{ "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", "\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "baby = pd.read_csv(path_data + 'baby.csv')" ] }, { "cell_type": "code", "execution_count": 3, "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='blue', 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": "markdown", "metadata": {}, "source": [ "# Prediction Intervals\n", "One of the primary uses of regression is to make predictions for a new individual who was not part of our original sample but is similar to the sampled individuals. In the language of the model, we want to estimate $y$ for a new value of $x$.\n", "\n", "Our estimate is the height of the true line at $x$. Of course, we don't know the true line. What we have as a substitute is the regression line through our sample of points.\n", "\n", "The **fitted value** at a given value of $x$ is the regression estimate of $y$ based on that value of $x$. In other words, the fitted value at a given value of $x$ is the height of the regression line at that $x$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we try to predict a baby's birth weight based on the number of gestational days. As we saw in the previous section, the data fit the regression model fairly well and a 95% confidence interval for the slope of the true line doesn't contain 0. So it seems reasonable to carry out our prediction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure below shows where the prediction lies on the regression line. The red line is at $x = 300$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "remove_input" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "scatter_fit(baby, 'Gestational Days', 'Birth Weight')\n", "s = slope(baby, 'Gestational Days', 'Birth Weight')\n", "i = intercept(baby, 'Gestational Days', 'Birth Weight')\n", "fit_300 = s*300 + i\n", "plt.scatter(300, fit_300, color='red', s=20)\n", "plt.plot([300,300], [0, fit_300], color='red', lw=2)\n", "plt.ylim([0, 200]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The height of the point where the red line hits the regression line is the fitted value at 300 gestational days. \n", "\n", "The function `fitted_value` computes this height. Like the functions `correlation`, `slope`, and `intercept`, its arguments include the name of the table and the labels of the $x$ and $y$ columns. But it also requires a fourth argument, which is the value of $x$ at which the estimate will be made." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def fitted_value(table, x, y, given_x):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * given_x + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fitted value at 300 gestational days is about 129.2 ounces. In other words, for a pregnancy that has a duration of 300 gestational days, our estimate for the baby's weight is about 129.2 ounces." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "129.21292417031435" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit_300 = fitted_value(baby, 'Gestational Days', 'Birth Weight', 300)\n", "fit_300" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Variability of the Prediction\n", "We have developed a method making one prediction of a new baby's birth weight based on the number of gestational days, using the data in our sample. But as data scientists, we know that the sample might have been different. Had the sample been different, the regression line would have been different too, and so would our prediction. To see how good our prediction is, we must get a sense of how variable the prediction can be.\n", "\n", "To do this, we must generate new samples. We can do that by bootstrapping the scatter plot as in the previous section. We will then fit the regression line to the scatter plot in each replication, and make a prediction based on each line. The figure below shows 10 such lines, and the corresponding predicted birth weight at 300 gestational days." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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slopeinterceptprediction at x = 300
00.471653-12.537173128.958602
10.441318-3.246474129.149006
20.427643-0.639165127.653674
30.528469-27.520703131.019992
40.488232-16.368378130.101243
50.509250-23.132587129.642469
60.491311-17.413579129.979797
70.4155432.894067127.556932
80.488195-16.437820130.020575
90.451464-6.920024128.519051
\n", "
" ], "text/plain": [ " slope intercept prediction at x = 300\n", "0 0.471653 -12.537173 128.958602\n", "1 0.441318 -3.246474 129.149006\n", "2 0.427643 -0.639165 127.653674\n", "3 0.528469 -27.520703 131.019992\n", "4 0.488232 -16.368378 130.101243\n", "5 0.509250 -23.132587 129.642469\n", "6 0.491311 -17.413579 129.979797\n", "7 0.415543 2.894067 127.556932\n", "8 0.488195 -16.437820 130.020575\n", "9 0.451464 -6.920024 128.519051" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = 300\n", "\n", "lines = pd.DataFrame(columns=['slope', 'intercept'])\n", "\n", "\n", "for i in range(10):\n", " rep = baby.sample(len(baby), replace=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines = lines.append({'slope':a, 'intercept': b}, ignore_index=True)\n", "\n", "lines['prediction at x = '+str(x)] = lines['slope']*x + lines['intercept']\n", "\n", "lines" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# HIDDEN \n", "x = 300\n", "\n", "lines = pd.DataFrame(columns=['slope', 'intercept'])\n", "\n", "\n", "for i in range(10):\n", " rep = baby.sample(len(baby), replace=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines = lines.append({'slope':a, 'intercept': b}, ignore_index=True)\n", "\n", "lines['prediction at x = '+str(x)] = lines['slope']*x + lines['intercept']\n", "\n", "xlims = np.array([291, 309])\n", "\n", "left = xlims[0]*lines.iloc[:,0] + lines.iloc[:,1]\n", "right = xlims[1]*lines.iloc[:,0] + lines.iloc[:,1]\n", "fit_x = x*lines['slope'] + lines['intercept']\n", "\n", "for i in range(10):\n", " \n", " plt.plot(xlims, np.array([left[i], right[i]]), lw=1)\n", " \n", " plt.scatter(x, fit_x[i], s=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The predictions vary from one line to the next. The table below shows the slope and intercept of each of the 10 lines, along with the prediction. " ] }, { "cell_type": "code", "execution_count": 9, "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", " \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", "
slopeinterceptprediction at x = 300
00.510387-22.786504130.329684
10.4219991.631657128.231383
20.479922-14.579319129.397208
30.514294-24.380318129.907938
40.498741-20.520979129.101311
50.516581-24.478420130.495795
60.4209512.657678128.943073
70.445955-5.322110128.464306
80.4215381.828003128.289515
90.4267930.280194128.318088
\n", "
" ], "text/plain": [ " slope intercept prediction at x = 300\n", "0 0.510387 -22.786504 130.329684\n", "1 0.421999 1.631657 128.231383\n", "2 0.479922 -14.579319 129.397208\n", "3 0.514294 -24.380318 129.907938\n", "4 0.498741 -20.520979 129.101311\n", "5 0.516581 -24.478420 130.495795\n", "6 0.420951 2.657678 128.943073\n", "7 0.445955 -5.322110 128.464306\n", "8 0.421538 1.828003 128.289515\n", "9 0.426793 0.280194 128.318088" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bootstrap Prediction Interval\n", "If we increase the number of repetitions of the resampling process, we can generate an empirical histogram of the predictions. This will allow us to create an interval of predictions, using the same percentile method that we used create a bootstrap confidence interval for the slope." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us define a function called ``bootstrap_prediction`` to do this. The function takes five arguments:\n", "- the name of the table\n", "- the column labels of the predictor and response variables, in that order\n", "- the value of $x$ at which to make the prediction\n", "- the desired number of bootstrap repetitions\n", "\n", "In each repetition, the function bootstraps the original scatter plot and finds the predicted value of $y$ based on the specified value of $x$. Specifically, it calls the function `fitted_value` that we defined earlier in this section to find the fitted value at the specified $x$.\n", "\n", "Finally, it draws the empirical histogram of all the predicted values, and prints the interval consisting of the \"middle 95%\" of the predicted values. It also prints the predicted value based on the regression line through the original scatter plot." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Bootstrap prediction of variable y at new_x\n", "# Data contained in table; prediction by regression of y based on x\n", "# repetitions = number of bootstrap replications of the original scatter plot\n", "\n", "def bootstrap_prediction(table, x, y, new_x, repetitions):\n", " \n", " # For each repetition:\n", " # Bootstrap the scatter; \n", " # get the regression prediction at new_x; \n", " # augment the predictions list\n", " predictions = np.array([])\n", " for i in np.arange(repetitions):\n", " bootstrap_sample = table.sample(len(table), replace=True)\n", " bootstrap_prediction = fitted_value(bootstrap_sample, x, y, new_x)\n", " predictions = np.append(predictions, bootstrap_prediction)\n", " \n", " # Find the ends of the approximate 95% prediction interval\n", " left = np.percentile(predictions, 2.5)\n", " right = np.percentile(predictions, 97.5)\n", " \n", " # Prediction based on original sample\n", " original = fitted_value(table, x, y, new_x)\n", " \n", " # Display results\n", " \n", " #Table().with_column('Prediction', predictions).hist(bins=20)\n", " pd.DataFrame({'Prediction':predictions}).hist(bins=20, ec='white');\n", " \n", " plt.xlabel('predictions at x='+str(new_x))\n", " plt.plot(np.array([left, right]), np.array([0, 0]), color='yellow', lw=8);\n", " print('Height of regression line at x='+str(new_x)+':', original)\n", " print('Approximate 95%-confidence interval:')\n", " print(left, right)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=300: 129.21292417031435\n", "Approximate 95%-confidence interval:\n", "127.27917987303 131.33090330196745\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_prediction(baby, 'Gestational Days', 'Birth Weight', 300, 5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows a bootstrap empirical histogram of the predicted birth weight of a baby at 300 gestational days, based on 5,000 repetitions of the bootstrap process. The empirical distribution is roughly normal. \n", "\n", "An approximate 95% prediction interval of scores has been constructed by taking the \"middle 95%\" of the predictions, that is, the interval from the 2.5th percentile to the 97.5th percentile of the predictions. The interval ranges from about 127 to about 131. The prediction based on the original sample was about 129, which is close to the center of the interval." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Effect of Changing the Value of the Predictor\n", "The figure below shows the histogram of 5,000 bootstrap predictions at 285 gestational days. The prediction based on the original sample is about 122 ounces, and the interval ranges from about 121 ounces to about 123 ounces. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=285: 122.2145710160761\n", "Approximate 95%-confidence interval:\n", "121.15453514561544 123.27634704011281\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_prediction(baby, 'Gestational Days', 'Birth Weight', 285, 5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that this interval is narrower than the prediction interval at 300 gestational days. Let us investigate the reason for this.\n", "\n", "The mean number of gestational days is about 279 days: " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "279.1013628620102" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(baby['Gestational Days'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So 285 is nearer to the center of the distribution than 300 is. Typically, the regression lines based on the bootstrap samples are closer to each other near the center of the distribution of the predictor variable. Therefore all of the predicted values are closer together as well. This explains the narrower width of the prediction interval. \n", "\n", "You can see this in the figure below, which shows predictions at $x = 285$ and $x = 300$ for each of ten bootstrap replications. Typically, the lines are farther apart at $x = 300$ than at $x = 285$, and therefore the predictions at $x = 300$ are more variable." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [ "remove_input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "x1 = 300\n", "x2 = 285\n", "\n", "lines = pd.DataFrame(columns=['slope', 'intercept'])\n", "\n", "for i in range(10):\n", " rep = baby.sample(len(baby), replace=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines = lines.append({'slope':a, 'intercept': b}, ignore_index=True)\n", "\n", "\n", "xlims = np.array([260, 310])\n", "left = xlims[0]*lines.iloc[:,0] + lines.iloc[:,1]\n", "right = xlims[1]*lines.iloc[:,0] + lines.iloc[:,1]\n", "fit_x1 = x1*lines['slope'] + lines['intercept']\n", "fit_x2 = x2*lines['slope'] + lines['intercept']\n", "\n", "\n", "\n", "plt.xlim(xlims)\n", "for i in range(10):\n", " plt.plot(xlims, np.array([left[i], right[i]]), lw=1)\n", " plt.scatter(x1, fit_x1[i], s=30)\n", " plt.scatter(x2, fit_x2[i], s=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Words of caution\n", "All of the predictions and tests that we have performed in this chapter assume that the regression model holds. Specifically, the methods assume that the scatter plot resembles points generated by starting with points that are on a straight line and then pushing them off the line by adding random normal noise.\n", "\n", "If the scatter plot does not look like that, then perhaps the model does not hold for the data. If the model does not hold, then calculations that assume the model to be true are not valid.\n", "\n", "Therefore, we must first decide whether the regression model holds for our data, before we start making predictions based on the model or testing hypotheses about parameters of the model. A simple way is to do what we did in this section, which is to draw the scatter diagram of the two variables and see whether it looks roughly linear and evenly spread out around a line. We should also run the diagnostics we developed in the previous section using the residual plot." ] } ], "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 }