{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "from datascience import *\n", "path_data = 'https://raw.githubusercontent.com/ChemeketaCS/datasci-textbook/main/assets/data/'\n", "import numpy as np\n", "from scipy import stats\n", "\n", "import matplotlib\n", "matplotlib.use('Agg')\n", "%matplotlib inline\n", "import matplotlib.pyplot as plots\n", "plots.style.use('fivethirtyeight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Visual Diagnostics\n", "Suppose a data scientist has decided to use linear regression to estimate values of one variable (called the response variable) based on another variable (called the predictor). To see how well this method of estimation performs, the data scientist must measure 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 for 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": 2, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "family_heights = Table.read_table(path_data + 'family_heights.csv')\n", "heights = family_heights.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": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "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": "code", "execution_count": 4, "metadata": {}, "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 estimating 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": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MidParent Child Fitted Value Residual
75.43 73.2 70.7124 2.48763
75.43 69.2 70.7124 -1.51237
75.43 69 70.7124 -1.71237
75.43 69 70.7124 -1.71237
73.66 73.5 69.5842 3.91576
73.66 72.5 69.5842 2.91576
73.66 65.5 69.5842 -4.08424
73.66 65.5 69.5842 -4.08424
72.06 71 68.5645 2.43553
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": {}, "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": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter_fit(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A *residual plot* can be drawn by plotting the residuals against the predictor variable. The function `residual_plot` does just that. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def residual_plot(table, x, y):\n", " x_array = table.column(x)\n", " t = Table().with_columns(\n", " x, x_array,\n", " 'residuals', residual(table, x, y)\n", " )\n", " t.scatter(x, 'residuals', color='r')\n", " xlims = make_array(min(x_array), max(x_array))\n", " plots.plot(xlims, make_array(0, 0), color='darkblue', lw=4)\n", " plots.title('Residual Plot')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "residual_plot(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The midparent heights are on the horizontal axis, as in the original scatter plot. But now the vertical axis shows the residuals. Notice that the plot appears to be centered around the horizontal line at the level 0 (shown in dark blue). Notice also that the plot shows no upward or downward trend. We will observe later that this lack of trend is true of all regressions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regression Diagnostics\n", "Residual plots help us make visual assessments of the quality of a linear regression analysis. Such assessments are called *diagnostics*. The function ``regression_diagnostic_plots`` draws the original scatter plot as well as the residual plot for ease of comparison." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def regression_diagnostic_plots(table, x, y):\n", " scatter_fit(table, x, y)\n", " residual_plot(table, x, y)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This residual plot indicates that linear regression was a reasonable method of estimation. Notice how the residuals are distributed fairly symmetrically above and below the horizontal line at 0, corresponding to the original scatter plot being roughly symmetrical above and below. Notice also that the vertical spread of the plot is fairly even across the most common values of the children's heights. In other words, apart from a few outlying points, the plot isn't narrower in some places and wider in others.\n", "\n", "In other words, the accuracy of the regression appears to be about the same across the observed range of the predictor variable. \n", "\n", "**The residual plot of a good regression shows no pattern. The residuals look about the same, above and below the horizontal line at 0, across the range of the predictor variable.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Detecting Nonlinearity\n", "Drawing the scatter plot of the data usually gives an indication of whether the relation between the two variables is non-linear. Often, however, it is easier to spot non-linearity in a residual plot than in the original scatter plot. This is usually because of the scales of the two plots: the residual plot allows us to zoom in on the errors and hence makes it easier to spot patterns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Our data are a [dataset](http://www.statsci.org/data/oz/dugongs.html) on the age and length of dugongs, which are marine mammals related to manatees and sea cows (image from [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Dugong_dugon.jpg)). The data are in a table called `dugong`. Age is measured in years and length in meters. Because dugongs tend not to keep track of their birthdays, ages are estimated based on variables such as the condition of their teeth." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Length Age
1.8 1
1.85 1.5
1.87 1.5
1.77 1.5
2.02 2.5
2.27 4
2.15 5
2.26 5
2.35 7
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(path_data + 'dugongs.csv')\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": {}, "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": {}, "outputs": [ { "data": { "image/png": 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9Ro4ciZ9//rnu64MPPnD7+kTkXc1dGx127jqXx5GVRf+KisiPPFZjS8htzbdb0yYLFizArl27MHToUCQlJUGhUGD+/Pn45ZdfYDAYMG+e6z0HLhszZgzGjBkDAJg1q/H1nBqNBtHR0W5fk4jE4+7aaHXVJrQxTXN6raqIv8MW6ryPWOS25tut8G7Xrh1yc3ORlZWF7du3o1u3bqitrcWf//xnzJo1CxERER4tat++fYiPj4dOp8OwYcPw1FNPwWAwePQ1iKhlXK6NdpRBV9TF5XXMMRcACb0hKLc13wqTySS47uYdHTt2xEsvvYS77rqr7rkPP/wQWq0WcXFxOH36NBYtWgSHw4EdO3ZAo9E0ep3La86JyLeSQgdDoXAeKf+tXA+ro4dIFclbQkJCk22S+3j8bbfdVvffffv2xYABA9CvXz9s27YNEyZMaPR7nA2wNYxGo9euLUUcr3/z5niDqnMRen6S0z427d2o0q+AGCu2A+Fn61Z4jx8/vsk2pVKJiIgIDBgwAHfffTeioqI8VhwAxMbGokOHDjh58qRHr0tEHiAI0BW2ddnNHFMAKBpfoOD88vJaey0mt8JbEAScOHEChYWFiIuLQ1RUFIqLi5Gfn4+YmBgYDAZ8+eWXWLVqFT755BP07t3bYwWWlpaioKCAb2ASSYz2wnQEWz902scaNhfV4X9r8WvIbe21mNxaKjh79mxoNBrs2LEDhw8fxhdffIHDhw8jNzcXGo0G6enpOHToENq3b4/nn3exAN9iwdGjR3H06FE4HA6cPXsWR48exZkzZ2CxWLBgwQIcPHgQ+fn52L17N9LS0mAwGDBu3DiPDJiIWkdh/x90BXqXwW2ONbUquAH5rb0Wk1vhvWjRIsyfPx/9+/ev9/yAAQOQnp6OF154AR07dsRDDz2Eb775xum1fvjhBwwfPhzDhw9HVVUVMjMzMXz4cLz44otQqVTIy8vD1KlTkZycjJkzZyI+Ph5ffPEFwsPDWz5KIvIIXYEeEcV9nfYpb7/HY5tIyW3ttZjcmjY5ceIEIiMb34ugffv2dfPR3bp1Q2VlpdNrXX/99TCZTE225+TkuFMSEYlIXfkO2pgfctrHHvQ7WAx7PPq6clt7LSa3wrtLly54++23MXr06AZt//73v9Gly8U1naWlpWjXrp1nKyQi3xFs0BW6XoRgjjkHKNQef3m5rb0Wk1vhPW/ePMyYMQMpKSmYMGECDAYDzp07hy1btuDYsWPIzs4GAOzcuRNJSUleLZiIxBF2bihUtcec9qnUvYqaNveIVBFdya3wvv322xEZGYnMzEwsX74cNTU1UKvVGDhwIDZt2oSRI0cCAF544QWoVCpv1ktEXqasOYLwEtfTEzwcwbfc/pBOamoqUlNT4XA4UFpaisjISCiVSuzZswezZ8/GypUrERIS4s1aicjLdAV6l33Koo5BULm/kyh5R7NPj1cqlSgvL0dmZiauueYajB8/Hps3b/ZCaUQkFk3Zcy6D26adfOlUGwa3FLh95202m7Fp0yasX78eBw8eBAD87ne/w6OPPlrvI+1EJCMOE3RFXV12k9omUuQivB0OB7766iusX78en332GaxWK2JjY/HAAw8gOzsbmZmZGDZsmFi1EpEHuTNFYmn3Eeya+vPf/Mi6NDQZ3gsWLMAHH3yAc+fOISQkBOPGjcOUKVMwcuRIlJWV4fXXXxezTiLykCDrNoRemOy0j4AQlMUWNtrGj6xLQ5PhvXLlSigUCowePRpZWVn11m/ztyyRHAlu3W3P/eAlLHh4RpPt/Mi6NDT5huWf/vQnhIWF4YsvvkBycjLmzp2LQ4cOiVkbEXlIm/NTkRw22Gmff++4HqnPPIr4bj2d9uNH1qWhyTvvFStWYOnSpfj444/x3nvvYc2aNXjjjTcQHx+PcePG8e6bSAaUNXkIL3F9oO/q7zYjryAfaeNdfwSdH1mXBrdP0iksLMT69euxYcMG/PTTTwCAQYMGYfr06Zg4caJfrvEOhA3dr8Tx+hd3pkjK2++HQ+25LZylwt9/tkAz1nnHxMRgzpw52LdvH77++ms88MADOHHiBP7617+iV69e3qyRiJohuCLbZXDXqofAHGvyy+AOFC06Bu3aa6/FtddeixdffBGfffYZ1q9f7+m6iKi5hGroCl0fWmKOKQEUkjsBkZqpVT9BtVqNCRMmNHm2JBG55ol10+HF/aG0O1/18b/qvyKs6+LWlOo2rgX3Pv76JfKx1qybVtm+R1jpKJf9zLEmFBiNEGsWmGvBvY/hTeRjLV037d4mUr9AUHn2UHB3cC249zV7Yyoi8qzmrpsOKXvSjU2k7r20iZT4wQ1wLbgYeOdN5GPurptWOM4joqi7y+tJYRMprgX3PoY3kY+5c9SXW5tIRX4Ge/BQzxTVSjy+zPs4bUIkYUHWrS6D26HQwxxrkkxwkzh4500kRYIDukLXh3mbY34DFG1EKIikhnfeRBLT5vxtLoO7Kvz5i2dIMrgDFu+8iSRCWfsrws8NdNmPB/8SwPAmkgS3NpEyHIIjqIf3iyFZ4LQJkQ+pqne43kQqeMTFTaQY3HQF3nkT+YJQA12hwWU3c0wpoFCJUBDJDe+8iUQWUvaUy+Cu0L916Q1JBjc1TvTw3rt3L9LS0tCnTx/o9XqsXbu2XrsgCMjMzETv3r0RExODsWPH4tixY2KXSeRxytpfoSvQQ1Oxwmk/c6wJtdqJIlVFciV6eFdUVCAxMRGLFy+GVqtt0P7KK69g5cqVWLJkCbZv3w6DwYBJkyahvLxc7FKJPCa8sJvLlSTm6LNcSUJuEz28x4wZg6effhoTJ06EUln/5QVBQFZWFubMmYOJEyciMTERWVlZsFgs2Lhxo9ilErWauuoD6Ar0UAoXmuxTqV9zMbSVYV6vRxAErP94B55e/hbWf7wDguDWKYgkQZJ6wzI/Px9FRUUYNer/9yfWarVISUnBgQMHMG3aNB9WR9QMjnLoijo776I0oDzaKFJBF3Gfbf8hqfAuKioCABgM9d/MMRgMKCgoaPL7jEbv/Q/gzWtLEcfbet01GWin/sppn6MVm2ETOgJl4v557z14BLU1NtTW2OoeJ/XuKGoNYvGHv8vODlGWVHhfdvVxSYIgOD1CyVunRAfCCdRX4nhbR1lzGOElI532sYbOQXXEQvhid2uj0Yhhg/vjTNHFO+9qWw2GDe7vlz/zQPi7LKnwjo6+eHhqcXExOnXqVPd8SUlJg7txIskQ7NAVRrrsZo45ByjUIhRU/wzJPvFdAADffHsUKYOuweRxw3Hs+Gnusy1zkgrvuLg4REdHIzc3F9deey0AwGq1Yt++fXjuued8XB1RQ6GltyDI9o3TPpZ2W2DXDBepoouunNv+cs/3EASgvT4MZ4p2IW38CDz32L2i1kOeJ3p4WywWnDx5EgDgcDhw9uxZHD16FG3btkXnzp0xc+ZMLFu2DAkJCYiPj8fLL7+M0NBQ3H777WKXStQkZa0R4ecGOe1Tq74OFe0/F6mi+q48Q7LKaqt7nudJ+g/Rw/uHH37A+PHj6x5nZmYiMzMTU6ZMQVZWFh555BFUVVVh7ty5MJlMSEpKQk5ODsLDw8UulahRbh38G30CgtL1VIq3JCbE4ehPp6AJVkMbEozLKwJ5nqT/UJhMJi70bEIgvOlxJY7XuWDLP6AtX+i0T43mJlS2W9/KylqvqTnvYYP7Y/K4EU4XAPiDQPi7LKk5byJJclRAV+R6Od2c9/6OZx+TxmcRGjtDMrlPJ78PtEDC8CZyIqKwMxSC860Znt7wR+zOi0Pa+G4iVUXE8KYAceU0gjtL5FTVexB2fpzL667+bjPMjnykjeeyOxIXw5sCQmMfC2/0k4WCAF1hW5fXM0efApR6pI132ZXIK7ifNwWEK5fONbVcTmua7TK4q0MfvrSJlN4LVRK5j3feFBCuXDp39XI5hb0IEcW9XF6D27WSlDC8KSBcno++cs77+PHj7h38234HHOoB3i1QRhp7/8Dflx5KEcObAsLVS+fUlRuQHPYXp99jV8XDEvWdlyuTH24rKw0MbwosQi10he1ddjPHFAOKYBEKkh933j8g7+MblhQwQktGuQzuSt0/Lh38y+BuSmJCHKptNQD4cXtf4p03+T2F/TdEFCe67Mc3JN3T2PsHJD6GN/m1sOLBUNl/cdqnLOo/EFTOjyyj/9fYR+9JfJw2Ib8UZP0MugK90+A+X3sDzLEmBjfJEu+8yb8IVugKY1x2M8dcwMnjx8FtmkiuGN7kN0LMj0JT+abTPuXt98Gh7iNSRZ7DtdV0NYY3yZ6y5meElwxx2semvQdV+ldFqsjzuLaarsbwJvkSBEQURkIBh9Nu5pgCQKEVqSjv4NpquhrfsCRZUleuha6wrdPgrmi77tKabXkHN8C11dQQ77xJXgQbQsqegqZydZNd/PFj7VxbTVdjeJNsqKr3Qlv2GFS1PzfZpyzqRwgq10eWyQ3XVtPVOG1CkqdwlEJrmo2w82ObDG5r2JOX1mz7X3ATNYZ33iRdggPqqrUIKXsaSuFCo11q1YNREfkZoFCJXByRbzG8SZKUNcegLXsMQbZ9jbbbtH+CNeI5CMp2IldGJA0Mb5IWoRKa8qXQVKyAArUNmu1BvVGlWw57cIoPiiOSDoY3SUaQ9Qtoy56A0n66QZsALarD56E6dDa3ayUCw5skQGH/DdqyDKitHzXaXqMZg6qIlyAEdRW3MCIJY3iT7wi1CK58HSHlL0AhWBo0O5SxqIpYjNqQCQD38SCqh+FNPqGyfQ+t+VGoao80aBOghK3NDFjDnwSUET6ojkj6JLfOOzMzE3q9vt5Xz549fV0WeYrDjBDzXISW3tBocNeqB8LSfjususUMbiInJHnnnZCQgK1bt9Y9Vqm4hlf2BAFq6yaElGVA6Shq2KyIgDX8Kdja3M8120RukGR4BwUFITo62tdlkIcoa08ixPwE1LbtjbbbQm6DNeIFCCrXhyhcJoX9raVQAwUuSYb3qVOn0KdPH6jVaiQnJ+Ppp59G165dfV0WNZdQDY3lVWgsL0OB6gbNdlU3WHUvo1ZzQ7MvLYX9raVQAwUuhclkEnxdxJW+/PJLWCwWJCQkoKSkBEuXLoXRaMT+/fvRrl3jn6YzGo0iV0muhKsOoYtmMbTKUw3aHEIQCmvuQYFtGgSEtOj6r779KX49W1z3uFunKDx8zy0tLVe2NZB/S0ho+qA+yd15jx49ut7j5ORkDBgwAOvWrcODDz7Y6Pc4G2BrGI1Gr11bijwxXoW9BCHlCxBctb7R9trg36NKtxyhQT0R34rXGTa4P84UXbzrrbbVYNjg/s2uvbXj9UQNYgqkv8+BMFbJhffVwsLC0Lt3b5w8edLXpZAzggPqqncvbSJlatDsUEbCGr4INdo0j6zZlsL+1lKogQKX5MPbarXCaDTi+uuv93Up1ARlzY/Qmh9DUM2BRttt2nthjVgIQdnWY68phf2tpVADBS7JhfeCBQtw0003oVOnTnVz3pWVlZgyZYqvS6OrOSoQYnkJwRUrm9hEKvHSJlLX+aA4Iv8mufD+7bff8MADD6C0tBTt27dHcnIyvvzyS3Tp0sXXpdEVgqyfQVs2F0r72QZtgqINrGHzYQudCSjUPqhOfFw2SGKTXHivWbPG1yWQEwr7WWjN86Gu3tpoe43mpkubSAXWL1suGySxSS68SaKEWgRXvIYQSyYUQkWDZoeyI6p0S1CrGRuQm0jlGfOhCb74rwxNsBp5xnwfV0T+TnJ7m5D0qGzfIaxkJLTlCxoEtwAVqkNno9ywH7Uh4wIyuAEgMSEO1bYaAEC1rQaJCXE+roj8He+8qWkOE0LKn0dw5Roo0PCzXLXqJFTp/g6H+hofFCctXDZIYmN4U0OCALV1I0LK/galo7hhsyIC1vCFsLW5l5tIXcJlgyQ2hjfVo6w9gRDz41DbdjTabgu5A9aIRRBU3DiMyJcY3nSRUI1Y9esIO/dWE5tI9UCVbhnsmpHi10ZEDTC8CarqndCaH4dOc7xBm4BgVIfNQXXYY4CiZZtIEZHnMbwDmMJejJCyBQi2vt9oe23wcFTplsER5N8b/BDJEcM7EAkOBFe+hZDyhVAI5gbNDqUB1ogXUBNyR8Au/SOSOoZ3gFHW/OfSJlLfNtpe3WYarOHPAEq9uIURUbMwvAOFw4IQy2IEV2RBAXuDZntQX/xS9hg6xN5W9xz36yCSLoZ3AAiyfgKtOR1KR2ObSIXWbSJVYfq1Xhv36yCSLoa3H1PUnoa2LB3q6s8aba/RjEWVbjEEVedG27lfB5F0cW8TfyTUINiyAuEl1zUa3A5lJ1S0XYfKdmubDG6A+3UQSRnvvP2MynYAWvOjUNXmNWgToIItdBasYemAMszltbhfB5F0Mbz9hMJxAZryZ6Gp/Hej7bXqwajSLYdD/Tv3r8n9Oogki+Etd4IAddX7CCn/G5SOkobNCh2qIp5FjfYeQMFZMiJ/wfCWMWWt8eKabdvuRttt2smwhi+CoDKIXBkReVvAhbe31y43dX2Pvq5ghcayHBrLP6CArUGzXRV/aRMpzlET+auAC29vr11u6vqeet2g6lyEmB+Hyn6yQZsADarDHkd12COAQtOKURCR1AVceHt77XJT12/t6yrsRQgp+xuCrRsbba8JToVVtwyOoO6tqJ6I5CLg3sHy9trlpq7f4tcV7AiuyEb4uUGNBrdDGYVK/RuobJfD4CYKIAF35+3O2uXL89N7Dx7BsMH9mzU/3dT1W7JmWllz5NImUoca1ggFbG2mwxq+gJtIEQWggAtvd9YuX56frq2x4UzRTgDuz083df1mrZl2lCPE8iKCK1ZDAUeDZntQP1Tp/g57cLJ71yMivxNw4e2Oy/PTtTU2cff0EAQEWT+Gtmw+lI7fGjYrwmANfxK2NjMABX90RIEs4Oa83eGLPT0UtflocyENoaZ7Gg3umpDxKDccgC10FoObiHjn3ZjL89FXznl7jVCD4IqVCClfAgWqGjQ7VJ1RFbEUtSE3ea8GIpIdhncjLs9PJ/XuiIQE753fqLLtg9b8GFS1xxq0CQhCdeiDqA6bCyhDvVYDEcmTZKdNsrOzcc011yA6OhojRozAN9984+uSPEbhOA+t6SGEld7caHDXqq+Dpf0uVEcsZHATUaMkGd45OTmYP38+Hn/8cezatQuDBw/GHXfcgTNnzvi6tNYRBKgr1yHs3CAEV73ToNmhaItK3auoiPwUDnWiDwokIrmQZHivXLkSU6dOxb333otevXph6dKliI6Oxpo1a3xdWosFVW2GrrAt2phnQekobdBu006BxfAtatpw9z8ick1yc942mw2HDx/GQw89VO/5UaNG4cCBAz6qquUU9gJEFPdpst2u6nlpE6nrRayKiOROcuFdWloKu90Og6H+NqYGgwHFxcWNfo/RaPRaPa25dl/tndCqfm20zSFoUGC7H4U1d0MwqwF4bwzN4c0/SynieP2XP4zV2YIJyYX3ZVd/HF0QhCY/ou6tFSFGo7FF1w6yfo7QC2lO+1RE7UdYUDfEt7Q4L2jpeOWK4/VfgTBWyYV3ZGQkVCpVg7vskpKSBnfjkiNYoSuMcd5FEY6y6NOAB/cQJ6LAI7l3xoKDgzFgwADk5ubWez43NxdDhgzxUVWuhZgfdRnc5e33oSzmDIObiFpNcnfeADB79mz85S9/QVJSEoYMGYI1a9agsLAQ06ZN83VpDShrfkZ4ifNfKjbt3ajSrxCpIiIKBJIM7z/+8Y84f/48li5diqKiIvTp0wfvv/8+unTp4uvS/p8gIKKwHRQQnHYzxxQACq1IRRFRoJBkeAPAAw88gAceeMDXZTRKXfk22pgfdtqnou1a1IaMFakiIgo0kg1vSXKYoCvq6rSLXdUdlqjvxamHiAIWw9tNbUr/CLVtu9M+ZVE/QlB1FKkiIgpkklttIjUq237oCvROg9sa9iTMsSYGNxGJhnfeTRFqkRw2CGi4DUk95phSQKESpyYiokt4592IYMs/oSts77SPJfILmGNNDG4i8gneeV9B4ShFRFEPp31qNKNR2e4DkSoiImocw/uSEPNcaCpfd9rHHH0KUOpFqYeIyJmAD2+V7RDCSm9w2qdS9+rFfbaJiCQicMNbqEbYuSFQ2U812eVC7QgoO23mXiREJDkBGd7BFW9AW/a40z5lUXk4cbICCQxuIpKggFttojXNchrclbpXL63Z7iBiVUREzRNQd97K2l8QXLWu0TZ7UG9Y2u8GFGqRqyIiar6ACm8ItkafLm+/Aw71AHFrISJqhYCaNnGofwdr6GMQFGEAgOrQ2TDHmhjcRCQ7gXXnDaA64mlUhy8AFAH1e4uI/ExgJhiDm4hkjilGRCRDDG8iIhlieBMRyRDDm4hIhhjeREQyxPAmIpIhhjcRkQwxvImIZEhhMpkEXxdBRETNwztvIiIZYngTEckQw5uISIYY3kREMsTwJiKSoYAM77179yItLQ19+vSBXq/H2rVrXX7P119/jdGjR6NTp07o3r07pkyZguPHj4tQbessX74cqamp6Ny5M3r06IHJkycjLy/P5ff9+OOPuOWWWxATE4M+ffpgyZIlEATpL0xqyXh3796NKVOmoFevXoiNjUVKSgreeecdkSpunZb+fC87ceIEOnXqhI4dO3qxSs9p6XgFQcCqVaswaNAgREVFoVevXli4cKH3C/aigAzviooKJCYmYvHixdBqtS77nzp1ClOnTsXQoUOxa9cubN68GVarFXfccYcI1bbOnj17MH36dGzbtg1btmxBUFAQbr31Vly4cKHJ7ykrK8OkSZMQFRWF7du3Y/HixVixYgX++c9/ilh5y7RkvAcPHkTfvn3x1ltvYd++fZg+fTrmzJmDDz74QMTKW6Yl473MZrPh/vvvR0pKigiVekZLx/u3v/0Nb7zxBhYuXIiDBw/i/fffl9W4GxPw67w7duyIl156CXfddVeTfT766CNMmzYN586dg0qlAgDs2rULEyZMwIkTJxAZGSlWua1msVjQpUsXrF27FjfffHOjfS7/Jf/ll1/qfrktXboUa9asQV5eHhQKhZglt4o7423MfffdB7vdLps78MuaM96MjAyYzWYMGzYM8+bNw//+9z+RqvQcd8ZrNBoxdOhQ7N27F7169RK5Qu8JyDvv5howYADUajXefvtt2O12lJeX47333sO1114rq+AGLv5ldzgc0Ov1TfY5ePAghg4dWu9fJTfccAMKCgqQn58vQpWe4854G1NeXt7s75ECd8e7bds2bNu2DUuWLBGnMC9xZ7yffvopunbtiq+++gr9+/dHv3798Ne//hXnzp0Tr1AvYHi7IS4uDps2bUJmZiaioqLQpUsX5OXlYcOGDb4urdnmz5+Pfv36YfDgwU32KS4uhsFgqPfc5cfFxcVerc/T3Bnv1T7//HPs3LkT9913n/cK8xJ3xltYWIhHHnkEq1evRnh4uIjVeZ474z116hTOnDmDnJwcrFq1CqtXr4bRaERaWhocDoeI1XoWw9sNRUVFeOihh5CWlobt27dj69atCAsLw3333SerH/6TTz6J/fv345133qmb/mnK1VMjl9+slNOUSXPGe9n+/fvx5z//GUuWLEFSUpKXK/Qsd8c7Y8YM3H///Rg0aJCI1Xmeu+N1OByorq7G6tWrMWzYMKSkpGD16tU4dOgQvv/+exEr9qyAOz2+JV5//XW0adMGzz33XN1z//rXv9C3b18cOHAAQ4cO9WF17snIyEBOTg4+/vhjdO3a1WnfqKioBnfYJSUlANDgjlyqmjPey/bt24c777wTGRkZmD59uncL9LDmjHfXrl3Yu3dv3ZSJIAhwOByIjIzEsmXLZPEvjuaMNzo6GkFBQYiPj697rkePHggKCsLZs2eRnJzs5Wq9g+Hthqqqqga/2S8/lsOdd3p6OnJycrB161b07NnTZf/Bgwdj4cKFsFqtCAkJAQDk5uYiNjYWcXFx3i631Zo7XuDi8tHJkycjPT0ds2bN8nKFntXc8X7zzTf1Hn/66adYtmwZvv76a3To0MFbZXpMc8d73XXXoba2Fr/++iu6desG4OJUSm1tLTp37uztcr0mIKdNLBYLjh49iqNHj8LhcODs2bM4evQozpw5AwB49tlnMWHChLr+Y8aMwZEjR7B48WKcOHEChw8fxuzZs9GpUycMGDDAR6NwzxNPPIF169YhOzsber0eRUVFKCoqgsViqetz9Xhvv/12aLVazJo1C3l5ediyZQv+8Y9/YNasWZKfNmnJeHfv3o077rgD06ZNw5133ln3PZf/tSFlLRlvYmJiva/Y2FgolUokJiZK/k3alox35MiR6N+/P2bPno0jR47gyJEjmD17NpKTkzFw4EBfDMMjAjK8f/jhBwwfPhzDhw9HVVUVMjMzMXz4cLz44osALr6h8+uvv9b1HzFiBLKzs/Hpp59i+PDhuO222xAUFISNGzciNDTUV8NwS3Z2NsrLyzFx4kT06tWr7mvFihV1fa4er06nw6ZNm1BQUIDU1FTMnTsXs2fPxoMPPuiLITRLS8a7bt06VFZWYsWKFfW+JzU11RdDaJaWjFfOWjJepVKJDRs2wGAwYOzYsbjtttvQsWNHrFu3DkqlfCMw4Nd5ExHJkXx/7RARBTCGNxGRDDG8iYhkiOFNRCRDDG8iIhlieBMRyRDDm/zC2rVrodfrcfLkSV+XUs/WrVsb3Qd99+7d0Ov12LFjh/hFkV9geBN50SeffIJVq1b5ugzyQwxvIiIZYnhTwHjrrbcwbNgwREdHo3v37njwwQcbHJ+l1+uxaNEivPbaa7jmmmvQqVMn3HLLLTh27Fi9fna7HYsWLao793L8+PH45ZdfoNfrkZmZCQCYOXMm3nvvPfz222/Q6/XQ6/Xo169fvetUVlZi7ty56N69O3r06IEZM2bAZDJ59c+B/AN3FaSAsHDhQvzzn//EX/7yFzz//PP47bff8MILL+DYsWP44osv6u0auWHDBiQkJGDx4sWoqanBU089halTp+Lbb79FUNDF/2UyMzOxbNkyPPzwwxg5ciSOHDmCKVOm1HvNefPmobS0FN9//z3ee+89AEBwcHC9PvPnz8eNN96I7OxsGI1GPPPMM1AqlXjttde8/CdCcsfwJr+Xn5+PV199Fenp6UhPT697Pj4+HjfddBM+++wzjBs3ru55tVqNDRs2QK1W1z1377334tChQxgyZAhMJhOysrJw//3349lnnwUApKamIigoCAsWLKj7nm7duiEyMhLBwcFNHnyQkpKCpUuXAgBGjRqF48eP4+2330ZWVpbkd3Ak3+K0Cfm9HTt2wOFw4M4770RtbW3dV3JyMiIiIhrsb52amlovuBMTEwEAZ8+eBQD8+OOPqKiowMSJE+t939WP3XHjjTfWe5yYmIjq6mrZHTdH4uOdN/m9ywfNNrV38/nz5+s9btu2bb3Hl6c6rFYrgIvH4gENTxWKiopqdm2uXouoKQxv8nvt2rUDAGzatKnRwwauDlBXoqOjAVz8pdCnT5+653m3TGJieJPfS01NhVKpxJkzZzxywELfvn0RGhqKjz76CMOHD697fvPmzQ36ajQaVFVVtfo1ia7G8Ca/8tVXX9XdGV8WERGBOXPmYN68eTh+/DiGDRuGkJAQnD17Fjt27MDdd99dL4Rd0ev1mDlzJpYtW4awsLC61SbvvPMOANQ7naVXr164cOEC3njjDQwcOBAajQZ9+/b1zGApoDG8ya/MmzevwXN9+vTBvn370LNnT2RnZyM7OxsKhQIdO3bEiBEj0KNHj2a/TkZGBgRBwDvvvIPVq1cjKSkJq1atwo033oiIiIi6fvfccw++++47PPfcczCbzejcuTP+85//tGqMRACPQSPymM2bN+O+++7Dp59+ipSUFF+XQ36Od95ELfDdd99h27ZtSE5ORkhICA4fPoy///3vGDRoEIYOHerr8igAMLyJWiA0NBTffPNN3WnmBoMBkyZNwjPPPMMP15AoOG1CRCRD/IQlEZEMMbyJiGSI4U1EJEMMbyIiGWJ4ExHJEMObiEiG/g/3vVDi4kgefwAAAABJRU5ErkJggg==\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(dugong, 'Length', 'Age')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While you can spot the non-linearity in the original scatter, it is more clearly evident in the residual plot.\n", "\n", "At the low end of the lengths, the residuals are almost all positive; then they are almost all negative; then positive again at the high end of lengths. In other words the regression estimates have a pattern of being too high, then too low, then too high. That means it would have been better to use a curve instead of a straight line to estimate the ages.\n", "\n", "**When a residual plot shows a pattern, there may be a non-linear relation between the variables.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Detecting Heteroscedasticity\n", "\n", "*Heteroscedasticity* is a word that will surely be of interest to those who are preparing for Spelling Bees. For data scientists, its interest lies in its meaning, which is \"uneven spread\". \n", "\n", "Recall the table `hybrid` that contains data on hybrid cars in the U.S. Here is a regression of fuel efficiency on the rate of acceleration. The association is negative: cars that accelearate quickly tend to be less efficient." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(hybrid, 'acceleration', 'mpg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how the residual plot flares out towards the low end of the accelerations. In other words, the variability in the size of the errors is greater for low values of acceleration than for high values. Uneven variation is often more easily noticed in a residual plot than in the original scatter plot.\n", "\n", "**If the residual plot shows uneven variation about the horizontal line at 0, the regression estimates are not equally accurate across the range of the predictor variable.**" ] } ], "metadata": { "celltoolbar": "Tags", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 1 }