{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# HIDDEN\n", "\n", "from datascience import *\n", "path_data = '../../../data/'\n", "import numpy as np\n", "from scipy import stats\n", "\n", "import matplotlib\n", "matplotlib.use('Agg', warn=False)\n", "%matplotlib inline\n", "import matplotlib.pyplot as plots\n", "plots.style.use('fivethirtyeight')\n", "import warnings\n", "warnings.simplefilter(action=\"ignore\", category=FutureWarning)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# HIDDEN \n", "\n", "galton = Table.read_table(path_data + 'galton.csv')\n", "heights = galton.select('midparentHeight', 'childHeight')\n", "heights = heights.relabel(0, 'MidParent').relabel(1, 'Child')\n", "hybrid = Table.read_table(path_data + 'hybrid.csv')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# HIDDEN\n", "\n", "def standard_units(x):\n", " return (x - np.mean(x))/np.std(x)\n", "\n", "def correlation(table, x, y):\n", " x_in_standard_units = standard_units(table.column(x))\n", " y_in_standard_units = standard_units(table.column(y))\n", " return np.mean(x_in_standard_units * y_in_standard_units)\n", "\n", "def slope(table, x, y):\n", " r = correlation(table, x, y)\n", " return r * np.std(table.column(y))/np.std(table.column(x))\n", "\n", "def intercept(table, x, y):\n", " a = slope(table, x, y)\n", " return np.mean(table.column(y)) - a * np.mean(table.column(x))\n", "\n", "def fit(table, x, y):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * table.column(x) + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visual Diagnostics ###\n", "Suppose a data scientist has decided to use linear regression to estimate values of a response variable based on a predictor. To see how well this method of estmation performs, the data scientist must how far off the estimates are from the actual values. These differences are called *residuals*.\n", "\n", "$$\n", "\\mbox{residual} ~=~ \\mbox{observed value} ~-~ \\mbox{regression estimate}\n", "$$\n", "\n", "A residual is what's left over – the residue – after estimation. \n", "\n", "Residuals are the vertical distances of the points from the regression line. There is one residual for each point in the scatter plot. The residual is the difference between the observed value of $y$ and the fitted value of $y$, so fr the point $(x, y)$,\n", "\n", "$$\n", "\\mbox{residual} ~~ = ~~ y ~-~\n", "\\mbox{fitted value of }y\n", "~~ = ~~ y ~-~\n", "\\mbox{height of regression line at }x\n", "$$\n", "\n", "The function `residual` calculates the residuals. The calculation assumes all the relevant functions we have already defined: `standard_units`, `correlation`, `slope`, `intercept`, and `fit`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def residual(table, x, y):\n", " return table.column(y) - fit(table, x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Continuing our example of using Galton's data to estimate the heights of adult children (the response) based on the midparent height (the predictor), let us calculate the fitted values and the residuals." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
MidParent | Child | Fitted Value | Residual | \n", "
---|---|---|---|
75.43 | 73.2 | 70.7124 | 2.48763 | \n", "
75.43 | 69.2 | 70.7124 | -1.51237 | \n", "
75.43 | 69 | 70.7124 | -1.71237 | \n", "
75.43 | 69 | 70.7124 | -1.71237 | \n", "
73.66 | 73.5 | 69.5842 | 3.91576 | \n", "
73.66 | 72.5 | 69.5842 | 2.91576 | \n", "
73.66 | 65.5 | 69.5842 | -4.08424 | \n", "
73.66 | 65.5 | 69.5842 | -4.08424 | \n", "
72.06 | 71 | 68.5645 | 2.43553 | \n", "
72.06 | 68 | 68.5645 | -0.564467 | \n", "
... (924 rows omitted)
" ], "text/plain": [ "MidParent | Child | Fitted Value | Residual\n", "75.43 | 73.2 | 70.7124 | 2.48763\n", "75.43 | 69.2 | 70.7124 | -1.51237\n", "75.43 | 69 | 70.7124 | -1.71237\n", "75.43 | 69 | 70.7124 | -1.71237\n", "73.66 | 73.5 | 69.5842 | 3.91576\n", "73.66 | 72.5 | 69.5842 | 2.91576\n", "73.66 | 65.5 | 69.5842 | -4.08424\n", "73.66 | 65.5 | 69.5842 | -4.08424\n", "72.06 | 71 | 68.5645 | 2.43553\n", "72.06 | 68 | 68.5645 | -0.564467\n", "... (924 rows omitted)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "heights = heights.with_columns(\n", " 'Fitted Value', fit(heights, 'MidParent', 'Child'),\n", " 'Residual', residual(heights, 'MidParent', 'Child')\n", " )\n", "heights" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When there are so many variables to work with, it is always helpful to start with visualization. The function `scatter_fit` draws the scatter plot of the data, as well as the regression line. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def scatter_fit(table, x, y):\n", " table.scatter(x, y, s=15)\n", " plots.plot(table.column(x), fit(table, x, y), lw=4, color='gold')\n", " plots.xlabel(x)\n", " plots.ylabel(y)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Length | Age | \n", "
---|---|
1.8 | 1 | \n", "
1.85 | 1.5 | \n", "
1.87 | 1.5 | \n", "
1.77 | 1.5 | \n", "
2.02 | 2.5 | \n", "
2.27 | 4 | \n", "
2.15 | 5 | \n", "
2.26 | 5 | \n", "
2.35 | 7 | \n", "
2.47 | 8 | \n", "
... (17 rows omitted)
" ], "text/plain": [ "Length | Age\n", "1.8 | 1\n", "1.85 | 1.5\n", "1.87 | 1.5\n", "1.77 | 1.5\n", "2.02 | 2.5\n", "2.27 | 4\n", "2.15 | 5\n", "2.26 | 5\n", "2.35 | 7\n", "2.47 | 8\n", "... (17 rows omitted)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dugong = Table.read_table('http://www.statsci.org/data/oz/dugongs.txt')\n", "dugong = dugong.move_to_start('Length')\n", "dugong" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we could measure the length of a dugong, what could we say about its age? Let's examine what our data say. Here is a regression of age (the response) on length (the predictor). The correlation between the two variables is substantial, at 0.83." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.8296474554905714" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(dugong, 'Length', 'Age')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "High correlation notwithstanding, the plot shows a curved pattern that is much more visible in the residual plot." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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