{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "path_data = '../../data/'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "plt.style.use('fivethirtyeight')\n", "np.set_printoptions(legacy='1.13')\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "\n", "def standard_units(any_numbers):\n", " \"Convert any array of numbers to standard units.\"\n", " return (any_numbers - np.mean(any_numbers))/np.std(any_numbers) \n", "\n", "def correlation(t, x, y):\n", " return np.mean(standard_units(t[x])*standard_units(t[y]))\n", "\n", "def slope(table, x, y):\n", " r = correlation(table, x, y)\n", " return r * np.std(table[y])/np.std(table[x])\n", "\n", "def intercept(table, x, y):\n", " a = slope(table, x, y)\n", " return np.mean(table[y]) - a * np.mean(table[x])\n", "\n", "def fit(table, x, y):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * table[x] + b\n", "\n", "def residual(table, x, y):\n", " return table.column(y) - fit(table, x, y)\n", "\n", "def scatter_fit(table, x, y):\n", " #fig, ax = plt.subplots(figsize=(7,6))\n", " plt.scatter(table[x], table[y], color='darkblue', s=20)\n", " \n", " plt.plot(table[x], fit(table, x, y), lw=2, color='gold')\n", " plt.xlabel(x)\n", " plt.ylabel(y)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "def draw_and_compare(true_slope, true_int, sample_size):\n", " x = np.random.normal(50, 5, sample_size)\n", " xlims = np.array([np.min(x), np.max(x)])\n", " eps = np.random.normal(0, 6, sample_size)\n", " y = (true_slope*x + true_int) + eps\n", " tyche = pd.DataFrame({'x':x,'y':y})\n", "\n", " plt.figure(figsize=(6, 16))\n", " \n", " plt.subplot(4, 1, 1)\n", " plt.scatter(tyche['x'], tyche['y'], s=20)\n", " plt.plot(xlims, true_slope*xlims + true_int, lw=2, color='green')\n", " plt.title('True Line, and Points Created')\n", "\n", "#---\n", " plt.subplot(4, 1, 2)\n", " plt.scatter(tyche['x'], tyche['y'], s=20)\n", " plt.title('What We Get to See')\n", " \n", "#---\n", " plt.subplot(4, 1, 3)\n", " scatter_fit(tyche, 'x', 'y')\n", " plt.xlabel(\"\")\n", " plt.ylabel(\"\")\n", " plt.title('Regression Line: Estimate of True Line')\n", "#---\n", " plt.subplot(4, 1, 4)\n", " scatter_fit(tyche, 'x', 'y')\n", " \n", " xlims = np.array([np.min(tyche['x']), np.max(tyche['x'])])\n", " plt.plot(xlims, true_slope*xlims + true_int, lw=2, color='green')\n", " plt.ylabel(\"\")\n", " plt.title(\"Regression Line and True Line\")" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "baby = pd.read_csv(path_data + 'baby.csv')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Inference for the True Slope\n", "\n", "Our simulations show that if the regression model holds and the sample size is large, then the regression line is likely to be close to the true line. This allows us to estimate the slope of the true line.\n", "\n", "We will use our familiar sample of mothers and their newborn babies to develop a method of estimating the slope of the true line. First, let's see if we believe that the regression model is an appropriate set of assumptions for describing the relation between birth weight and the number of gestational days." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter_fit(baby, 'Gestational Days', 'Birth Weight')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.40754279338885196" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(baby, 'Gestational Days', 'Birth Weight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By and large, the scatter looks fairly evenly distributed around the line, though there are some points that are scattered on the outskirts of the main cloud. The correlation is 0.4 and the regression line has a positive slope. \n", "\n", "Does this reflect the fact that the true line has a positive slope? To answer this question, let us see if we can estimate the true slope. We certainly have one estimate of it: the slope of our regression line. That's about 0.47 ounces per day." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4665568769492164" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slope(baby, 'Gestational Days', 'Birth Weight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But had the scatter plot come out differently, the regression line would have been different and might have had a different slope. How do we figure out how different the slope might have been?\n", "\n", "We need another sample of points, so that we can draw the regression line through the new scatter plot and find its slope. But from where will get another sample?\n", "\n", "You have guessed it – we will *bootstrap our original sample*. That will give us a bootstrapped scatter plot, through which we can draw a regression line." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bootstrapping the Scatter Plot\n", "We can simulate new samples by random sampling with replacement from the original sample, as many times as the original sample size. Each of these new samples will give us a scatter plot. We will call that a *bootstrapped scatter plot*, and for short, we will call the entire process *bootstrapping the scatter plot*.\n", "\n", "Here is the original scatter diagram from the sample, and four replications of the bootstrap resampling procedure. Notice how the resampled scatter plots are in general a little more sparse than the original. That is because some of the original points do not get selected in the samples." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [ "remove_input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "plt.figure(figsize=(8, 18))\n", "plt.subplot(5, 1, 1)\n", "plt.scatter(baby.iloc[:,1], baby.iloc[:,0], s=10)\n", "plt.xlim([150, 400])\n", "plt.title('Original sample')\n", "\n", "for i in np.arange(1, 5, 1):\n", " plt.subplot(5,1,i+1)\n", " rep = baby.sample(len(baby), replace=True)\n", " plt.scatter(rep.iloc[:,1], rep.iloc[:,0], s=10)\n", " plt.xlim([150, 400])\n", " plt.title('Bootstrap sample '+str(i))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating the True Slope\n", "We can bootstrap the scatter plot a large number of times, and draw a regression line through each bootstrapped plot. Each of those lines has a slope. We can simply collect all the slopes and draw their empirical histogram. Recall that by default, the `sample` method draws at random with replacement, the same number of times as the number of rows in the table. That is, `sample` generates a bootstrap sample by default." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "slopes = np.array([])\n", "for i in np.arange(5000):\n", " bootstrap_sample = baby.sample(len(baby), replace=True)\n", " bootstrap_slope = slope(bootstrap_sample, 'Gestational Days', 'Birth Weight')\n", " slopes = np.append(slopes, bootstrap_slope)\n", "\n", "pd.DataFrame({'Bootstrap Slopes':slopes}).hist(bins=20, ec='white');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then construct an approximate 95% confidence interval for the slope of the true line, using the bootstrap percentile method. The confidence interval extends from the 2.5th percentile to the 97.5th percentile of the 5000 bootstrapped slopes." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.38225576134670686, 0.55888349421281591)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "left = np.percentile(slopes, 2.5)\n", "right = np.percentile(slopes, 97.5)\n", "left, right" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An approximate 95% confidence interval for the true slope extends from about 0.38 ounces per day to about 0.56 ounces per day. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A Function to Bootstrap the Slope\n", "Let us collect all the steps of our method of estimating the slope and define a function `bootstrap_slope` that carries them out. Its arguments are the name of the table and the labels of the predictor and response variables, and the desired number of bootstrap replications. In each replication, the function bootstraps the original scatter plot and calculates the slope of the resulting regression line. It then draws the histogram of all the generated slopes and prints the interval consisting of the \"middle 95%\" of the slopes. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def bootstrap_slope(table, x, y, repetitions):\n", " \n", " # For each repetition:\n", " # Bootstrap the scatter, get the slope of the regression line,\n", " # augment the list of generated slopes\n", " slopes = np.array([])\n", " for i in np.arange(repetitions):\n", " bootstrap_sample = table.sample(len(table), replace=True)\n", " bootstrap_slope = slope(bootstrap_sample, x, y)\n", " slopes = np.append(slopes, bootstrap_slope)\n", " \n", " # Find the endpoints of the 95% confidence interval for the true slope\n", " left = np.percentile(slopes, 2.5)\n", " right = np.percentile(slopes, 97.5)\n", " \n", " # Slope of the regression line from the original sample\n", " observed_slope = slope(table, x, y)\n", " \n", " # Display results\n", " pd.DataFrame({'Bootstrap Slopes':slopes}).hist(bins=20, ec='white')\n", " plt.plot(np.array([left, right]), np.array([0, 0]), color='yellow', lw=8);\n", " print('Slope of regression line:', observed_slope)\n", " print('Approximate 95%-confidence interval for the true slope:')\n", " print(left, right)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we call `bootstrap_slope` to find a confidence interval for the true slope when the response variable is birth weight and the predictor is gestational days, we get an interval very close to the one we obtained earlier: approximately 0.38 ounces per day to 0.56 ounces per day." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope of regression line: 0.4665568769492164\n", "Approximate 95%-confidence interval for the true slope:\n", "0.381798869241 0.555611704253\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_slope(baby, 'Gestational Days', 'Birth Weight', 5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have a function that automates our process of estimating the slope of the true line in a regression model, we can use it on other variables as well.\n", "\n", "For example, let's examine the relation between birth weight and the mother's height. Do taller women tend to have heavier babies?\n", "\n", "The regression model seems reasonable, based on the scatter plot, but the correlation is not high. It's just about 0.2." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter_fit(baby, 'Maternal Height', 'Birth Weight')" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.20370417718968062" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(baby, 'Maternal Height', 'Birth Weight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, we can use `bootstrap_slope` to estimate the slope of the true line in the regression model." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope of regression line: 1.4780193519284357\n", "Approximate 95%-confidence interval for the true slope:\n", "1.05686977213 1.91804340448\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_slope(baby, 'Maternal Height', 'Birth Weight', 5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A 95% confidence interval for the true slope extends from about 1 ounce per inch to about 1.9 ounces per inch." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Could the True Slope Be 0?\n", "Suppose we believe that our data follow the regression model, and we fit the regression line to estimate the true line. If the regression line isn't perfectly flat, as is almost invariably the case, we will be observing some linear association in the scatter plot.\n", "\n", "But what if that observation is spurious? In other words, what if the true line was flat – that is, there was no linear relation between the two variables – and the association that we observed was just due to randomness in generating the points that form our sample?\n", "\n", "Here is a simulation that illustrates why this question arises. We will once again call the function ``draw_and_compare``, this time requiring the true line to have slope 0. Our goal is to see whether our regression line shows a slope that is not 0.\n", "\n", "Remember that the arguments to the function ``draw_and_compare`` are the slope and the intercept of the true line, and the number of points to be generated." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_and_compare(0, 10, 25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the simulation a few times, keeping the slope of the true line 0 each time. You will notice that while the slope of the true line is 0, the slope of the regression line is typically not 0. The regression line sometimes slopes upwards, and sometimes downwards, each time giving us a false impression that the two variables are correlated." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To decide whether or not the slope that we are seeing is real, we would like to test the following hypotheses:\n", "\n", "**Null Hypothesis.** The slope of the true line is 0. \n", "\n", "**Alternative Hypothesis.** The slope of the true line is not 0. \n", "\n", "We are well positioned to do this. Since we can construct a 95% confidence interval for the true slope, all we have to do is see whether the interval contains 0. \n", "\n", "If it doesn't, then we can reject the null hypothesis (with the 5% cutoff for the P-value). \n", "\n", "If the confidence interval for the true slope does contain 0, then we don't have enough evidence to reject the null hypothesis. Perhaps the slope that we are seeing is spurious." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use this method in an example. Suppose we try to estimate the birth weight of the baby based on the mother's age. Based on the sample, the slope of the regression line for estimating birth weight based on maternal age is positive, about 0.08 ounces per year. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.08500766941582515" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slope(baby, 'Maternal Age', 'Birth Weight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Though the slope is positive, it's pretty small. The regression line is so close to flat that it raises the question of whether the true line is flat." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter_fit(baby, 'Maternal Age', 'Birth Weight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use `bootstrap_slope` to estimate the slope of the true line. The calculation shows that an approximate 95% bootstrap confidence interval for the true slope has a negative left end point and a positive right end point – in other words, the interval contains 0. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope of regression line: 0.08500766941582515\n", "Approximate 95%-confidence interval for the true slope:\n", "-0.0983199011229 0.268808441978\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_slope(baby, 'Maternal Age', 'Birth Weight', 5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because the interval contains 0, we cannot reject the null hypothesis that the slope of the true linear relation between maternal age and baby's birth weight is 0. Based on this analysis, it would be unwise to predict birth weight based on the regression model with maternal age as the predictor." ] } ], "metadata": { "anaconda-cloud": {}, "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 }