{ "cells": [ { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# HIDDEN\n", "\n", "from datascience import *\n", "import numpy as np\n", "import matplotlib\n", "matplotlib.use('Agg', warn=False)\n", "%matplotlib inline\n", "import matplotlib.pyplot as plots\n", "plots.style.use('fivethirtyeight')" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# HIDDEN\n", "\n", "baby = Table.read_table('baby.csv')" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# HIDDEN\n", "\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.column(x))*standard_units(t.column(y)))\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\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", " plots.scatter(table.column(x), table.column(y), s=20)\n", " plots.plot(table.column(x), fit(table, x, y), lw=2, color='gold')\n", " plots.xlabel(x)\n", " plots.ylabel(y)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": 45, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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4FMmjR4925joI4o6jLZmQ3uJWngTUXWZqa60UT6OkLl5kodUKiI4WYDaz2LDB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\nUhUtoPZqWrlcjqCgIAwZMgQ3b97Evn374OLiopq/fNrbb78Nc3NzfP3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# HIDDEN\n", "\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", "plots.scatter(300, fit_300, color='red', s=20)\n", "plots.plot([300,300], [0, fit_300], color='red', lw=2)\n", "plots.ylim([0, 200]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 27, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "129.2129241703143" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit_300 = fitted_value(baby, 'Gestational Days', 'Birth Weight', 300)\n", "fit_300" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### The Variability of the Prediction ###\n", "\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": 35, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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Ye5ws28sJYx/h5jBmZt1LRGIGpyo/xFF/hqzUWeRm5pMcO3nURkNXlrgKDw/H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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# HIDDEN \n", "\n", "x = 300\n", "\n", "lines = Table(['slope','intercept'])\n", "for i in range(10):\n", " rep = baby.sample(with_replacement=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines.append([a, b])\n", "\n", "lines['prediction at x='+str(x)] = lines.column('slope')*x + lines.column('intercept')\n", "\n", "xlims = np.array([291, 309])\n", "left = xlims[0]*lines[0] + lines[1]\n", "right = xlims[1]*lines[0] + lines[1]\n", "fit_x = x*lines['slope'] + lines['intercept']\n", "\n", "for i in range(10):\n", " plots.plot(xlims, np.array([left[i], right[i]]), lw=1)\n", " plots.scatter(x, fit_x[i], s=30)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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", "
slope intercept prediction at x=300
0.503931 -21.6998 129.479
0.53227 -29.5647 130.116
0.518771 -25.363 130.268
0.430556 -1.06812 128.099
0.470229 -11.7611 129.308
0.48713 -16.5314 129.608
0.51241 -23.2954 130.428
0.52473 -27.2053 130.214
0.409943 5.22652 128.21
0.468065 -11.6967 128.723
" ], "text/plain": [ "slope | intercept | prediction at x=300\n", "0.503931 | -21.6998 | 129.479\n", "0.53227 | -29.5647 | 130.116\n", "0.518771 | -25.363 | 130.268\n", "0.430556 | -1.06812 | 128.099\n", "0.470229 | -11.7611 | 129.308\n", "0.48713 | -16.5314 | 129.608\n", "0.51241 | -23.2954 | 130.428\n", "0.52473 | -27.2053 | 130.214\n", "0.409943 | 5.22652 | 128.21\n", "0.468065 | -11.6967 | 128.723" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lines" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Bootstrap Prediction Interval ###\n", "\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": { "deletable": true, "editable": true }, "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": 28, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "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 = make_array()\n", " for i in np.arange(repetitions):\n", " bootstrap_sample = table.sample()\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 = percentile(2.5, predictions)\n", " right = percentile(97.5, predictions)\n", " \n", " # Prediction based on original sample\n", " original = fitted_value(table, x, y, new_x)\n", " \n", " # Display results\n", " Table().with_column('Prediction', predictions).hist(bins=20)\n", " plots.xlabel('predictions at x='+str(new_x))\n", " plots.plot(make_array(left, right), make_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": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=300: 129.21292417\n", "Approximate 95%-confidence interval:\n", "127.300774171 131.361729528\n" ] }, { "data": { "image/png": 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zc3Ns374dr732mtbD2dvbQ6VSIS8vD87OzurleXl5sLe3r3XbjIwMbcdrMGPL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\ncvXqVVRUVKiLTmN4Xk43Nzc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_prediction(baby, 'Gestational Days', 'Birth Weight', 300, 5000)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "### The Effect of Changing the Value of the Predictor ###\n", "\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": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=285: 122.214571016\n", "Approximate 95%-confidence interval:\n", "121.177089926 123.291373304\n" ] }, { "data": { "image/png": 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PPwgODsa9e/fQoEEDvPrqq9i/fz9cXV0BAKGhoSgqKkJ4eLjyBv+0tDTew0hERAYjujD6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\nCgUePXpUYZvqsG2KyVkeQ47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9nwSpVMo7XslooqOjsWjRIty9e7fMRRRERNUBfzMRERGp\nYGEko6sOz+IkIqoID6USERGp4B4jERGRChZGIiIiFSyMREREKlgYiYiIVLAwEhERqWBhJCIiUvH/\nAGhPlREzLMHBAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_prediction(baby, 'Gestational Days', 'Birth Weight', 285, 5000)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 46, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "279.10136286201021" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(baby.column('Gestational Days'))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 32, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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GLPaoqKhg2rRp5zzO1+1m88Xwdbwpf7GIuRq9q22ujnY5ebncSr9T5tuZnswO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\n8PbBTlYesTItzovXJwYTKO2khBCizznrg6zUEcjEUTeRFjMIXdk+9C/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# HIDDEN\n", "\n", "x1 = 300\n", "x2 = 285\n", "\n", "lines = Table(['slope','intercept'])\n", "for i in range(10):\n", " rep = baby.sample(with_replacement=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines.append([a, b])\n", "\n", "xlims = np.array([260, 310])\n", "left = xlims[0]*lines[0] + lines[1]\n", "right = xlims[1]*lines[0] + lines[1]\n", "fit_x1 = x1*lines['slope'] + lines['intercept']\n", "fit_x2 = x2*lines['slope'] + lines['intercept']\n", "\n", "plots.xlim(xlims)\n", "for i in range(10):\n", " plots.plot(xlims, np.array([left[i], right[i]]), lw=1)\n", " plots.scatter(x1, fit_x1[i], s=30)\n", " plots.scatter(x2, fit_x2[i], s=30)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Words of caution ###\n", "\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." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [] } ], "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }