{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "# Install datascience package if needed\n", "try:\n", " import datascience\n", "except ImportError:\n", " import micropip\n", " await micropip.install('datascience')\n", "from datascience import *\n", "path_data = '../../../assets/data/'\n", "import numpy as np\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": [ "# 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": "code", "execution_count": 2, "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "baby = Table.read_table(path_data + 'baby.csv')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "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": {}, "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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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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": {}, "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": [ "129.2129241703143" ] }, "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", "\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": { "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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": {}, "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": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "<table border=\"1\" class=\"dataframe\">\n", " <thead>\n", " <tr>\n", " <th>slope</th> <th>intercept</th> <th>prediction at x=300</th>\n", " </tr>\n", " </thead>\n", " <tbody>\n", " <tr>\n", " <td>0.431704</td> <td>-1.10973 </td> <td>128.402 </td>\n", " </tr>\n", " <tr>\n", " <td>0.512942</td> <td>-23.6503 </td> <td>130.232 </td>\n", " </tr>\n", " <tr>\n", " <td>0.450939</td> <td>-6.73161 </td> <td>128.55 </td>\n", " </tr>\n", " <tr>\n", " <td>0.447632</td> <td>-5.68583 </td> <td>128.604 </td>\n", " </tr>\n", " <tr>\n", " <td>0.353555</td> <td>20.1531 </td> <td>126.22 </td>\n", " </tr>\n", " <tr>\n", " <td>0.469301</td> <td>-11.6276 </td> <td>129.163 </td>\n", " </tr>\n", " <tr>\n", " <td>0.445023</td> <td>-5.01298 </td> <td>128.494 </td>\n", " </tr>\n", " <tr>\n", " <td>0.540571</td> <td>-31.3711 </td> <td>130.8 </td>\n", " </tr>\n", " <tr>\n", " <td>0.487377</td> <td>-16.8051 </td> <td>129.408 </td>\n", " </tr>\n", " <tr>\n", " <td>0.451658</td> <td>-5.45954 </td> <td>130.038 </td>\n", " </tr>\n", " </tbody>\n", "</table>" ], "text/plain": [ "slope | intercept | prediction at x=300\n", "0.431704 | -1.10973 | 128.402\n", "0.512942 | -23.6503 | 130.232\n", "0.450939 | -6.73161 | 128.55\n", "0.447632 | -5.68583 | 128.604\n", "0.353555 | 20.1531 | 126.22\n", "0.469301 | -11.6276 | 129.163\n", "0.445023 | -5.01298 | 128.494\n", "0.540571 | -31.3711 | 130.8\n", "0.487377 | -16.8051 | 129.408\n", "0.451658 | -5.45954 | 130.038" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lines" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "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": 9, "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 = 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": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=300: 129.2129241703143\n", "Approximate 95%-confidence interval:\n", "127.30986480617071 131.3039886526053\n" ] }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "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", "\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": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=285: 122.21457101607608\n", "Approximate 95%-confidence interval:\n", "121.15559627774567 123.29019769886106\n" ] }, { "data": { "image/png": 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4ubnB0dER3t7euHTpksHbIiKihqFGIbZr1y48/vjjGDJkCKZMmYIpU6ZgyJAh6NmzJ3bs2FHrIlJSUhATE4MePXroTV+9ejWioqIQHh6OgwcPQi6XY/z48cjLy6v1toiIqOGQHGJxcXEICAhAixYtsHTpUsTHxyMuLg5Lly6FjY0NZs+ejbi4mp/uyc3NxcyZM7F27Vo4ODjopouiiOjoaAQHB8PHxwfu7u6Ijo5Gfn4+du7cWePtEBFRwyM5xD7++GN4eHjg8OHDmDdvHp577jmMGTMG8+bNw5EjR9CnTx98/PHHNS7gQUgNHTpUb3pGRgbUajW8vLx002xsbODp6Ynk5OQab4eIiBoeyQM7bty4gVmzZsHa2rrcPGtra0yePBkffPBBjTYeExODtLQ0rF+/vtw8tVoNAJDL5XrT5XI5bt68WWmbqampNaqhMbHkvsnXFkOr1RrURklpiVHbqG1bxq7DlG0AQL423yjfLUv+fpqrhtCnSqWyyvmSQ8zNza3K8Pjrr7/QrVs3yYWlpqYiLCwM33//PZo1a1bpcv8cti+KYpVD+avb4cYqNTXVovvmwu8ZkMlkBrVh1dTKaG1otdpat2XMOkzdBgDYymyhVDob1Ialfz/NUWPpU8mnE8PCwhATE4Pdu3eXm7dr1y7Exsbiww8/lLzh//73v8jOzsbTTz+N1q1bo3Xr1jh69Cg2btyI1q1bo1WrVgCAzMxMvfWysrLKHZ0REVHjJPlIbO3atWjdujVmzJiBxYsXo0uXLhAEAWlpabh9+zZcXFywZs0arFmzRreOIAjYvn17he15e3ujb9++etNee+01uLi4YP78+XB1dYVCoUBSUhL69esHACgsLMSxY8cQFhZWm30lIqIGRnKIXb58GYIgwMnJCcD904cA0Lx5czg5OaGoqAi//fab3jpVnfZzcHDQG40IAC1atEDLli3h7u4OAAgMDMTKlSuhVCrh6uqKyMhIyGQy+Pn5SS2biIgaMMkhdu7cubqso0JBQUEoKChASEgINBoNPDw8kJCQADs7u3qvhYiIzE+NHztVl/bu3av3WRAEhIaGIjQ01EQVERGROavVY6eIiIjMAUOMiIgsFkOMiIgsllldEyMiyyMI929GN4SVwH+KqHb4zSEig+Tm3cOqTeUfglAT82f4GKkaamwkn07s3bs3vvvuu0rn79u3D7179zZKUURERFJIDrGrV69W+bBQrVaLa9euGaUoIiIiKWo0sKOqJ3BcuXKFNyETEVG9qvKaWHx8PLZu3ar7HBkZiZiYmHLLaTQaXLx4EaNGjTJ+hURERJWoMsS0Wq3uvV7A/bcwl5WV6S0jCAJatGiBadOmYfHixXVTJRERUQWqDLGZM2di5syZAIBevXph+fLlGDNmTL0URkREVB3JQ+zPnj1bl3UQERHVWI3vE8vLy8P169eRk5MDURTLzR84cKBRCiMiIqqO5BDLycnBokWLsHv3bpSWlpabL4oiBEHAnTt3jFogERFRZSSH2Jtvvok9e/Zg5syZGDhwYLkXWhIREdU3ySH2448/Yvbs2Vi2bFld1kNERCSZ5JudmzVrBhcXl7qshYiIqEYkh5iPjw8OHDhQl7UQERHViOQQmzdvHm7duoU5c+YgJSUFt27dwu3bt8v9IiIiqi+Sr4l5eHhAEAScPn0a27dvr3Q5jk4kIqL6IjnEFi5cWOUDgGvqs88+w+bNm3VPvndzc8OCBQt0z18URRHLly9HTEwMNBoNPDw8EBkZie7duxutBiIismySQyw0NNSoG27fvj2WLl0KFxcXlJWVYevWrZg6dSp+/vlnPP7441i9ejWioqIQFRUFpVKJFStWYPz48UhJSeHT8omICEANX8XyQGlpKe7cuYOSkpJab9jb2xvPPvssHnvsMbi6uuK9996Dra0tUlJSIIoioqOjERwcDB8fH7i7uyM6Ohr5+fnYuXNnrbdJREQNS41C7OTJk/D19UX79u3h6uqKo0ePAgCys7Pxwgsv4NChQ7UqorS0FLt27YJWq8WTTz6JjIwMqNVqeHl56ZaxsbGBp6cnkpOTa7UNIiJqeCSfTvzvf/+LcePGQaFQ4MUXX0RsbKxuXuvWrZGfn48vv/wSQ4cOlbzxCxcuYOTIkSgsLIRMJsOWLVvQo0cPXVDJ5XK95eVyOW7evFllm6mpqZK339hYct/ka4urfLO4FCWlJUZto7ZtGbsOU7ZhzHYs+ftprhpCnyqVyirnSw6xDz/8EC4uLvjpp5+g1Wr1QgwABg8ejK+++qrGxR05cgS5ublITExEYGAg9uzZo5v/z4EkD57PWF2bVF5qaqpF982F3zMgk8kMasOqqZXR2tBqtbVuy5h1mLoNY7Zjyd9Pc2TpP/NSST6dePLkSbz00kuwtrauMEg6dOig9wJNKZo1a4bHHnsMffv2xfvvv4+ePXti3bp1UCgUAIDMzEy95bOyssodnRERUeMlOcSaNGmCJk0qX1ytVsPGxsagYsrKylBcXAxnZ2coFAokJSXp5hUWFuLYsWMYMGCAQdsgIqKGQ3KI9enTB/v27atwXnFxMXbs2IEnn3xS8oY/+OAD/Prrr8jIyMCFCxewdOlS/PLLL5g0aRIEQUBgYCBWrVqFxMREXLx4EXPnzoVMJoOfn5/kbRARUcMm+ZrY/Pnz4efnh9dffx2TJk0CANy6dQs//vgjIiMj8eeffyIqKkryhtVqNWbNmoXMzEzY29ujR48e2LlzJ0aMGAEACAoKQkFBAUJCQnQ3OyckJPAeMSIi0pEcYsOHD8f69esREhKC+Ph4AEBgYCBEUcSjjz6KjRs34oknnpC84ejo6CrnC4KA0NBQo99kTUREDYfkEAMAPz8/jBkzBklJSfjjjz9QVlaGLl26YMSIEbC1ta2rGomIiCpUoxADgBYtWsDb27suaiEiIqoRyQM7vvvuO4SEhFQ6PyQkpNKBH0RERHVBcoitXbsW9+7dq3R+YWEhVq9ebZSiiIiIpJAcYhcvXkSfPn0qnd+7d29cvnzZKEURERFJIfmaWElJCQoKCiqdX1BQgKKiIqMURQ2L+nYOsnLuGtRGUXGxkaohooZEcoi5u7sjMTERr7/+erknd5SVlSExMRFubm5GL5AsX1bOXYStiTOojeBXxxupGiJqSCSfTpwzZw5OnDgBf39/nD59GkVFRSgqKsLp06cxZcoUnDhxArNnz67LWomIiPRIPhKbOHEi/vzzT6hUKhw4cADA/RuSHzxZftGiRZg8eXKdFUpERPRPNbpPbMGCBfDz88O3336L9PR0iKKILl26YOzYsejcuXMdlUhERFQxSSFWVFSEhIQEdO3aFR4eHpg3b15d10VERFQtSdfEmjdvjqCgIJw7d66u6yEiIpJM8sAOpVJZ45deEhER1SXJIbZw4UJ89tlnuHDhQl3WQ0REJJnkgR2HDx+GXC7HkCFD8OSTT6JLly7l3uQsCAIiIyONXiQREVFFJIfYpk2bdH8+fvw4jh8/Xm4ZhhgREdUnySGWk5NTl3UQERHVWI3fJ0ZEZGzWzZvjwu8ZBrXRpqU9FPKWRqqILEWNQ+z48eM4fPgwbt++jdmzZ8PV1RVarRaXL1+GUqmEvb19XdRJRA3YXW0BPo3ZblAbS96YyhBrhCSPTiwuLsZLL72EMWPGQKVS4fPPP8eNGzcAAE2bNoWfnx82bNggecMff/wxhg8fjo4dO8LFxQWTJ0/GxYsX9ZYRRREqlQpubm5wdHSEt7c3Ll26JHkbRETUsEkOMZVKhf379yMiIgIpKSkQRVE3z9raGr6+vvj+++8lb/iXX37BjBkzsH//fiQmJsLKygq+vr56195Wr16NqKgohIeH4+DBg5DL5Rg/fjzy8vIkb4eIiBouySG2Y8cOvPLKK5gxYwZatWpVbr5SqUR6errkDSckJOCll16Cu7s7evTogfXr1yMrK0s36lEURURHRyM4OBg+Pj5wd3dHdHQ08vPzsXPnTsnbISKihktyiN2+fRs9e/asdH7z5s2h1WprXUh+fj7Kysrg4OAAAMjIyIBarYaXl5duGRsbG3h6eiI5ObnW2yEiooZDcogpFIoqj7ROnDgBZ2fnWheyePFi9OzZE08++SQA6B5xJZfL9ZaTy+XIzMys9XaIiKjhkDw6cdy4cdi8eTOmTJmiO50oCAIA4Pvvv8eOHTuwYMGCWhXx9ttv4/jx49i3bx+aNm2qN+/BNh548P6yyqSmptaqhsbAVH2Try026CgdAEpKS8yujdq2ZY77Yg7tGNpGvjafP///0BD6Q6lUVjlfcogtWrQIhw8fxtChQzFgwAAIgoCPP/4YYWFhOHnyJDw8PBAUFFTjAkNDQ5GQkIBvv/1W751kCoUCAJCZmQknJyfd9KysrHJHZw+rbocbq9TUVJP1zYXfMyCTyQxqw6qplVm1odVqa92Wue2LoYzVjqFt2MpsoVTW/mxQQ2PKn/n6JPl0op2dHX744QfMnz8ft2/fhrW1NY4fPw6tVovQ0FB8++23sLa2rtHGFy1ahJ07dyIxMRFdu3bVm+fs7AyFQoGkpCTdtMLCQhw7dgwDBgyo0XaIiKhhqtHNztbW1njrrbfw1ltvGbzhBQsW4KuvvsKWLVvg4OCguwYmk8lga2sLQRAQGBiIlStXQqlUwtXVFZGRkZDJZPDz8zN4+0REZPmqDbGioiJ89913SE9PR6tWrTBq1Cg4OjoavOGNGzcCAHx8fPSmL1q0CKGhoQCAoKAgFBQUICQkBBqNBh4eHkhISICdnZ3B2yciIstXZYip1WqMGTMGf/75p+7m5hYtWmD79u0YOHCgQRvWaDTVLiMIAkJDQ3WhRkRE9LAqr4l99NFHSE9Px9y5c/HVV19BpVLB2toaCxcurK/6iIiIKlXlkdjBgwfh7++Pjz76SDetbdu2CAgIwI0bN9ChQ4c6L5CIiKgyVR6JqdXqciMBn3rqKYiiiOvXr9dpYURERNWpMsRKS0vLDZt/8LmwsLDuqiIiIpKg2tGJ6enpOHHihO7z3bt3Ady/kc7W1rbc8h4eHkYsj4iIqHLVhphKpYJKpSo3/Z+DOx48DurOnTvGq46IiKgKVYZYVFRUfdVBRERUY1WG2JQpU+qrDiIiohqT/OxEIiIic1OjZydS46O+nYOsnLsGtVFUXGykaoiI9DHEqEpZOXcRtibOoDaCXx1vpGqIiPTxdCIREVkshhgREVkshhgREVkshhgREVkshhgREVkshhgREVkshhgREVkshhgREVkshhgREVkskz6x4+jRo1i7di3OnDmDmzdvIioqClOnTtXNF0URy5cvR0xMDDQaDTw8PBAZGYnu3bubsGoiMkeCAFz4PcOgNtq0tIdC3tJIFVF9MGmIabVauLu7w9/fH3PmzCk3f/Xq1YiKikJUVBSUSiVWrFiB8ePHIyUlBXZ2diaomIjMVW7ePazatNugNpa8MZUhZmFMejpx5MiRWLJkCXx8fNCkiX4poigiOjoawcHB8PHxgbu7O6Kjo5Gfn4+dO3eaqGIiIjInZntNLCMjA2q1Gl5eXrppNjY28PT0RHJysgkrIyIic2G2IaZWqwEAcrlcb7pcLkdmZqYpSiIiIjNj9q9iEQRB77MoiuWmPSw1NbWuS7JYtembfG0xtFqtQdstKS1pkG3Uti1z3BdzaMcc9idfm9+g/g1pCPuiVCqrnG+2IaZQKAAAmZmZcHJy0k3Pysoqd3T2sOp2uLFKTU2tVd9c+D0DMpnMoG1bNbVqcG1otdpat2Vu+2IoY7VjDvtjK7OFUulsUBvmorY/85bGbE8nOjs7Q6FQICkpSTetsLAQx44dw4ABA0xYGRERmQuTHonl5+cjLS0NAFBWVobr16/j7NmzaNmyJTp27IjAwECsXLkSSqUSrq6uiIyMhEwmg5+fnynLJiIiM2HSEDt16hTGjh2r+6xSqaBSqeDv74/o6GgEBQWhoKAAISEhupudExISeI8YEREBMHGIDR48GBqNptL5giAgNDQUoaGh9VgVERFZCrO9JkZERFQdsx2dSIZT385BVs5dAPeHytfmuXJFxcXGLouIyGgYYg1YVs5dhK2JA4BaDwkPfnW8scsiIjIank4kIiKLxRAjIiKLxd7KnqIAABKtSURBVBAjIiKLxRAjIiKLxRAjIiKLxRAjIiKLxRAjIiKLxfvEiIj+jyCgVg8FeFiblvZQyFsaqSKqDkOMiOj/5Obdw6pNuw1qY8kbUxli9YghZqYefmRUbfGRUUTU0DHEzNTDj4yqLT4yiogaOg7sICIii8UQIyIii8UQIyIii8UQIyIii8WBHURERsR7zeoXQ4yIyIh4r1n9sogQ27hxI9asWQO1Wg03NzeoVCp4enqauqwGb9+XKwCswOjhhrbENhpuG8ar5fln6raO0S8vNHQDZIbM/ppYQkICFi9ejLfeeguHDx/Gk08+iUmTJuHatWumLo2IiEzM7I/EoqKiMGXKFEybNg0AEBERgZ9++gmbNm3C+++/b+LqKsanbRAR1Q9Bo9GIpi6iMsXFxWjXrh0+//xz+Pr66qYvWLAAFy9exHfffWfC6oiIyNTM+nRidnY2SktLIZfL9abL5XJkZmaaqCoiIjIXZh1iDwiCoPdZFMVy04iIqPEx6xBr3bo1mjZtWu6oKysrq9zRGRERNT5mHWLNmjVDnz59kJSUpDc9KSkJAwYMMFFVRERkLsx+dOJrr72G2bNnw8PDAwMGDMCmTZtw69YtTJ8+3dSlERGRiZn1kRgATJgwASqVChERERg8eDCOHz+O7du3o1OnTqYuzaSOHj2KF198Ed27d4eDgwPi4v7/3WN///033n//fXh6eqJ9+/bo1q0bAgICyt1b98UXX+D5559Hp06d4ODggIwMwx6VY8kM7c+cnByEhITgiSeegKOjI3r06IH58+fjzp07ptgds2CM7+gbb7yBPn36wNHRES4uLvD398dvv/1W37tiFozRnw+IooiJEyfCwcEB33zzTX3tQp0w+xADgICAAJw7dw6ZmZk4dOgQBg4caOqSTE6r1cLd3R3Lly+HjY2N3rx79+7hzJkzWLBgAQ4dOoT4+HjcuHEDfn5+KCkp0VvOy8sLixcvru/yzY6h/Xnz5k3cvHkTS5cuxa+//or169fj119/xYwZM0yxO2bBGN/Rvn37Yt26dUhOTsauXbsgiiJ8fX3x999/1/fumJwx+vOBTz/9FE2bNq2v0uuUWd8nRtJ06NABK1aswNSpUytd5vLly3jqqadw9OhR9OjRQ2/eqVOnMHz4cJw5cwbOzs51Xa7ZM7Q/H/jhhx8wefJkZGRkwN7evq7KtQjG6tPz589j0KBBSElJgVKprKtyzZ4h/Xnq1Cm89NJL+Pnnn6FUKhETEwMfH5/6KLtOWMSRGBkuLy8PAODg4GDiShoGKf2Zl5eH5s2bo0WLFvVVlkWrrk+1Wi3i4uLg5OTU6C8nSFFRf+bl5WHGjBn45JNPGswIb4ZYI1BcXIx3330Xo0ePRocOHUxdjsWT0p8ajQbLli3Dv/71L1hZmf34KZOrqk83btyIDh06oEOHDvjxxx+RmJiI5s2bm6hSy1BZf86fPx8jRozAyJEjTVidcfGnq4ErKSnBrFmzkJubi61bt5q6HIsnpT+1Wi38/f3Rrl07hIWF1XOFlqe6Pp00aRKGDx+OW7duYe3atZg2bRr279/PI9xKVNaf27Ztw/nz58vdsmTpeCTWgJWUlGDGjBm4cOECvvnmG7Rq1crUJVk0Kf2Zn58PPz8/AMBXX30Fa2vr+i7Tokjp00cffRQuLi4YOHAgYmNj8ccffyAxMdEE1Zq/qvrz0KFDuHz5Mjp06IDWrVujdevWAIDp06dj9OjRpirZYDwSa6D+/vtvvPrqq7h06RL27NkDhUJh6pIsmpT+zMvLw6RJkyCKInbu3AlbW1sTVGo5avMdFUURoiiimG95KKe6/nzvvfcwb948vWmenp748MMP4e3tXZ+lGhVDzELl5+cjLS0NAFBWVobr16/j7NmzaNmyJdq1a4dp06bh1KlT2Lp1KwRBgFqtBgDY29vrhueq1Wqo1WpcuXIFAPDbb78hNzcXHTt2RMuWjeutsob2Z15eHiZMmIC8vDzExcXh3r17uHfvHgCgZcuWaNasmcn2zVQM7dO0tDQkJiZi2LBhaN26Nf766y988sknaNasGUaNGmXKXTMJQ/uzffv2aN++fbl2nZyc0Llz5/rcFaPiEHsLdeTIEYwdO7bcdH9/fyxevBi9e/eucL2oqCjdsFyVSoXw8PAql2ksDO3PytYHgG+//RaDBw82ar2WwNA+vX79OoKDg3H69Gnk5uaibdu28PT0REhICLp27VrX5ZsdY/zM/5ODg4PFD7FniBERkcXiwA4iIrJYDDEiIrJYDDEiIrJYDDEiIrJYDDEiIrJYDDEiIrJYDDFqVHr27InAwEDd57i4uBq/EDQjIwMqlQrp6enVtm9Jqtqv+lRaWoq1a9di7NixUCqVcHJywpAhQxAbG4uysrJyy+/btw+jR49G586d4ezsjFGjRmHv3r16yxw5cgQODg7lfvFp+JaPT+ygRm3UqFE4cOAAHB0dJa9z9epVhIeH4+mnny73pIMtW7ZY7LvDqtqv+lRQUICIiAi8+OKLmDNnDmxtbfHDDz8gKCgIqamp+PDDD3XL/vjjj/D398fYsWPx1ltvAQBiYmLw0ksvYdu2beWe7BEeHo5+/frpPvMNA5aPf4NkEYqKiurk9Rtt2rRBmzZtjNZeZU9NIOlsbGxw5swZvUefDR06FBqNBhs2bMDbb7+te3Tatm3b0L59e2zevFn3pmIvLy/07NkT27dvLxdi3bp1wxNPPFF/O0N1jqcTqd6oVCo4ODjgwoULeP7559GuXTt069YNy5Yt0ztN9ODUT2JiIt544w24uLjovcX33LlzePHFF+Hs7AxHR0eMGjUKv/76a7ntRUdHo2fPnlAoFBg2bFiFy1R2OjEmJgZDhgyBo6MjnJ2dMWbMGCQnJ+s9+sfX11d3WurIkSMAKj6deOLECfj4+KBDhw5o3749xo0bhxMnTugtExgYCHd3d5w5cwbPPfcc2rVrh379+mHTpk16y6nVasyZMwdubm5o27YtunXrhsmTJ+P27dtV9v2GDRvw7LPPonPnzujUqROeeeYZ7N+/X6/Pq9qvf7p48SIcHR0RGhqqNz0sLAxt27bFmTNnqqynKk2bNq3w2Z39+vVDUVERsrOzddOKi4vRokULXYA9WF8mk1V46pEaHoYY1bupU6di2LBhiIuLg5+fHyIiIip8huOiRYsgiiLWr1+PdevWAQBOnz6NUaNGQaPRYM2aNYiNjUXLli3h6+uL06dP69aNjY1FaGgoBg8ejLi4OEyZMgUBAQHIzc2ttr53330XQUFB6N27NzZv3owNGzbA09MT169fR+/evREZGQng/qmpAwcO4MCBA5UegZ0/fx7e3t7QaDRYt24doqOjkZeXB29vb5w7d05v2by8PMycORMvvPAC4uPj0a9fP8yfPx+HDx/WLTN79mykpKQgLCwMu3fvRnh4ONq3b6972HBlrl69ipdffhkxMTHYvHkz+vbti8mTJ+PAgQMAUOP9cnd3x0cffYT//Oc/ujYOHz6MVatWYcmSJXrrlZSUSPpVnaNHj+LRRx/VO/X7yiuvIC0tDZGRkcjOzkZWVhbCw8Nx9epVzJw5s1wbM2fORKtWrdClSxcEBATg2rVr1W6XzBtPJ1K9mzZtGt58800A90/95OXlISoqCoGBgXqvUu/Xrx/Wrl2rt+6SJUvg5OSExMRE3ZPhR4wYgaeffhorVqxAfHw8ysrKEB4ejhEjRujCD7h/6vDVV1+tsra0tDSsW7cOc+fOxb///W/d9IdPS3Xr1k33e3WnplasWIFmzZrhm2++0e3b8OHD0atXL4SHh2PLli26ZR88AX/IkCEA7r8m4+DBg9i1a5duWkpKCt577z288MILuvV8fX2rrAEAPvroI92fy8rKMHToUFy5cgWbNm3Cs88+C3t7+xrtFwAEBATg4MGDmDt3LhITEzF79mwMHz4cr732mt5yUk/XajSaSuf99NNP2L17N9555x2961heXl7YunUrZs6cqdtHOzs7fPnll/D09NQtZ29vj9dffx0DBw6EnZ0dzp49i48//hhHjx7F4cOHIZfLJdVI5ochRvVu/Pjxep8nTpyI2NhYXLp0CU8//bRu+vPPP6+3XEFBAY4ePYr58+ejSZMmev97Hzp0KHbs2AEAuHHjBm7cuIHFixfrrT9u3LhqL+T//PPPKCsrwyuvvFKbXSvn119/xejRo/XC2d7eHs899xz27dunt2yLFi10YQUAzZs3h4uLC65fv66b1rdvX6xduxaiKGLIkCFwd3eHIAjV1nH69GmoVCqcPHkSWVlZEMX7z/1++DRtbXz66acYNGgQhg0bBnt7e0RHR5erx9A3CV++fBkzZszAoEGDEBwcrDcvJSUFs2bNwsiRIzF58mQIgoD4+Hi88sor2LZtm64/e/furXd0OGjQIHh6emLEiBFYv3493n33XYNqJNNhiFG9++f/eh98vnnzpt70f44YzMnJQWlpKSIiIhAREVFh22VlZbr3KLVt21ZvnpWVVbVvt75z5w4AVPjepdrIycmp8GWPCoWi3JHHw0H3QLNmzVBYWKj7vHnzZoSHh2PNmjUIDQ2Fo6Mjpk+fjpCQEDRpUvHVgevXr2PcuHFwc3PDihUr4OTkBCsrKyxbtgy//fabQfvXqlUrjBw5El988QUmTpxYrs+B+9cJays9PR3jx4+Hs7Mz4uLiyv0nZOHChejevTs+++wz3bQRI0Zg9OjReOeddyq9pgcAffr0gaurK06ePFnr+sj0GGJU727fvg2ZTKb3GQDatWunt9w//0f/6KOPokmTJggICIC/v3+FbTdp0kQXGpmZmXrzSkpKdCFVmQevbL9586bBRynA/RdiPgjVh6nV6lq9eFQulyMyMhKRkZFITU3F1q1boVKp0KZNG8yYMaPCdX766SfcvXsXmzdvRocOHXTTq7uOJsXPP/+MmJgY9O3bF59//jkmT56Mvn376i1T29OJN27cwLhx42BnZ4ddu3ZVeOvCxYsXK9zvvn37lhsUUxFRFCUdyZL5YohRvdu9e7fumhgA7Nq1C7a2tujevXuV68lkMjz99NM4f/48evfuXemRR4cOHeDk5ISvv/4aL7/8sm56YmJitQMIhg0bhiZNmuCLL77AsmXLKlzmwVD/goKCKtsCgIEDB+KHH35AXl4e7OzsANy/9rVv3z4MGjSo2vWrolQqsWTJEmzatAmXLl2qdLkHYfXII4/opl25cgXJycl6R5w12S8AyM7Oxpw5czBy5Ehs2bIFo0ePRkBAAA4dOgRbW1vdcrU5nZiVlaW71rd79+5Kg7Bt27Y4depUueknT54s95+ifzp16hSuXLki6ZoimS+GGNW7mJgYlJWVoV+/fvjpp58QGxuLxYsXV3g67Z+WLVsGb29vTJgwAS+//DIUCgWys7Nx9uxZlJaW4oMPPkCTJk2wcOFCvPHGG5g7dy4mTpyItLQ0fPLJJ9XeiNylSxfMnTsXUVFRyM/Px3PPPYemTZvixIkT6Nq1KyZMmABXV1dYWVlhy5YtaNmyJZo3bw5XV1ddSD0sJCQE+/fvh4+PD4KCgiAIAlavXo2CggIsXLiwRv2Wm5sLX19fTJo0CV27dsUjjzyCvXv3QqPRYPjw4ZWuN2zYMFhZWWHOnDl4/fXXcevWLahUKjg5OekNQ6/JfgHAa6+9BlEUERUVhUceeQQbN27EkCFDsHDhQr0BNf88MqtOQUEBJkyYgKtXr+LTTz/FX3/9hb/++ks3v1u3brq/x1mzZuG9995DQECAbrDLtm3bkJycjOXLl+vWmTlzJpydndGrVy88+uijOHv2LD755BO0b98es2fPrlF9ZF4YYlTv4uPjsXDhQkRERMDe3h4LFiyQ/A96nz59cPDgQYSHh2PRokW4e/cu2rRpg169eumNPPzXv/4FrVaLqKgo7Nq1C927d8fnn3+OWbNmVbuNjz76CI899hg2btyIrVu3okWLFujRowe8vLwA3L8OFBERgVWrVsHb2xulpaX49ttvMXjw4HJtPf7449izZw8+/PBDzJ07F6Ioon///ti7d2+NrxVZW1ujd+/eiI2NxbVr19CkSRO4urris88+g7e3d6XrPbhm9O9//xv+/v7o0qULPvjgA/z444/45ZdfdMvVZL82bNiA/fv3IyEhQXeU1KVLF0RGRmL27Nl45plnMGHChBrt3wOZmZk4e/YsAFQ4TP7hmubNmweFQoH169frlnV1dcXGjRvh5+en1wc7d+7Ehg0bcO/ePSgUCowdOxahoaG6U8hkmQSNRiOaughqHFQqFcLDw5GVlcXH/RCRUfBmZyIislgMMSIislg8nUhERBaLR2JERGSxGGJERGSxGGJERGSxGGJERGSxGGJERGSxGGJERGSx/hdn4F40+lHb9gAAAABJRU5ErkJggg==", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "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": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "279.1013628620102" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(baby.column('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": 13, "metadata": { "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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": {}, "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." ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 1 }