"\n",
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"names(lm.fit)\n",
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"coef(lm.fit)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<table>\n",
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"<caption>A matrix: 2 × 2 of type dbl</caption>\n",
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"<thead>\n",
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"\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
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"</thead>\n",
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"<tbody>\n",
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"\t<tr><th scope=row>(Intercept)</th><td>33.448457</td><td>35.6592247</td></tr>\n",
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"\t<tr><th scope=row>lstat</th><td>-1.026148</td><td>-0.8739505</td></tr>\n",
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"</tbody>\n",
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"</table>\n"
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],
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"text/latex": [
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"A matrix: 2 × 2 of type dbl\n",
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"\\begin{tabular}{r|ll}\n",
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" & 2.5 \\% & 97.5 \\%\\\\\n",
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"\\hline\n",
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"\t(Intercept) & 33.448457 & 35.6592247\\\\\n",
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"\tlstat & -1.026148 & -0.8739505\\\\\n",
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"\\end{tabular}\n"
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],
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"text/markdown": [
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"\n",
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2020-08-01 22:25:45 +00:00
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"A matrix: 2 × 2 of type dbl\n",
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"\n",
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2020-08-01 22:25:45 +00:00
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"| <!--/--> | 2.5 % | 97.5 % |\n",
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"|---|---|---|\n",
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"| (Intercept) | 33.448457 | 35.6592247 |\n",
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"| lstat | -1.026148 | -0.8739505 |\n",
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"\n"
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],
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"text/plain": [
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" 2.5 % 97.5 % \n",
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"(Intercept) 33.448457 35.6592247\n",
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"lstat -1.026148 -0.8739505"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"# confidence interval\n",
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"confint(lm.fit)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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"text/html": [
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"<table>\n",
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"<caption>A matrix: 3 × 3 of type dbl</caption>\n",
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"<thead>\n",
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"\t<tr><th></th><th scope=col>fit</th><th scope=col>lwr</th><th scope=col>upr</th></tr>\n",
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"</thead>\n",
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"<tbody>\n",
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"\t<tr><th scope=row>1</th><td>29.80359</td><td>29.00741</td><td>30.59978</td></tr>\n",
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"\t<tr><th scope=row>2</th><td>25.05335</td><td>24.47413</td><td>25.63256</td></tr>\n",
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"\t<tr><th scope=row>3</th><td>20.30310</td><td>19.73159</td><td>20.87461</td></tr>\n",
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"</tbody>\n",
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"</table>\n"
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],
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"text/latex": [
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"A matrix: 3 × 3 of type dbl\n",
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"\\begin{tabular}{r|lll}\n",
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" & fit & lwr & upr\\\\\n",
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"\\hline\n",
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"\t1 & 29.80359 & 29.00741 & 30.59978\\\\\n",
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"\t2 & 25.05335 & 24.47413 & 25.63256\\\\\n",
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"\t3 & 20.30310 & 19.73159 & 20.87461\\\\\n",
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"\\end{tabular}\n"
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],
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"text/markdown": [
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"\n",
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"A matrix: 3 × 3 of type dbl\n",
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"\n",
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"| <!--/--> | fit | lwr | upr |\n",
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"|---|---|---|---|\n",
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"| 1 | 29.80359 | 29.00741 | 30.59978 |\n",
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"| 2 | 25.05335 | 24.47413 | 25.63256 |\n",
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"| 3 | 20.30310 | 19.73159 | 20.87461 |\n",
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"\n"
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],
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"text/plain": [
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" fit lwr upr \n",
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"1 29.80359 29.00741 30.59978\n",
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"2 25.05335 24.47413 25.63256\n",
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"3 20.30310 19.73159 20.87461"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"# confidence interval for lstat[5,10,15]\n",
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"predict(lm.fit, data.frame(lstat=c(5, 10, 15)), interval=\"confidence\")\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"text/html": [
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"<table>\n",
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"<caption>A matrix: 3 × 3 of type dbl</caption>\n",
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"<thead>\n",
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"\t<tr><th></th><th scope=col>fit</th><th scope=col>lwr</th><th scope=col>upr</th></tr>\n",
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"</thead>\n",
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"<tbody>\n",
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"\t<tr><th scope=row>1</th><td>29.80359</td><td>17.565675</td><td>42.04151</td></tr>\n",
|
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|
|
"\t<tr><th scope=row>2</th><td>25.05335</td><td>12.827626</td><td>37.27907</td></tr>\n",
|
|
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"\t<tr><th scope=row>3</th><td>20.30310</td><td> 8.077742</td><td>32.52846</td></tr>\n",
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"</tbody>\n",
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"</table>\n"
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],
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"text/latex": [
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"A matrix: 3 × 3 of type dbl\n",
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"\\begin{tabular}{r|lll}\n",
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" & fit & lwr & upr\\\\\n",
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"\\hline\n",
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"\t1 & 29.80359 & 17.565675 & 42.04151\\\\\n",
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"\t2 & 25.05335 & 12.827626 & 37.27907\\\\\n",
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"\t3 & 20.30310 & 8.077742 & 32.52846\\\\\n",
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"\\end{tabular}\n"
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],
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"text/markdown": [
|
2020-03-28 01:06:31 +00:00
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"\n",
|
2020-08-01 22:25:45 +00:00
|
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|
|
"A matrix: 3 × 3 of type dbl\n",
|
2020-03-28 01:06:31 +00:00
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"\n",
|
2020-08-01 22:25:45 +00:00
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"| <!--/--> | fit | lwr | upr |\n",
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"|---|---|---|---|\n",
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"| 1 | 29.80359 | 17.565675 | 42.04151 |\n",
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"| 2 | 25.05335 | 12.827626 | 37.27907 |\n",
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"| 3 | 20.30310 | 8.077742 | 32.52846 |\n",
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"\n"
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],
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"text/plain": [
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" fit lwr upr \n",
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"1 29.80359 17.565675 42.04151\n",
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"2 25.05335 12.827626 37.27907\n",
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"3 20.30310 8.077742 32.52846"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
|
|
|
|
|
|
"# prediction interval for lstat[5,10,15]\n",
|
|
|
|
|
|
"predict(lm.fit, data.frame(lstat=c(5, 10, 15)), interval=\"predict\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAACXBIWXMAABJ0AAASdAHeZh94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\nfXE8M
|
|
|
|
|
|
"text/plain": [
|
|
|
|
|
|
"plot without title"
|
|
|
|
|
|
]
|
|
|
|
|
|
},
|
|
|
|
|
|
"metadata": {
|
|
|
|
|
|
"image/png": {
|
|
|
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|
|
"height": 420,
|
|
|
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|
|
"width": 420
|
|
|
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|
|
},
|
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|
"text/plain": {
|
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|
"height": 420,
|
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"width": 420
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|
|
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|
}
|
|
|
|
|
|
},
|
|
|
|
|
|
"output_type": "display_data"
|
|
|
|
|
|
}
|
|
|
|
|
|
],
|
|
|
|
|
|
"source": [
|
|
|
|
|
|
"# plot y and X\n",
|
|
|
|
|
|
"plot(medv ~ lstat, data = Boston, pch=20)\n",
|
|
|
|
|
|
"# plot regression line\n",
|
|
|
|
|
|
"abline(lm.fit, lwd =3 , col =\"blue\")"
|
|
|
|
|
|
]
|
|
|
|
|
|
},
|
|
|
|
|
|
{
|
|
|
|
|
|
"cell_type": "code",
|
|
|
|
|
|
"execution_count": 8,
|
|
|
|
|
|
"metadata": {},
|
|
|
|
|
|
"outputs": [
|
|
|
|
|
|
{
|
|
|
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|
|
"data": {
|
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"\\end{description*}\n",
|
2020-03-28 01:06:31 +00:00
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"\n",
|
2020-08-01 22:25:45 +00:00
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"\\end{enumerate}\n"
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],
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"text/markdown": [
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"1. 1\n",
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": -5.822595097668252\n",
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|
2020-03-28 01:06:31 +00:00
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"\n",
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"\n",
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"\n",
|
2020-08-01 22:25:45 +00:00
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"\n"
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],
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"text/plain": [
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"[[1]]\n",
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" 1 2 3 4 5 \n",
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" -5.822595098 -4.270389786 3.974858016 1.639304221 6.709922176 \n",
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" 6 7 8 9 10 \n",
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" -0.904083746 0.155272588 10.739604245 10.381136279 0.592003070 \n",
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" 11 12 13 14 15 \n",
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" -0.125331595 -3.046685955 2.071434468 -6.306433217 -6.606334510 \n",
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" 16 17 18 19 20 \n",
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" -6.606922853 -5.202516132 -3.116616860 -3.247763934 -5.637284169 \n",
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" 21 22 23 24 25 \n",
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" -0.983803463 -1.814658317 -1.568916977 -1.166859727 -3.468036413 \n",
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" 2.399351507 12.537357383 4.326482788 6.146463047 5.073104692 \n",
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" 146 147 148 149 150 \n",
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" 161 162 163 164 165 \n",
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" 171 172 173 174 175 \n",
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" 176 177 178 179 180 \n",
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" 181 182 183 184 185 \n",
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" 12.428532235 10.624125514 7.925397006 3.342439450 5.127849086 \n",
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" 186 187 188 189 190 \n",
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|
" 7.539308123 19.673878745 3.792488804 -0.421615826 5.466925137 \n",
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" 191 192 193 194 195 \n",
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|
" 7.291410825 0.401890590 4.572800766 1.324907370 -1.292624710 \n",
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" 196 197 198 199 200 \n",
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|
" 18.267805701 2.622360484 3.926084056 6.335485842 4.678384174 \n",
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" 201 202 203 204 205 \n",
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" 2.573878745 -3.394974181 10.700812611 17.565847158 18.182301259 \n",
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" 206 207 208 209 210 \n",
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" -1.626804404 0.268200531 5.104050449 3.773882647 7.382798699 \n",
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" 211 212 213 214 215 \n",
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|
|
|
" 3.553511460 7.528342624 3.075450261 2.457622059 17.220117524 \n",
|
|
|
|
|
|
" 216 217 218 219 220 \n",
|
|
|
|
|
|
" -0.556873499 1.581325890 3.352137359 3.971043540 -1.578322665 \n",
|
|
|
|
|
|
" 221 222 223 224 225 \n",
|
|
|
|
|
|
" 1.371138346 7.534218252 2.380149203 2.766534209 14.179363445 \n",
|
|
|
|
|
|
" 226 227 228 229 230 \n",
|
|
|
|
|
|
" 19.844887629 6.019813598 3.088473011 15.870352587 0.518344691 \n",
|
|
|
|
|
|
" 231 232 233 234 235 \n",
|
|
|
|
|
|
" 0.814234092 2.133918228 9.492781024 17.498854068 2.094056418 \n",
|
|
|
|
|
|
" 236 237 238 239 240 \n",
|
|
|
|
|
|
" -0.217303910 -0.390370045 1.439892564 -4.811526989 -4.251977142 \n",
|
|
|
|
|
|
" 241 242 243 244 245 \n",
|
|
|
|
|
|
" -1.742279234 -2.673228893 -1.694287130 -5.923084733 -5.078223957 \n",
|
|
|
|
|
|
" 246 247 248 249 250 \n",
|
|
|
|
|
|
" 1.484070191 -1.551388799 -4.410839939 -1.009371032 -2.121517119 \n",
|
|
|
|
|
|
" 251 252 253 254 255 \n",
|
|
|
|
|
|
" -4.548549692 -6.343163699 -1.600166661 11.609333833 -6.412016625 \n",
|
|
|
|
|
|
" 256 257 258 259 260 \n",
|
|
|
|
|
|
" -4.865884357 12.400812611 20.310411812 8.847043586 2.101499662 \n",
|
|
|
|
|
|
" 261 262 263 264 265 \n",
|
|
|
|
|
|
" 8.357132423 15.443517429 19.860950801 7.134214350 9.641558886 \n",
|
|
|
|
|
|
" 266 267 268 269 270 \n",
|
|
|
|
|
|
" -1.825825133 10.197389063 22.514526313 11.948315078 -0.885667201 \n",
|
|
|
|
|
|
" 271 272 273 274 275 \n",
|
|
|
|
|
|
" -1.103199281 -3.093015638 -2.809959375 6.897483868 1.199833339 \n",
|
|
|
|
|
|
" 276 277 278 279 280 \n",
|
|
|
|
|
|
" 0.277306195 4.393957711 2.498364432 1.377013974 5.153898486 \n",
|
|
|
|
|
|
" 281 282 283 284 285 \n",
|
|
|
|
|
|
" 14.418344691 5.206885654 14.305807675 18.448315078 5.104046548 \n",
|
|
|
|
|
|
" 286 287 288 289 290 \n",
|
|
|
|
|
|
" -4.734934698 -2.169702735 -4.570488494 -5.033465791 -0.718871525 \n",
|
|
|
|
|
|
" 291 292 293 294 295 \n",
|
|
|
|
|
|
" -2.890176531 6.128334820 -2.188608917 -2.502417424 -2.973327600 \n",
|
|
|
|
|
|
" 296 297 298 299 300 \n",
|
|
|
|
|
|
" 0.002968569 -0.432976155 0.794940884 -7.332095591 -1.050606943 \n",
|
|
|
|
|
|
" 301 302 303 304 305 \n",
|
|
|
|
|
|
" -3.987041302 -3.528372019 0.083087018 3.163398980 8.130001142 \n",
|
|
|
|
|
|
" 306 307 308 309 310 \n",
|
|
|
|
|
|
" 2.330099850 4.992978439 0.800030754 -7.440616813 -4.781848822 \n",
|
|
|
|
|
|
" 311 312 313 314 315 \n",
|
|
|
|
|
|
" -6.445217048 -6.772545744 -4.019262453 -5.448450985 -1.937382877 \n",
|
|
|
|
|
|
" 316 317 318 319 320 \n",
|
|
|
|
|
|
" -7.428273311 0.660563775 0.389945820 -1.611329574 -1.459712606 \n",
|
|
|
|
|
|
" 321 322 323 324 325 \n",
|
|
|
|
|
|
" -3.913485532 -4.927001819 -6.838460855 -4.900261466 -3.739538834 \n",
|
|
|
|
|
|
" 326 327 328 329 330 \n",
|
|
|
|
|
|
" -5.127590162 -5.711037354 -0.202709645 -5.781848822 -4.980478623 \n",
|
|
|
|
|
|
" 331 332 333 334 335 \n",
|
|
|
|
|
|
" -6.117892254 -5.644727412 -7.714954439 -6.957560550 -7.441007742 \n",
|
|
|
|
|
|
" 336 337 338 339 340 \n",
|
|
|
|
|
|
" -5.843945556 -5.743357213 -6.021319704 -5.868920879 -6.300360174 \n",
|
|
|
|
|
|
" 341 342 343 344 345 \n",
|
|
|
|
|
|
" -7.027882383 3.361930073 -9.835913969 -3.832486519 1.025886641 \n",
|
|
|
|
|
|
" 346 347 348 349 350 \n",
|
|
|
|
|
|
" -7.049821184 -5.316715567 -5.411526989 -4.363045250 -2.358050186 \n",
|
|
|
|
|
|
" 351 352 353 354 355 \n",
|
|
|
|
|
|
" -5.972545744 -5.238069927 -8.552956414 -0.178618787 -8.705943582 \n",
|
|
|
|
|
|
" 356 357 358 359 360 \n",
|
|
|
|
|
|
" -8.662065979 -0.032972253 -0.246685955 -0.947274298 0.083284433 \n",
|
|
|
|
|
|
" 361 362 363 364 365 \n",
|
|
|
|
|
|
" -2.152956414 -1.172640550 -4.072837965 -3.845118340 -7.628079798 \n",
|
|
|
|
|
|
" 366 367 368 369 370 \n",
|
|
|
|
|
|
" -0.289489481 0.646850073 1.210317006 18.543320014 18.989843210 \n",
|
|
|
|
|
|
" 371 372 373 374 375 \n",
|
|
|
|
|
|
" 18.258305208 24.500129462 23.882597382 12.279375151 15.319533083 \n",
|
|
|
|
|
|
" 376 377 378 379 380 \n",
|
|
|
|
|
|
" -6.785177565 1.425306102 -1.074792606 1.052828311 -3.661765955 \n",
|
|
|
|
|
|
" 381 382 383 384 385 \n",
|
|
|
|
|
|
" -7.803491501 -3.626800502 -0.832676131 1.079371249 3.346170826 \n",
|
|
|
|
|
|
" 386 387 388 389 390 \n",
|
|
|
|
|
|
" 1.917179710 2.813554845 3.238237947 4.736670333 -3.245311854 \n",
|
|
|
|
|
|
" 391 392 393 394 395 \n",
|
|
|
|
|
|
" -3.198496437 6.469084997 -0.456573475 -6.341592183 -6.320533945 \n",
|
|
|
|
|
|
" 396 397 398 399 400 \n",
|
|
|
|
|
|
" -5.188995943 -3.651384897 -7.128857753 -0.491831148 0.219138253 \n",
|
|
|
|
|
|
" 401 402 403 404 405 \n",
|
|
|
|
|
|
" -3.521019679 -8.048838011 -3.158338505 -7.471365156 -0.041489573 \n",
|
|
|
|
|
|
" 406 407 408 409 410 \n",
|
|
|
|
|
|
" -7.721706730 -0.479688963 4.870257782 7.727462060 11.738135338 \n",
|
|
|
|
|
|
" 411 412 413 414 415 \n",
|
|
|
|
|
|
" -9.948841913 2.806206407 15.999355409 0.823150144 7.578984223 \n",
|
|
|
|
|
|
" 416 417 418 419 420 \n",
|
|
|
|
|
|
" 0.245092847 -2.552068046 1.155473905 -6.163823205 -4.549718575 \n",
|
|
|
|
|
|
" 421 422 423 424 425 \n",
|
|
|
|
|
|
" -3.584099586 -5.438066025 -0.358144991 0.972808570 -6.550993969 \n",
|
|
|
|
|
|
" 426 427 428 429 430 \n",
|
|
|
|
|
|
" -3.082137141 -9.447566519 -9.859124263 -3.108778787 -2.176652441 \n",
|
|
|
|
|
|
" 431 432 433 434 435 \n",
|
|
|
|
|
|
" -3.294970279 -1.747369104 -7.024747154 -4.844040361 -8.441592183 \n",
|
|
|
|
|
|
" 436 437 438 439 440 \n",
|
|
|
|
|
|
" 0.953807583 -7.805450044 -0.725035472 6.166838135 -0.016711665 \n",
|
|
|
|
|
|
" 441 442 443 444 445 \n",
|
|
|
|
|
|
" -3.048249668 1.091122506 -0.392522101 -1.245410561 -1.152166753 \n",
|
|
|
|
|
|
" 446 447 448 449 450 \n",
|
|
|
|
|
|
" 0.028342624 -2.752462876 -6.335029504 -3.229446096 -3.208387858 \n",
|
|
|
|
|
|
" 451 452 453 454 455 \n",
|
|
|
|
|
|
" -4.584980150 -2.509465837 -2.046488540 -0.850014697 -1.878417471 \n",
|
|
|
|
|
|
" 456 457 458 459 460 \n",
|
|
|
|
|
|
" -3.229446096 -3.793402664 -4.960004827 -4.234539868 -0.588115379 \n",
|
|
|
|
|
|
" 461 462 463 464 465 \n",
|
|
|
|
|
|
" -2.554030491 -2.935617847 -1.762650420 -4.577833029 -0.594188423 \n",
|
|
|
|
|
|
" 466 467 468 469 470 \n",
|
|
|
|
|
|
" -1.229643511 0.739505538 4.801211343 1.770553904 -0.431112418 \n",
|
|
|
|
|
|
" 471 472 473 474 475 \n",
|
|
|
|
|
|
" 0.822463093 -2.726705697 2.288867841 6.323734585 -3.519945602 \n",
|
|
|
|
|
|
" 476 477 478 479 480 \n",
|
|
|
|
|
|
" 1.642348546 -0.106918951 1.111888523 -2.824451031 -0.698693852 \n",
|
|
|
|
|
|
" 481 482 483 484 485 \n",
|
|
|
|
|
|
" -1.350310820 -3.500458881 -2.893994910 -2.854326613 -1.280182500 \n",
|
|
|
|
|
|
" 486 487 488 489 490 \n",
|
|
|
|
|
|
" -3.302318717 -1.222101560 -3.075775779 -2.195949551 -4.781157870 \n",
|
|
|
|
|
|
" 491 492 493 494 495 \n",
|
|
|
|
|
|
" 1.743623940 -3.786449057 -1.770682007 -1.343748141 2.857329838 \n",
|
|
|
|
|
|
" 496 497 498 499 500 \n",
|
|
|
|
|
|
" 5.267027747 5.230202459 -2.858144991 -1.079203229 -2.708095638 \n",
|
|
|
|
|
|
" 501 502 503 504 505 \n",
|
|
|
|
|
|
" -4.139633640 -2.966863629 -5.327392747 -5.295562524 -6.397521067 \n",
|
|
|
|
|
|
" 506 \n",
|
|
|
|
|
|
"-15.167451972 \n"
|
|
|
|
|
|
]
|
|
|
|
|
|
},
|
|
|
|
|
|
"metadata": {},
|
|
|
|
|
|
"output_type": "display_data"
|
|
|
|
|
|
}
|
|
|
|
|
|
],
|
|
|
|
|
|
"source": [
|
|
|
|
|
|
"array(lm.fit[\"residuals\"])"
|
|
|
|
|
|
]
|
|
|
|
|
|
},
|
|
|
|
|
|
{
|
|
|
|
|
|
"cell_type": "code",
|
|
|
|
|
|
"execution_count": 13,
|
|
|
|
|
|
"metadata": {},
|
|
|
|
|
|
"outputs": [
|
|
|
|
|
|
{
|
|
|
|
|
|
"data": {
|
|
|
|
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAADAFBMVEUAAAABAQECAgIDAwME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\nx6AKQ
|
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|
|
|
|
"text/plain": [
|
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|
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|
|
"plot without title"
|
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|
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|
|
]
|
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|
},
|
|
|
|
|
|
"metadata": {
|
|
|
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|
|
"image/png": {
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|
"height": 420,
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"width": 420
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},
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"text/plain": {
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"height": 420,
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"width": 420
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}
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},
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"output_type": "display_data"
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}
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],
|
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|
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|
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"source": [
|
|
|
|
|
|
"plot(predict(lm.fit), residuals(lm.fit))"
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|
]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
|
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"outputs": [
|
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{
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|
"data": {
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|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAADAFBMVEUAAAABAQECAgIDAwME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\n0vraI
|
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|
|
"text/plain": [
|
|
|
|
|
|
"plot without title"
|
|
|
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|
|
]
|
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|
|
|
|
},
|
|
|
|
|
|
"metadata": {
|
|
|
|
|
|
"image/png": {
|
|
|
|
|
|
"height": 420,
|
|
|
|
|
|
"width": 420
|
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|
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|
},
|
|
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|
"text/plain": {
|
|
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|
"height": 420,
|
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|
"width": 420
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|
}
|
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|
|
},
|
|
|
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|
|
"output_type": "display_data"
|
|
|
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|
|
}
|
|
|
|
|
|
],
|
|
|
|
|
|
"source": [
|
|
|
|
|
|
"plot(predict(lm.fit), rstudent(lm.fit))"
|
|
|
|
|
|
]
|
|
|
|
|
|
},
|
|
|
|
|
|
{
|
|
|
|
|
|
"cell_type": "markdown",
|
|
|
|
|
|
"metadata": {},
|
|
|
|
|
|
"source": [
|
|
|
|
|
|
"# Multiple regression\n",
|
|
|
|
|
|
"the function is `lm(y∼x1+x2+x3)`"
|
|
|
|
|
|
]
|
|
|
|
|
|
},
|
|
|
|
|
|
{
|
|
|
|
|
|
"cell_type": "code",
|
|
|
|
|
|
"execution_count": 20,
|
|
|
|
|
|
"metadata": {},
|
|
|
|
|
|
"outputs": [
|
|
|
|
|
|
{
|
|
|
|
|
|
"data": {
|
|
|
|
|
|
"text/plain": [
|
2020-03-28 01:06:31 +00:00
|
|
|
|
"\n",
|
2020-08-01 22:25:45 +00:00
|
|
|
|
"Call:\n",
|
|
|
|
|
|
"lm(formula = medv ~ lstat + age, data = Boston)\n",
|
2020-03-28 01:06:31 +00:00
|
|
|
|
"\n",
|
2020-08-01 22:25:45 +00:00
|
|
|
|
"Residuals:\n",
|
|
|
|
|
|
" Min 1Q Median 3Q Max \n",
|
|
|
|
|
|
"-15.981 -3.978 -1.283 1.968 23.158 \n",
|
2020-03-28 01:06:31 +00:00
|
|
|
|
"\n",
|
2020-08-01 22:25:45 +00:00
|
|
|
|
"Coefficients:\n",
|
|
|
|
|
|
" Estimate Std. Error t value Pr(>|t|) \n",
|
|
|
|
|
|
"(Intercept) 33.22276 0.73085 45.458 < 2e-16 ***\n",
|
|
|
|
|
|
"lstat -1.03207 0.04819 -21.416 < 2e-16 ***\n",
|
|
|
|
|
|
"age 0.03454 0.01223 2.826 0.00491 ** \n",
|
|
|
|
|
|
"---\n",
|
|
|
|
|
|
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
|
2020-03-28 01:06:31 +00:00
|
|
|
|
"\n",
|
2020-08-01 22:25:45 +00:00
|
|
|
|
"Residual standard error: 6.173 on 503 degrees of freedom\n",
|
|
|
|
|
|
"Multiple R-squared: 0.5513,\tAdjusted R-squared: 0.5495 \n",
|
|
|
|
|
|
"F-statistic: 309 on 2 and 503 DF, p-value: < 2.2e-16\n"
|
|
|
|
|
|
]
|
|
|
|
|
|
},
|
|
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"model = lm(medv~lstat+age, data=Boston)\n",
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"summary(model)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# or just `lm(y~., data=DF)` to include all other rows"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 48,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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2020-03-28 01:06:31 +00:00
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"\n",
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2020-08-01 22:25:45 +00:00
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"Call:\n",
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"lm(formula = medv ~ ., data = Boston)\n",
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2020-03-28 01:06:31 +00:00
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"\n",
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2020-08-01 22:25:45 +00:00
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"Residuals:\n",
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" Min 1Q Median 3Q Max \n",
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"-15.595 -2.730 -0.518 1.777 26.199 \n",
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2020-03-28 01:06:31 +00:00
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"\n",
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2020-08-01 22:25:45 +00:00
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"Coefficients:\n",
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" Estimate Std. Error t value Pr(>|t|) \n",
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"(Intercept) 3.646e+01 5.103e+00 7.144 3.28e-12 ***\n",
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"crim -1.080e-01 3.286e-02 -3.287 0.001087 ** \n",
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"zn 4.642e-02 1.373e-02 3.382 0.000778 ***\n",
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"indus 2.056e-02 6.150e-02 0.334 0.738288 \n",
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"chas 2.687e+00 8.616e-01 3.118 0.001925 ** \n",
|
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"nox -1.777e+01 3.820e+00 -4.651 4.25e-06 ***\n",
|
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"rm 3.810e+00 4.179e-01 9.116 < 2e-16 ***\n",
|
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"age 6.922e-04 1.321e-02 0.052 0.958229 \n",
|
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"dis -1.476e+00 1.995e-01 -7.398 6.01e-13 ***\n",
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"rad 3.060e-01 6.635e-02 4.613 5.07e-06 ***\n",
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"tax -1.233e-02 3.760e-03 -3.280 0.001112 ** \n",
|
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"ptratio -9.527e-01 1.308e-01 -7.283 1.31e-12 ***\n",
|
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"black 9.312e-03 2.686e-03 3.467 0.000573 ***\n",
|
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"lstat -5.248e-01 5.072e-02 -10.347 < 2e-16 ***\n",
|
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"---\n",
|
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"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
|
2020-03-28 01:06:31 +00:00
|
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|
"\n",
|
2020-08-01 22:25:45 +00:00
|
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|
|
"Residual standard error: 4.745 on 492 degrees of freedom\n",
|
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|
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|
|
"Multiple R-squared: 0.7406,\tAdjusted R-squared: 0.7338 \n",
|
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|
"F-statistic: 108.1 on 13 and 492 DF, p-value: < 2.2e-16\n"
|
2020-03-28 01:06:31 +00:00
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]
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},
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"metadata": {},
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"output_type": "display_data"
|
2020-08-01 22:25:45 +00:00
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},
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{
|
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"data": {
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|
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"text/plain": [
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"Plot with title “”"
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]
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},
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"metadata": {
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"image/png": {
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"height": 420,
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"width": 420
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},
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"text/plain": {
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"height": 420,
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"width": 420
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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"Plot with title “”"
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]
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},
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"metadata": {
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"image/png": {
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"height": 420,
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"width": 420
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},
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"text/plain": {
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"height": 420,
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}
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"output_type": "display_data"
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2020-03-28 01:06:31 +00:00
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}
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],
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"source": [
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2020-08-01 22:25:45 +00:00
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"model = lm(medv~., data=Boston)\n",
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"summary(model)\n",
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"plot(model)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We can use the vif function in the car package to check for correlation of features"
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2020-03-28 01:06:31 +00:00
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]
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},
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{
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"cell_type": "code",
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2020-08-01 22:25:45 +00:00
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"execution_count": 29,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<style>\n",
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".dl-inline {width: auto; margin:0; padding: 0}\n",
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".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
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".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
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".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
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"</style><dl class=dl-inline><dt>crim</dt><dd>1.79219154743324</dd><dt>zn</dt><dd>2.29875817874944</dd><dt>indus</dt><dd>3.99159641834602</dd><dt>chas</dt><dd>1.07399532755379</dd><dt>nox</dt><dd>4.39371984757749</dd><dt>rm</dt><dd>1.93374443578326</dd><dt>age</dt><dd>3.10082551281534</dd><dt>dis</dt><dd>3.95594490637272</dd><dt>rad</dt><dd>7.48449633527446</dd><dt>tax</dt><dd>9.00855394759705</dd><dt>ptratio</dt><dd>1.7990840492489</dd><dt>black</dt><dd>1.34852107640638</dd><dt>lstat</dt><dd>2.94149107809193</dd></dl>\n"
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],
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"text/latex": [
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"\\begin{description*}\n",
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"\\item[crim] 1.79219154743324\n",
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"\\item[zn] 2.29875817874944\n",
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"\\item[indus] 3.99159641834602\n",
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"\\item[chas] 1.07399532755379\n",
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"\\item[nox] 4.39371984757749\n",
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"\\item[rm] 1.93374443578326\n",
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"\\item[age] 3.10082551281534\n",
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"\\item[dis] 3.95594490637272\n",
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"\\item[rad] 7.48449633527446\n",
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"\\item[tax] 9.00855394759705\n",
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"\\item[ptratio] 1.7990840492489\n",
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"\\item[black] 1.34852107640638\n",
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"\\item[lstat] 2.94149107809193\n",
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"\\end{description*}\n"
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],
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"text/markdown": [
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"crim\n",
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": 1.79219154743324zn\n",
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": 2.29875817874944indus\n",
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": 3.99159641834602chas\n",
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": 1.07399532755379nox\n",
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": 4.39371984757749rm\n",
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": 1.93374443578326age\n",
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": 3.10082551281534dis\n",
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": 3.95594490637272rad\n",
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": 7.48449633527446tax\n",
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": 9.00855394759705ptratio\n",
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": 1.7990840492489black\n",
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": 1.34852107640638lstat\n",
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": 2.94149107809193\n",
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"\n"
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],
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"text/plain": [
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" crim zn indus chas nox rm age dis \n",
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"1.792192 2.298758 3.991596 1.073995 4.393720 1.933744 3.100826 3.955945 \n",
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" rad tax ptratio black lstat \n",
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"7.484496 9.008554 1.799084 1.348521 2.941491 "
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
|
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"library(car)\n",
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"vif(model)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"metadata": {},
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"outputs": [],
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"source": [
|
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"model = lm(medv~.-tax, data=Boston)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"Plot with title “”"
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},
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"metadata": {
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"height": 420,
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"width": 420
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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"Plot with title “”"
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]
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},
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"metadata": {
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"image/png": {
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"height": 420,
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"width": 420
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},
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"text/plain": {
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"height": 420,
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"width": 420
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}
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"plot(model)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# As we see, there's a clear nonlinearity. Especially when the graph is drawn\n",
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"\n",
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"quick note:\n",
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"y~x1:x2 does y ~ x1 * x2 \n",
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" \n",
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" \n",
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"y~x1 * x2 does y ~ x1,x2, `x1 * x2`"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 66,
|
2020-03-28 01:06:31 +00:00
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"\n",
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"Call:\n",
|
2020-08-01 22:25:45 +00:00
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"lm(formula = medv ~ . + lstat:age, data = Boston)\n",
|
2020-03-28 01:06:31 +00:00
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"\n",
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"Residuals:\n",
|
2020-08-01 22:25:45 +00:00
|
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|
" Min 1Q Median 3Q Max \n",
|
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|
"-15.4559 -2.7480 -0.5557 1.8049 26.2582 \n",
|
2020-03-28 01:06:31 +00:00
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"\n",
|
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"Coefficients:\n",
|
2020-08-01 22:25:45 +00:00
|
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|
" Estimate Std. Error t value Pr(>|t|) \n",
|
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"(Intercept) 38.034385 5.467840 6.956 1.12e-11 ***\n",
|
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|
"crim -0.111723 0.033199 -3.365 0.000825 ***\n",
|
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"zn 0.043109 0.014336 3.007 0.002774 ** \n",
|
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|
"indus 0.018945 0.061550 0.308 0.758365 \n",
|
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"chas 2.709592 0.862357 3.142 0.001779 ** \n",
|
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|
"nox -18.026578 3.834758 -4.701 3.37e-06 ***\n",
|
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|
"rm 3.759388 0.422759 8.893 < 2e-16 ***\n",
|
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|
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|
"age -0.010315 0.019023 -0.542 0.587897 \n",
|
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|
"dis -1.475346 0.199527 -7.394 6.19e-13 ***\n",
|
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|
"rad 0.307676 0.066401 4.634 4.61e-06 ***\n",
|
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|
|
"tax -0.012335 0.003762 -3.279 0.001116 ** \n",
|
|
|
|
|
|
"ptratio -0.958239 0.131052 -7.312 1.08e-12 ***\n",
|
|
|
|
|
|
"black 0.009187 0.002691 3.414 0.000694 ***\n",
|
|
|
|
|
|
"lstat -0.635696 0.146950 -4.326 1.84e-05 ***\n",
|
|
|
|
|
|
"age:lstat 0.001257 0.001562 0.804 0.421562 \n",
|
2020-03-28 01:06:31 +00:00
|
|
|
|
"---\n",
|
|
|
|
|
|
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
|
|
|
|
|
|
"\n",
|
2020-08-01 22:25:45 +00:00
|
|
|
|
"Residual standard error: 4.747 on 491 degrees of freedom\n",
|
|
|
|
|
|
"Multiple R-squared: 0.741,\tAdjusted R-squared: 0.7336 \n",
|
|
|
|
|
|
"F-statistic: 100.3 on 14 and 491 DF, p-value: < 2.2e-16\n"
|
2020-03-28 01:06:31 +00:00
|
|
|
|
]
|
|
|
|
|
|
},
|
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|
"metadata": {},
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"output_type": "display_data"
|
2020-08-01 22:25:45 +00:00
|
|
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},
|
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{
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"text/plain": [
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"Plot with title “”"
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]
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},
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"metadata": {
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"image/png": {
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"height": 420,
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"width": 420
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},
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"text/plain": {
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"height": 420,
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"width": 420
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}
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},
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"output_type": "display_data"
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2020-03-28 01:06:31 +00:00
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}
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],
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"source": [
|
2020-08-01 22:25:45 +00:00
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"model2 = lm(medv~.+lstat:age, data=Boston)\n",
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"summary(model2)\n",
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"plot(model2)"
|
2020-03-28 01:06:31 +00:00
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]
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},
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{
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"cell_type": "code",
|
2020-08-01 22:25:45 +00:00
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"execution_count": 62,
|
2020-03-28 01:06:31 +00:00
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"metadata": {},
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"outputs": [],
|
2020-08-01 22:25:45 +00:00
|
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"source": [
|
|
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"model3 = lm(medv ~ lstat + I(lstat^2), data=Boston)\n",
|
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"## or this\n",
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"model4 = lm(medv~lstat + poly(lstat,2), data=Boston)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 65,
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"metadata": {},
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"outputs": [
|
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{
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"data": {
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"text/html": [
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"<table>\n",
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"<caption>A anova: 4 × 6</caption>\n",
|
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"<thead>\n",
|
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"\t<tr><th></th><th scope=col>Res.Df</th><th scope=col>RSS</th><th scope=col>Df</th><th scope=col>Sum of Sq</th><th scope=col>F</th><th scope=col>Pr(>F)</th></tr>\n",
|
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|
"\t<tr><th></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n",
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"</thead>\n",
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"<tbody>\n",
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"\t<tr><th scope=row>1</th><td>493</td><td>11321.04</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td></tr>\n",
|
|
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|
"\t<tr><th scope=row>2</th><td>491</td><td>11064.20</td><td> 2</td><td> 2.568379e+02</td><td> 5.698892</td><td>3.575134e-03</td></tr>\n",
|
|
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|
"\t<tr><th scope=row>3</th><td>503</td><td>15347.24</td><td>-12</td><td>-4.283039e+03</td><td>15.839158</td><td>1.824240e-28</td></tr>\n",
|
|
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|
|
"\t<tr><th scope=row>4</th><td>503</td><td>15347.24</td><td> 0</td><td> 1.818989e-12</td><td> NA</td><td> NA</td></tr>\n",
|
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"</tbody>\n",
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"</table>\n"
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],
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"text/latex": [
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"A anova: 4 × 6\n",
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"\\begin{tabular}{r|llllll}\n",
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" & Res.Df & RSS & Df & Sum of Sq & F & Pr(>F)\\\\\n",
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" & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
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"\\hline\n",
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"\t1 & 493 & 11321.04 & NA & NA & NA & NA\\\\\n",
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"\t2 & 491 & 11064.20 & 2 & 2.568379e+02 & 5.698892 & 3.575134e-03\\\\\n",
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"\t3 & 503 & 15347.24 & -12 & -4.283039e+03 & 15.839158 & 1.824240e-28\\\\\n",
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"\t4 & 503 & 15347.24 & 0 & 1.818989e-12 & NA & NA\\\\\n",
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"\\end{tabular}\n"
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],
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"text/markdown": [
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"\n",
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"A anova: 4 × 6\n",
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"\n",
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"| <!--/--> | Res.Df <dbl> | RSS <dbl> | Df <dbl> | Sum of Sq <dbl> | F <dbl> | Pr(>F) <dbl> |\n",
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"|---|---|---|---|---|---|---|\n",
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"| 1 | 493 | 11321.04 | NA | NA | NA | NA |\n",
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"| 2 | 491 | 11064.20 | 2 | 2.568379e+02 | 5.698892 | 3.575134e-03 |\n",
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"| 3 | 503 | 15347.24 | -12 | -4.283039e+03 | 15.839158 | 1.824240e-28 |\n",
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"| 4 | 503 | 15347.24 | 0 | 1.818989e-12 | NA | NA |\n",
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"\n"
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],
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"text/plain": [
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" Res.Df RSS Df Sum of Sq F Pr(>F) \n",
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"1 493 11321.04 NA NA NA NA\n",
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"2 491 11064.20 2 2.568379e+02 5.698892 3.575134e-03\n",
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"3 503 15347.24 -12 -4.283039e+03 15.839158 1.824240e-28\n",
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"4 503 15347.24 0 1.818989e-12 NA NA"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"anova(model, model2, model3, model4)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Categorical data\n",
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"lm automagically creates the dummy vars for us if we have categorical data"
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]
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2020-03-28 01:06:31 +00:00
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "R",
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"language": "R",
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"name": "ir"
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},
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"language_info": {
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"codemirror_mode": "r",
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"file_extension": ".r",
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"mimetype": "text/x-r-source",
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"name": "R",
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"pygments_lexer": "r",
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"version": "3.6.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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