{ "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": [ "
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": {}, "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": [ "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(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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\n", 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