Done some lab stuff
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ISLR/notebooks/3.6.2.R.ipynb
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"cells": [
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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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"source": [
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"library(MASS)"
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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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"data": {
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"text/html": [
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"\n",
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"<table width=\"100%\" summary=\"page for Boston {MASS}\"><tr><td>Boston {MASS}</td><td style=\"text-align: right;\">R Documentation</td></tr></table>\n",
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"\n",
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"<h2>\n",
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"Housing Values in Suburbs of Boston\n",
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"</h2>\n",
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"\n",
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"<h3>Description</h3>\n",
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"\n",
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"<p>The <code>Boston</code> data frame has 506 rows and 14 columns.\n",
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"</p>\n",
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"\n",
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"\n",
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"<h3>Usage</h3>\n",
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"\n",
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"<pre>\n",
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"Boston\n",
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"</pre>\n",
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"\n",
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"\n",
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"<h3>Format</h3>\n",
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"\n",
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"<p>This data frame contains the following columns:\n",
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"</p>\n",
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"\n",
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"<dl>\n",
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"<dt><code>crim</code></dt><dd>\n",
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"<p>per capita crime rate by town.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>zn</code></dt><dd>\n",
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"<p>proportion of residential land zoned for lots over 25,000 sq.ft.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>indus</code></dt><dd>\n",
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"<p>proportion of non-retail business acres per town.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>chas</code></dt><dd>\n",
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"<p>Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>nox</code></dt><dd>\n",
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"<p>nitrogen oxides concentration (parts per 10 million).\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>rm</code></dt><dd>\n",
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"<p>average number of rooms per dwelling.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>age</code></dt><dd>\n",
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"<p>proportion of owner-occupied units built prior to 1940.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>dis</code></dt><dd>\n",
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"<p>weighted mean of distances to five Boston employment centres.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>rad</code></dt><dd>\n",
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"<p>index of accessibility to radial highways.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>tax</code></dt><dd>\n",
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"<p>full-value property-tax rate per \\$10,000.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>ptratio</code></dt><dd>\n",
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"<p>pupil-teacher ratio by town.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>black</code></dt><dd>\n",
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"<p><i>1000(Bk - 0.63)^2</i> where <i>Bk</i> is the proportion of blacks\n",
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"by town.\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>lstat</code></dt><dd>\n",
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"<p>lower status of the population (percent).\n",
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"</p>\n",
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"</dd>\n",
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"<dt><code>medv</code></dt><dd>\n",
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"<p>median value of owner-occupied homes in \\$1000s.\n",
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"</p>\n",
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"</dd>\n",
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"</dl>\n",
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"\n",
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"\n",
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"\n",
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"<h3>Source</h3>\n",
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"\n",
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"<p>Harrison, D. and Rubinfeld, D.L. (1978)\n",
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"Hedonic prices and the demand for clean air.\n",
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"<em>J. Environ. Economics and Management</em>\n",
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"<b>5</b>, 81–102.\n",
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"</p>\n",
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"<p>Belsley D.A., Kuh, E. and Welsch, R.E. (1980)\n",
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"<em>Regression Diagnostics. Identifying Influential Data and Sources\n",
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"of Collinearity.</em>\n",
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"New York: Wiley.\n",
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"</p>\n",
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"\n",
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"<hr /><div style=\"text-align: center;\">[Package <em>MASS</em> version 7.3-51.5 ]</div>"
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],
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"text/latex": [
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"\\inputencoding{utf8}\n",
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"\\HeaderA{Boston}{Housing Values in Suburbs of Boston}{Boston}\n",
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"\\keyword{datasets}{Boston}\n",
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"%\n",
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"\\begin{Description}\\relax\n",
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"The \\code{Boston} data frame has 506 rows and 14 columns.\n",
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"\\end{Description}\n",
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"%\n",
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"\\begin{Usage}\n",
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"\\begin{verbatim}\n",
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"Boston\n",
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"\\end{verbatim}\n",
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"\\end{Usage}\n",
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"%\n",
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"\\begin{Format}\n",
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"This data frame contains the following columns:\n",
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"\\begin{description}\n",
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"\n",
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"\\item[\\code{crim}] \n",
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"per capita crime rate by town.\n",
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"\n",
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"\\item[\\code{zn}] \n",
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"proportion of residential land zoned for lots over 25,000 sq.ft.\n",
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"\n",
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"\\item[\\code{indus}] \n",
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"proportion of non-retail business acres per town.\n",
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"\n",
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"\\item[\\code{chas}] \n",
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"Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).\n",
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"\n",
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"\\item[\\code{nox}] \n",
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"nitrogen oxides concentration (parts per 10 million).\n",
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"\n",
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"\\item[\\code{rm}] \n",
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"average number of rooms per dwelling.\n",
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"\n",
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"\\item[\\code{age}] \n",
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"proportion of owner-occupied units built prior to 1940.\n",
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"\n",
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"\\item[\\code{dis}] \n",
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"weighted mean of distances to five Boston employment centres.\n",
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"\n",
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"\\item[\\code{rad}] \n",
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"index of accessibility to radial highways.\n",
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"\n",
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"\\item[\\code{tax}] \n",
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"full-value property-tax rate per \\bsl{}\\$10,000.\n",
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"\n",
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"\\item[\\code{ptratio}] \n",
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"pupil-teacher ratio by town.\n",
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"\n",
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"\\item[\\code{black}] \n",
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"\\eqn{1000(Bk - 0.63)^2}{} where \\eqn{Bk}{} is the proportion of blacks\n",
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"by town.\n",
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"\n",
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"\\item[\\code{lstat}] \n",
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"lower status of the population (percent).\n",
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"\n",
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"\\item[\\code{medv}] \n",
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"median value of owner-occupied homes in \\bsl{}\\$1000s.\n",
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"\n",
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"\n",
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"\\end{description}\n",
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"\n",
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"\\end{Format}\n",
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"%\n",
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"\\begin{Source}\\relax\n",
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"Harrison, D. and Rubinfeld, D.L. (1978)\n",
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"Hedonic prices and the demand for clean air.\n",
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"\\emph{J. Environ. Economics and Management}\n",
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"\\bold{5}, 81--102.\n",
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"\n",
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"Belsley D.A., Kuh, E. and Welsch, R.E. (1980)\n",
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"\\emph{Regression Diagnostics. Identifying Influential Data and Sources\n",
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"of Collinearity.}\n",
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"New York: Wiley.\n",
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"\\end{Source}"
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],
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"text/plain": [
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"Boston package:MASS R Documentation\n",
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"\n",
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"_\bH_\bo_\bu_\bs_\bi_\bn_\bg _\bV_\ba_\bl_\bu_\be_\bs _\bi_\bn _\bS_\bu_\bb_\bu_\br_\bb_\bs _\bo_\bf _\bB_\bo_\bs_\bt_\bo_\bn\n",
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"\n",
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"_\bD_\be_\bs_\bc_\br_\bi_\bp_\bt_\bi_\bo_\bn:\n",
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"\n",
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" The ‘Boston’ data frame has 506 rows and 14 columns.\n",
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"\n",
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"_\bU_\bs_\ba_\bg_\be:\n",
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"\n",
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" Boston\n",
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" \n",
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"_\bF_\bo_\br_\bm_\ba_\bt:\n",
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"\n",
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" This data frame contains the following columns:\n",
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"\n",
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" ‘crim’ per capita crime rate by town.\n",
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"\n",
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" ‘zn’ proportion of residential land zoned for lots over 25,000\n",
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" sq.ft.\n",
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"\n",
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" ‘indus’ proportion of non-retail business acres per town.\n",
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"\n",
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" ‘chas’ Charles River dummy variable (= 1 if tract bounds river; 0\n",
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" otherwise).\n",
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"\n",
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" ‘nox’ nitrogen oxides concentration (parts per 10 million).\n",
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"\n",
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" ‘rm’ average number of rooms per dwelling.\n",
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"\n",
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" ‘age’ proportion of owner-occupied units built prior to 1940.\n",
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"\n",
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" ‘dis’ weighted mean of distances to five Boston employment\n",
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" centres.\n",
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"\n",
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" ‘rad’ index of accessibility to radial highways.\n",
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"\n",
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" ‘tax’ full-value property-tax rate per \\$10,000.\n",
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"\n",
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" ‘ptratio’ pupil-teacher ratio by town.\n",
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"\n",
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" ‘black’ 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by\n",
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" town.\n",
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"\n",
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" ‘lstat’ lower status of the population (percent).\n",
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"\n",
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" ‘medv’ median value of owner-occupied homes in \\$1000s.\n",
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"\n",
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"_\bS_\bo_\bu_\br_\bc_\be:\n",
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"\n",
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" Harrison, D. and Rubinfeld, D.L. (1978) Hedonic prices and the\n",
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" demand for clean air. _J. Environ. Economics and Management_ *5*,\n",
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" 81-102.\n",
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"\n",
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" Belsley D.A., Kuh, E. and Welsch, R.E. (1980) _Regression\n",
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" Diagnostics. Identifying Influential Data and Sources of\n",
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" Collinearity._ New York: Wiley.\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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"source": [
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"?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": 23,
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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",
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"lm(formula = medv ~ lstat, data = Boston)\n",
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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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"\n",
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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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"\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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"source": [
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"lm.fit = lm(medv~lstat, data=Boston)\n",
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"summary(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": null,
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"metadata": {},
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"outputs": [],
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"source": []
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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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ISLR/notebooks/3.6.2.python.ipynb
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ISLR/notebooks/3.6.2.python.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 59,
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"metadata": {},
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"outputs": [],
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"source": [
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"import seaborn as sns\n",
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"import pandas as pd\n",
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"import numpy as np\n",
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"from matplotlib import pyplot as plt\n",
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"from sklearn import linear_model\n",
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"from sklearn.metrics import classification_report as summary\n",
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"\n",
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"sns.set()\n",
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"sns.set(style=\"whitegrid\")\n",
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"tips = sns.load_dataset(\"tips\")\n",
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"plt.rcParams[\"figure.figsize\"] = (5,8)"
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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,
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"metadata": {},
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||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"Boston = pd.read_csv(\"../../datasets/Boston.csv\")\n"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 67,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
"[-0.95004935] 34.5538408793831\n",
|
||||||
|
"0.5441462975864797\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"X = np.array(Boston[\"lstat\"]).reshape(-1,1)\n",
|
||||||
|
"y = Boston[\"medv\"]\n",
|
||||||
|
"model = linear_model.LinearRegression()\n",
|
||||||
|
"model.fit(X, y)\n",
|
||||||
|
"print(model.coef_, model.intercept_)\n",
|
||||||
|
"print(model.score(X,y))\n"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": []
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": []
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"metadata": {
|
||||||
|
"kernelspec": {
|
||||||
|
"display_name": "Python 3",
|
||||||
|
"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": "3.8.2"
|
||||||
|
}
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 4
|
||||||
|
}
|
||||||
20
islr-ch3.md
20
islr-ch3.md
@ -314,6 +314,26 @@ The second solution is to combine the collinear variables together into a single
|
|||||||
Go read it again, it's just an answer of the questions asked at the start of the chapter about a particular dataset, answered with the concepts introduced so far.
|
Go read it again, it's just an answer of the questions asked at the start of the chapter about a particular dataset, answered with the concepts introduced so far.
|
||||||
|
|
||||||
|
|
||||||
|
## 3.5 Comparison with K nearest neighbours (KNN)
|
||||||
|
Linear regression is a parametric approach, because it makes an assumption about the form of Y. TThese approaches have advantages, such as ease of fitting, ease of interpreting, etx. Recall the disadvantages too. if the assumed form is far removed from reality, it makes a poor predictor. We'll take a look at one of the simplest and best known nonparametric approaches, K-nearest neighbours.
|
||||||
|
KNN regression is closely related to KNN classification. The predicted response for a set of predictors is the average of the $\mathcal{N}$ nearest neighbours. In general, the optimal value for K will depend on the bias-variance tradeoff.
|
||||||
|
|
||||||
|
Where will least squares linear regression outperform KNN?
|
||||||
|
**the parametric approach will outperform the nonparametric approach if the parametric form that has been selected is close to the true form of f**.
|
||||||
|
In this case, a non-parametric approach incurs a cost in variance
|
||||||
|
that is not offset by a reduction in bias.
|
||||||
|
|
||||||
|
In a real life situation in which the true relationship is unknown, one might draw the conclusion that KNN should be favored over linear regression because it will at worst be slightly inferior than linear regression if the true relationship is linear, and may give substantially better results if the true relationship is non-linear.
|
||||||
|
But in reality, even when the true relationship is highly non-linear, KNN may still provide inferior results to linear regression. In higher
|
||||||
|
dimensions, KNN often performs worse than linear regression.
|
||||||
|
This decrease in performance as the dimension increases is a common
|
||||||
|
problem for KNN, and results from the fact that in higher dimensions
|
||||||
|
there is effectively a reduction in sample size.
|
||||||
|
As a general rule, parametric methods will tend to outperform non-parametric approaches when there is a small number of observations per predictor.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user