{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "from datascience import *\n", "%matplotlib inline\n", "path_data = '../../../assets/data/'\n", "import matplotlib.pyplot as plots\n", "plots.style.use('fivethirtyeight')\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Method of Least Squares\n", "We have developed the equation of the regression line that runs through a football shaped scatter plot. But not all scatter plots are football shaped, not even linear ones. Does every scatter plot have a \"best\" line that goes through it? If so, can we still use the formulas for the slope and intercept developed in the previous section, or do we need new ones?\n", "\n", "To address these questions, we need a reasonable definition of \"best\". Recall that the purpose of the line is to *predict* or *estimate* values of $y$, given values of $x$. Estimates typically aren't perfect. Each one is off the true value by an *error*. A reasonable criterion for a line to be the \"best\" is for it to have the smallest possible overall error among all straight lines.\n", "\n", "In this section we will make this criterion precise and see if we can identify the best straight line under the criterion." ] }, { "cell_type": "code", "execution_count": 2, "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", " \"\"\"Return the height of the regression line at each x value.\"\"\"\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * table.column(x) + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our first example is a dataset that has one row for every chapter of the novel \"Little Women.\" The goal is to estimate the number of characters (that is, letters, spaces punctuation marks, and so on) based on the number of periods. Recall that we attempted to do this in the very first lecture of this course." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Periods Characters
189 21759
188 22148
231 20558
\n", "

... (44 rows omitted)

" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "little_women = Table.read_table(path_data + 'little_women.csv')\n", "little_women = little_women.move_to_start('Periods')\n", "little_women.show(3)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "little_women.scatter('Periods', 'Characters')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To explore the data, we will need to use the functions `correlation`, `slope`, `intercept`, and `fit` defined in the previous section." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9229576895854816" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(little_women, 'Periods', 'Characters')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The scatter plot is remarkably close to linear, and the correlation is more than 0.92." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Error in Estimation\n", "\n", "The graph below shows the scatter plot and line that we developed in the previous section. We don't yet know if that's the best among all lines. We first have to say precisely what \"best\" means." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lw_with_predictions = little_women.with_column('Linear Prediction', fit(little_women, 'Periods', 'Characters'))\n", "lw_with_predictions.scatter('Periods')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Corresponding to each point on the scatter plot, there is an error of prediction calculated as the actual value minus the predicted value. It is the vertical distance between the point and the line, with a negative sign if the point is below the line." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "actual = lw_with_predictions.column('Characters')\n", "predicted = lw_with_predictions.column('Linear Prediction')\n", "errors = actual - predicted" ] }, { "cell_type": "code", "execution_count": 8, "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", "
Periods Characters Linear Prediction Error
189 21759 21183.6 575.403
188 22148 21096.6 1051.38
231 20558 24836.7 -4278.67
195 25526 21705.5 3820.54
255 23395 26924.1 -3529.13
140 14622 16921.7 -2299.68
131 14431 16138.9 -1707.88
214 22476 23358 -882.043
337 33767 34056.3 -289.317
185 18508 20835.7 -2327.69
\n", "

... (37 rows omitted)

" ], "text/plain": [ "Periods | Characters | Linear Prediction | Error\n", "189 | 21759 | 21183.6 | 575.403\n", "188 | 22148 | 21096.6 | 1051.38\n", "231 | 20558 | 24836.7 | -4278.67\n", "195 | 25526 | 21705.5 | 3820.54\n", "255 | 23395 | 26924.1 | -3529.13\n", "140 | 14622 | 16921.7 | -2299.68\n", "131 | 14431 | 16138.9 | -1707.88\n", "214 | 22476 | 23358 | -882.043\n", "337 | 33767 | 34056.3 | -289.317\n", "185 | 18508 | 20835.7 | -2327.69\n", "... (37 rows omitted)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lw_with_predictions.with_column('Error', errors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use `slope` and `intercept` to calculate the slope and intercept of the fitted line. The graph below shows the line (in light blue). The errors corresponding to four of the points are shown in red. There is nothing special about those four points. They were just chosen for clarity of the display. The function `lw_errors` takes a slope and an intercept (in that order) as its arguments and draws the figure. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "lw_reg_slope = slope(little_women, 'Periods', 'Characters')\n", "lw_reg_intercept = intercept(little_women, 'Periods', 'Characters')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "\n", "sample = [[131, 14431], [231, 20558], [392, 40935], [157, 23524]]\n", "def lw_errors(slope, intercept):\n", " little_women.scatter('Periods', 'Characters')\n", " xlims = np.array([50, 450])\n", " plots.plot(xlims, slope * xlims + intercept, lw=2)\n", " for x, y in sample:\n", " plots.plot([x, x], [y, slope * x + intercept], color='r', lw=2)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope of Regression Line: 87.0 characters per period\n", "Intercept of Regression Line: 4745.0 characters\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print('Slope of Regression Line: ', np.round(lw_reg_slope), 'characters per period')\n", "print('Intercept of Regression Line:', np.round(lw_reg_intercept), 'characters')\n", "lw_errors(lw_reg_slope, lw_reg_intercept)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Had we used a different line to create our estimates, the errors would have been different. The graph below shows how big the errors would be if we were to use another line for estimation. The second graph shows large errors obtained by using a line that is downright silly." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lw_errors(-100, 50000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Root Mean Squared Error\n", "\n", "What we need now is one overall measure of the rough size of the errors. You will recognize the approach to creating this – it's exactly the way we developed the SD.\n", "\n", "If you use any arbitrary line to calculate your estimates, then some of your errors are likely to be positive and others negative. To avoid cancellation when measuring the rough size of the errors, we will take the mean of the squared errors rather than the mean of the errors themselves. \n", "\n", "The mean squared error of estimation is a measure of roughly how big the squared errors are, but as we have noted earlier, its units are hard to interpret. Taking the square root yields the root mean square error (rmse), which is in the same units as the variable being predicted and therefore much easier to understand. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Minimizing the Root Mean Squared Error\n", "\n", "Our observations so far can be summarized as follows.\n", "\n", "- To get estimates of $y$ based on $x$, you can use any line you want.\n", "- Every line has a root mean squared error of estimation.\n", "- \"Better\" lines have smaller errors.\n", "\n", "Is there a \"best\" line? That is, is there a line that minimizes the root mean squared error among all lines? \n", "\n", "To answer this question, we will start by defining a function `lw_rmse` to compute the root mean squared error of any line through the Little Women scatter diagram. The function takes the slope and the intercept (in that order) as its arguments." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def lw_rmse(slope, intercept):\n", " lw_errors(slope, intercept)\n", " x = little_women.column('Periods')\n", " y = little_women.column('Characters')\n", " fitted = slope * x + intercept\n", " mse = np.mean((y - fitted) ** 2)\n", " print(\"Root mean squared error:\", mse ** 0.5)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Root mean squared error: 4322.167831766537\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lw_rmse(50, 10000)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Root mean squared error: 16710.11983735375\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lw_rmse(-100, 50000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bad lines have big values of rmse, as expected. But the rmse is much smaller if we choose a slope and intercept close to those of the regression line." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Root mean squared error: 2715.5391063834586\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lw_rmse(90, 4000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is the root mean squared error corresponding to the regression line. By a remarkable fact of mathematics, no other line can beat this one. \n", "\n", "- **The regression line is the unique straight line that minimizes the mean squared error of estimation among all straight lines.**" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Root mean squared error: 2701.690785311856\n" ] }, { "data": { "image/png": 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rjqJ1d2JngoZRmp5Z3K+9JFEIIUQzSs6bmfKxnm8qGgn2UPN+ooahPj23uF97SaIQQogmnKhqZEqOnu+rzIT5OPNegoZgz775J7NvHrUQQrTgWEUDd32s5+x5C6M0LmxL0KB17/nF/dpLEoUQQvzCl2X1TNutp6JOITrQlc3xGrxd+/YCUUkUQgjxk/1n6rjn7wZMjQqJg9z53xh/+jn3rrpN7dG306QQQvzkgx9q+O1uPaZGhemh/dgUK0niIkkUQog+7+2iamblllNvgQeGebBurB8uvawC7JWQoSchRJ+29qiJtLxKABaO8uLxa72uuLhfbyOJQgjRJymKwjP5VazMv1B47+koHx6K8OziVnVPkiiEEH2ORVF47FAlrx6rxkkFf7nZl3vDPLq6Wd2WJAohRJ/SYFF4+EAFW76rwdUJMmP8mTS4X1c3q1uTRCGE6DNqGxVm7yvno1O1eDireDvOn3FB7l3drG5PEoUQok84V2/hd383cODHenxdVWQlaLlB17eK+7WXJAohRK9nqDUzbbeBr/QNDOjnxPZELSP8+l5xv/aSRCGE6NWKq81MydHzbWUjQ7zUvJ+oZYiX/OlrC+ktIUSv9V1lI3fm6DldbWaErzPbE7UM6N93i/u1lyQKIUSvVGCoZ+rHBspqLdyoc+Hd27T4uUkxivaQRCGE6HUOltSRvMfAuXqF8UFubIz1x9NFkkR7SaIQQvQqu0/XMmtvOTVmhcmD3dkwzh83tZTkuBKSKIQQvcb24+dJ+aSCRgXuDevPS9G+OEtxvysm52JCiF7h9X9Xc9/+C0ni4QhPXr5ZkkRHkTMKIUSPt6qgimVfngNgyXXe/OHXnlIBtgNJohBC9FiKovDkP86x+msTKuCFm3y4b5hUgO1okiiEED2S2aKQetDIm9+ex1kF68b6MS20f1c3q1fq1DmKDRs2EB0dzaBBgxg0aBC33XYbOTk51u3z5s3D19fX5is+Pt5mH3V1dSxcuJDQ0FCCgoK4++67KS4utokxGo2kpKQQEhJCSEgIKSkpGI1Gm5hTp06RnJxMUFAQoaGhLFq0iPr6escdvBCiw9SZFe7bX8Gb357HXQ1vxWkkSThQpyaKoKAgli1bxv79+8nNzWXs2LHcc889fP3119aYmJgYCgsLrV9bt2612UdaWho7d+4kMzOT7OxsqqqqSE5Oxmw2W2Puv/9+CgoK2Lp1K1lZWRQUFDBnzhzrdrPZTHJyMiaTiezsbDIzM9mxYwfp6emO7wQhxBWpbrAwY4+B90/U4O2iYnuClsRBUgHWkTp16GnixIk2Py9ZsoTMzEwOHz7Mf/3XfwHg5uZGYGBgk8+vrKxk48aNrFmzhvHjxwOwfv16Ro4cyb59+4iLi6OwsJA9e/awa9cuRo8eDcCqVatISkqiqKiIsLAw9u7dy7Fjxzhy5AjBwcEALFu2jPnz57NkyRK8vb0d1QVCiCtgrLMwfbeBvLJ6tO5ObEvQMEojFWAdrcuWx5rNZrZt20Z1dTVRUVHWxw8ePMjQoUO5/vrrmT9/PmVlZdZt+fn5NDQ0EBsba30sODiY8PBwDh06BEBeXh6enp7WJAEwZswYPDw8bGLCw8OtSQIgLi6Ouro68vPzHXbMQoj2Kzlv5vaPysgrqyfYQ82u27WSJDpJp09mHz16lISEBGpra/Hw8GDTpk1EREQAEB8fz6RJkxg8eDAnT54kIyODyZMns2/fPtzc3CgtLUWtVqPRaGz2qdPpKC0tBaC0tBSNRmOzNE6lUqHVam1idDqdzT40Gg1qtdoaI4ToPk5UNTIlR8/3VWbCfJx5L0FDsKesxeksnd7TYWFhfPrpp1RWVrJjxw7mzZvHBx98wIgRI5g6dao1LiIigsjISEaOHElOTg6TJ09udp+KolyWGNoT09LjFxUVFbW4vSfoDcfgKNI3zeuqvvmuWsX/O+pGWb0Twzws/GXYOWrOnqM7/U/19PdNWFhYi9s7PVG4uroSGhoKwLXXXss///lPXnnlFf76179eFnvVVVcRFBTE8ePHAQgICMBsNmMwGNBqtdY4vV5PdHS0NUav19skBkVRMBgM1rOIgIAA6zDURQaDAbPZfNmZxqVa69Du7uI8jbic9E3zuqpvviyrZ95hPRX1CtGBrmyO1+Dt2r0KSvSF902X97jFYml2WarBYODs2bPWye3IyEhcXFzIzc21xhQXF1NYWGidk4iKisJkMpGXl2eNycvLo7q62iamsLDQZlltbm4ubm5uREZGdvgxCiHabv+ZOu7cpaeiTiFxkDvbErTdLkn0FZ16RvHkk0+SkJDAwIEDMZlMZGVlceDAAd59911MJhPPPvsskydPJjAwkJMnT7J8+XJ0Oh133HEHAD4+PsycOZOlS5ei0+nw8/MjPT2diIgIYmJiAAgPDyc+Pp7U1FRWr16NoiikpqaSmJhozfqxsbEMHz6cuXPnkpGRQUVFBUuXLmXWrFmy4kmIbuCDH2r4n33l1Ftgemg/1tzqh4vUbeoynZooSkpKSElJobS0FG9vbyIiIsjKyiIuLo6amhq++eYbNm/eTGVlJYGBgdx66628/vrreHl5WfexYsUK1Go1s2fPpra2lrFjx7Ju3TrU6p/vWrVhwwYWL17MXXfdBUBSUhIrV660bler1WzZsoUFCxYwYcIE3N3dmTZtGhkZGZ3XGUKIJr1dVM3DnxmxKPDAMA+eG+ODk9Rt6lIqo9GodHUjROfpC+Op7SV907zO6pu1R02k5VUCsHCUF49f69Xti/v1hfeNrC8TQnQ5RVF4Jr+KlflVADwd5cNDEVLcr7uQRCGE6FIWReGxQ5W8eqwalaLw6+Iv+PZkGaWBMwjQ+nZ18wTdYNWTEKLvarAozPu0glePVeOkmPn1d7kMKPmWM6XlrHjlna5unviJnFEIIbpEbaPC7H3lfHSqFg9nFSO/zcWn8sKSdSeVCoOxqotbKC6SMwohRKc7V29h2m49H52qxddVxf9N0BLufB6LcmFtjUVR8PfxamUvorPIGYUQwm4l+gpWrNlMeWUV/j5epD/U9nkEQ62ZabsNfKVvYEA/J7Ynahnh50LIQzNY8co7GIw/71t0D5IohBB2W7FmM2dKy3FSqazzCC8tnWf384urzUzJ0fNtZSNDvNS8n6hliNeFP0MBWt827Ut0HkkUQgi7lVdWWS9+a+s8wneVjdyZo+d0tZkRvs5sT9QyoL+69SeKLidzFEIIu/n7eLVrHqHAUM+E7DJOV5u5UefCh7frJEn0IJIohBB2S39oBgMD/XF1dSYowN+ueYSDJXXcsUtPWa2F8UFuvJeoxc9N/vT0JDL0JISwW1vnEXafrmXW3nJqzAqTB7uzYZw/buruXZJDXE4ShRA9QEesNups24+fJ+WTChoVuDesPy9F++IsFWB7JDn/E6IHuLjaqL6+sUdctfz6v6u5b/+FJPFwhCcv3yxJoieTMwoheoArWW3U2VYVVLHsy3MALLnOmz/82rPbV4AVLZMzCiF6gPauNupMiqLwxOFKln15DhXw4k0+/HFU9y8TLloniUKIHqA9q406k9mi8MjnRlZ/bcJZBRvG+XHfMCkT3lvI0JMQPUB3vmq5zqww55MK3j9Rg7sa3hivIXGQe1c3S3QgSRRCiHarbrAwc285e8/U4e2iYnO8hugBbl3dLNHB7B56+vDDD9m0aZP155MnT3LbbbcRHBzMrFmzMJlMDmmgEKJ7MtZZmJJjYO+ZOrTuTuxM0kqS6KXsThQvvPACBoPB+nN6ejpnzpzhv//7v/n888959tlnHdJAIUT3U3LezO0flZFXVk+wh5pdt2sZpXHt6mYJB7E7UXz//fdEREQAUFNTw+7du3n66ad5+umnWbp0KR988IHDGimE6D5OVDUyIbuMbyoaCfNxZtftWob6uHR1s4QD2T1HUVdXh7v7hQmqvLw8GhsbGT9+PABDhw7lxx9/dEwLhRDdxrGKBu76WM/Z8xZGaVzYlqBB6y7F/Xo7uxNFSEgIX3zxBbfccgsffvghkZGR+Pj4AFBWVoa3t7fDGimEsI8jS318WVbPtN16KuoUogNd2RyvwdtVVtj3BXb/L//+97/n2WefJSYmhszMTGbOnGnddvjwYcLDwx3SQCGE/RxV6uOw0Yk7d11IEomD3NmWoJUk0YfYfUYxb948tFoteXl5zJkzhxkzfr7gx2Qycc899zikgUII+zmi1McHP9TwyFE3GhSF6aH9WHOrHy5St6lPsStR1NfXk5mZybhx4/jtb3972faXXnqpwxsmhGg7fx8v661KO6LUx9tF1Tz8mRGLouKBYR48N8bHmohE32HXuaOrqyvLli2joqLC0e0RQlyBjiz1sfaoiQcPGLEocN+gBlZKkuiz7B5kvOaaazhx4sQVvdiGDRuIjo5m0KBBDBo0iNtuu42cnBzrdkVReOaZZxg2bBgDBgxg4sSJHDt2zGYfdXV1LFy4kNDQUIKCgrj77rspLi62iTEajaSkpBASEkJISAgpKSkYjUabmFOnTpGcnExQUBChoaEsWrSI+vr6Kzo+IbraxVIfG/+8iNVPzGvXRLaiKKz46hxpeZUAPB3lw9zBDVLcrw+zO1E8/vjjPP/88xw9erTdLxYUFMSyZcvYv38/ubm5jB07lnvuuYevv/4agNWrV7NmzRqee+459u7di06nY8qUKVRV/TzOmpaWxs6dO8nMzCQ7O5uqqiqSk5Mxm83WmPvvv5+CggK2bt1KVlYWBQUFzJkzx7rdbDaTnJyMyWQiOzubzMxMduzYQXp6eruPTYjewKIoLD5Uycr8KpxU8NdbfHkoQor79XUqo9Go2BOYlJTEf/7zH8rLywkJCWHAgAG2O1KpyM7ObnMDhgwZwhNPPMHvf/97hg0bxgMPPMCCBQuACxf2hYWF8dRTTzF79mwqKysZOnQoa9asYfr06QCcPn2akSNHkpWVRVxcHIWFhYwePZpdu3YxZswYAA4ePEhSUhKHDx8mLCyM3bt3M336dI4cOUJwcDAAW7ZsYf78+RQVFfXqpb5FRUWEhYV1dTO6pb7eNw0WhYcPVLDluxpcnSAzxp9Jg/sB0jct6Qt9Y/cZhZOTE+Hh4dx0000MHDgQtVpt8+Xk1LalcmazmW3btlFdXU1UVBQ//PADJSUlxMbGWmP69etHdHQ0hw4dAiA/P5+GhgabmODgYMLDw60xeXl5eHp6Mnr0aGvMmDFj8PDwsIkJDw+3JgmAuLg46urqyM/Pb9NxCNEb1DYqzNpbzpbvavBwVrH1No01SQhh9/LYDz/8sENe8OjRoyQkJFBbW4uHhwebNm0iIiLC+kdcp9PZxOt0Os6ePQtAaWkparUajUZzWUxpaak1RqPR2IynqlQqtFqtTcylr6PRaFCr1dYYIfqKc/UWfvd3Awd+rMfXVUVWgpYbdFK3Sfys08uMh4WF8emnn1JZWcmOHTuYN2+eTZ2oSyfMFEVpdRLt0pim4u2Jaenxi4qKilrc3hP0hmNwlL7WN8YGmH/UjWMmNVpXCy9H1OFj/IEi4+Wxfa1v2qKn901rQ2dtShRnzpzhr3/9K59//jnl5eVs3ryZESNG8MorrxAVFcUNN9zQ6j5cXV0JDQ0F4Nprr+Wf//wnr7zyinVeorS01GZISK/XWz/9BwQEYDabMRgMaLVam5jo6GhrjF6vt0kMiqJgMBhs9nPxDOYig8GA2Wy+7EzjUj19LLIvjKe2V1/rm+JqM/fk6PnW1MgQLzXvJwYyxKvpPwl9rW/aoi/0jd0TC8eOHSM6OpotW7YwYMAATp8+bV1OeurUKdatW9euBlgsFurr6xk8eDCBgYHk5uZat9XW1nLw4EHrfENkZCQuLi42McXFxdYJbICoqChMJhN5eXnWmLy8PKqrq21iCgsLbZbV5ubm4ubmRmRkZLuOQ4ie5LvKRhI/LOPbykZG+Dqz63Zds0lCCLvfGX/6058IDw9n27ZtuLu723zyHj16NE888USr+3jyySdJSEhg4MCBmEwmsrKyOHDgAO+++y4qlYp58+bx4osvEhYWxtChQ3nhhRfw8PBg2rRpAPj4+DBz5kyWLl2KTqfDz8+P9PR0IiIiiImJASA8PJz4+HhSU1NZvXo1ijJHhV4AACAASURBVKKQmppKYmKiNevHxsYyfPhw5s6dS0ZGBhUVFSxdupRZs2b16hVPQgAUGOqZ+rGBsloLN+pcePc2LX5uUrdJNM/uRPHFF1/w2muv4enpaXPNAthOJrekpKSElJQUSktL8fb2JiIiwrqsFeCRRx6hpqaGhQsXYjQauf7669m+fTteXj+XIVixYgVqtZrZs2dTW1vL2LFjWbduHWr1z6WON2zYwOLFi7nrrruAC0t7V65cad2uVqvZsmULCxYsYMKECbi7uzNt2jQyMjLs7Q4heqSDJXUk7zFwrl5hfJAbG2P98XSRJCFaZneiaGn5q8FgsN6roiVr165tcbtKpSItLY20tLRmY9zd3Xn++ed5/vnnm43x8/Pj1VdfbfG1Bg0axJYtW1pusBC9yO7TtczaW06NWWHyYHc2jPPHTS1XW4vW2f1R4rrrruOtt95qctv7779vc92CEKJ72X78PDP2GKgxK9wb1p+/xUiSEPaz+4xi4cKF/OY3v2HKlClMmzYNlUrF/v37WbduHR988EG7rsoWQjje6/+u5g8HjSjAwxGePHWjt9RtEm1i9xnFLbfcwltvvcUPP/zAww8/jKIoPPnkkxw8eJC33nrLrqWxQojOtaqgitSfksSS67wlSYh2adN6uMTERBITEzl+/DhlZWX4+/v3+vXDQvREiqLw5D/OsfprEyrghZt8uG+YFPcT7WP3GcVzzz1nLaURGhrK6NGjrUnixx9/5LnnnnNMC4UQbWK2KDzyuZHVX5twVsGGcX6SJMQVaVOiOHPmTJPbJFEI0T3UmRXu21/Bm9+ex10Nb8VpmBbav6ubJXo4u4eeFKX5auRGoxE3N7cOaZAQon2qGyzM3FvO3jN1eLuo2ByvIXqA/F6KK9diovj000/55JNPrD+//vrr7Nq1yyamtraWjz/+mGHDhjmmhUKIVhnrLEzfbSCvrB6tuxPbEjSM0kgFWNExWkwUn332GS+88AJw4WK4pq6jcHV1JTw8XIaehOgiJefNTPlYzzcVjQR7qHk/UcNQH5eubpboRVpMFI899hiPPfYYcOFq5927d8syWCG6kRNVjUzJ0fN9lZkwH2feS9AQ7CnF/UTHsvsdVVFR4ch2CCHa6FhFA3d9rOfseQujNC5sS9CgdVe3/kQh2sjuVU+bNm3imWeeaXLbM888w9tvv91hjRJCtGx3kZ6Ybac5e95CYK2e1290kSQhHMbuRLFu3Tr8/f2b3KbT6Vot+CeE6Bj7z9Qx45Nq6tSu6IyniDj6EX/ZsLmrmyV6MbuHnr7//vtmVzZdc801nDhxoqPaJIRoxgc/1PA/+8ppdHLmKsN3/NeJz3BCwWCs6uqmiV7M7kShVqspLy9vcpvBYOiwBgnR25ToK1ixZjPllVX4+3iR/tAMArS+bd7P20XVPPyZEYsC4VXfM+j7T3FSqbAoCv4+Xq3vQIh2snvo6frrr+dvf/tbk9v+9re/ce2113ZYo4ToTVas2cyZ0nLq6xs5U1rOilfeafM+1h418eCBC0li4SgvdsyIIDjQH1dXZ4IC/El/aIYDWi7EBXafUfzxj3/kN7/5DXFxccyaNYurrrqKs2fP8uabb/Kvf/2L9957z5HtFKLHKq+swumniq1OKlWbhokUReGZ/CpW5l94ztNRPjwUcaFu00tL53V8Y4Vogt2J4pZbbuGNN94gLS2NRx991Pp4SEgIb775JrfeeqtDGihET+fv48WZ0vI2DxNZFIXHDlXy6rFqnFTwl5t9uTfMw8GtFeJybboyZ+LEiUycOJGioiLKy8vRaDQMHTrUUW0ToldIf2gGK155B4Px5zmK1jRYFB4+UMGW72pwdYLMGH8mDe7XCa0V4nLtuoRT7kEheoqOmki+EgFa3zYNE9U2KszeV85Hp2rxcFbxdpw/44Javye9EI7S5kRx5MgR/vOf/1BbW3vZthkzZEJNdC8XJ5KdVCrrRHJnj+23JVmdq7fwu78bOPBjPb6uKrIStNygk+J+omvZnSiMRiPJyckcPnwY+Lns+C9vqyiJQnQ3VzKR3FHsTVaGWjPTdhv4St/AgH5ObE/UMsJPivuJrmd3onjqqacoLy8nOzubpKQkNm3ahLe3N5s2beLw4cPNLp0Voiu1ZyK5o4er7ElWxdVmpuTo+baykSFeat5P1DLES4r7ie7B7uso/v73v/OHP/yBG2+8EYCBAwdy6623sn79emJiYqSEh+iW0h+awcA2Xm/QEdc9/JK/jxeWn87Am0pW31U2kvhhGd9WNjLC15ldt+skSYhuxe53Y0lJCUOGDEGtVuPu7k5V1c+fiiZNmsT//M//OKSBQlyJtk4kQ8cOV5XoK6ipraPw+ElAxehRw2ySVYGhnqkfGyirtXCjzoV3b9Pi52b35zchOoXd78iAgAAqKysBGDRokHWuAuD48eMd3zIhukhrZwBtsWLNZirOVTP86sGEhw7Co7+bdRjrYEkdd+zSU1ZrYXyQG+8lSpIQ3ZPdZxRjxozh8OHDTJgwgeTkZJ577jlOnjyJs7Mz77zzDklJSY5spxAdqql5iIvac91Dc5o7O9l9upZZe8upMStMHuzOhnH+uKlVLe1KiC5jd6J47LHHOHv2LADz58+nvLyc9957j/Pnz5OUlMTKlSsd1kghOlpTK5EemhEPtG+4qjlNTaZvP36elE8qaFTg3rD+vBTti7OTJAnRfdl9nvurX/2K6OhoAFxcXHj66af55ptvOHHiBK+99lqz96r4pT//+c+MHz+eQYMGcfXVV5OcnMw333xjEzNv3jx8fX1tvuLj421i6urqWLhwIaGhoQQFBXH33XdTXFxsE2M0GklJSSEkJISQkBBSUlIwGo02MadOnSI5OZmgoCBCQ0NZtGgR9fX19naJ6ME6a9nspZPpV0+cxn37LySJhyM8eflmSRKi+7MrUdTX1zNkyBCys7Ov6MUOHDjAfffdR05ODjt27MDZ2Znf/OY3l91mNSYmhsLCQuvX1q1bbbanpaWxc+dOMjMzyc7OpqqqiuTkZMxmszXm/vvvp6CggK1bt5KVlUVBQQFz5syxbjebzSQnJ2MymcjOziYzM5MdO3aQnp5+RccoeoaOnIdoycWzk41/XsSQKfey9Eg9CrDkOm+eutHb5jokIboru4aeXF1dcXZ2xt39ysoIbN++3ebn9evXExISwhdffGEzx+Hm5kZgYGCT+6isrGTjxo2sWbOG8ePHW/czcuRI9u3bR1xcHIWFhezZs4ddu3YxevRoAFatWkVSUhJFRUWEhYWxd+9ejh07xpEjRwgODgZg2bJlzJ8/nyVLluDt7X1Fxyq6t6bmISoryhzyWoqi8OQ/zrH6axMq4IWbfLhvmKdDXksIR7B76GnixIn83//9X4e+uMlkwmKx4OtrezHTwYMHGTp0KNdffz3z58+nrOznX+D8/HwaGhqIjY21PhYcHEx4eDiHDh0CIC8vD09PT2uSgAuT8R4eHjYx4eHh1iQBEBcXR11dHfn5+R16nKL7+eUn/dVPzHNY/SezReGRz42s/tqEswo2jPOTJCF6HLsns+Pj43nssceYNWsWEydOZMCAAZfFjBs3rk0v/thjjzFy5EiioqJsXmfSpEkMHjyYkydPkpGRweTJk9m3bx9ubm6UlpaiVqvRaDQ2+9LpdJSWlgJQWlqKRqOxOa1XqVRotVqbGJ1OZ7MPjUaDWq22xjSlqKioTcfYHfWGY3CUjuybegs88a0re/TOuDkpPDusjlHmYnpq98v7pnk9vW9aK/Rqd6KYNWsWAGfOnGHnzp3Wx1UqFYqioFKpmr1ValMef/xxvvjiC3bt2oVarbY+PnXqVOv3ERERREZGMnLkSHJycpg8eXKz+7vYhl+2qz0xLT0OPb9y7sWhN3G5juyb6gYLM/eW8/eZF8rwf/TvEqIHuHXIvruCvG+a1xf6xu5E8cvkcKXS0tLYvn07O3fuZMiQIS3GXnXVVQQFBVkv6gsICMBsNmMwGNBqtdY4vV5vXZUVEBCAXq+3SQyKomAwGKxnEQEBAdZhqIsMBgNms/myMw0h2sJYZ2H6bgN5ZT+voOvJSUKINt3hriMsXryY7du388EHH3DNNde0Gm8wGDh79qx1cjsyMhIXFxdyc3P57W9/C0BxcTGFhYXWOYmoqChMJhN5eXnWx/Ly8qiurraJeeGFFyguLmbgwIEA5Obm4ubmRmRkZIccq+h7Ss6bmfKxnm8qGgn2ULf+BCF6gE6tPLZgwQK2bNnCpk2b8PX1paSkBAAPDw88PT0xmUw8++yzTJ48mcDAQE6ePMny5cvR6XTccccdAPj4+DBz5kyWLl2KTqfDz8+P9PR0IiIiiImJASA8PJz4+HhSU1NZvXo1iqKQmppKYmKi9RQxNjaW4cOHM3fuXDIyMqioqGDp0qXMmjVLVjz1YJ11o6KmXue8mydTcvR8X2UmzMeZ9xI0re9IiB5AZTQaFXuDv/nmGzZu3NjkjYtUKhU7duxo8fmXrm66aPHixaSlpVFTU8M999xDQUEBlZWVBAYGcuutt5Kenm6zOqm2tpYlS5aQlZVFbW0tY8eO5cUXX7SJqaioYPHixXz00UcA1qvHf9mGU6dOsWDBAj755BPc3d2ZNm0aGRkZuLn13mGC3j6e+siytTZXQg8M9Lf7Kuu29M2lr9N/4GDyro7j7HkLozQubEvQoHVX4/PT+63ykos9e5re/r65En2hb+w+o/jHP/7BxIkTCQkJ4bvvviMiIgKj0cjp06cZOHAgv/rVr1rdx6VXRl+qX79+l11r0RR3d3eef/55nn/++WZj/Pz8ePXVV1vcz6BBg9iyZUurryd6js664vqXr3POQ8c+XTQN5y1EB7qyOV6Dt6sU9xO9h93v5uXLlzNp0iS++OILFEXh5Zdf5siRI7z//vuYzWYWLFjgyHYKYZfOuuL64usYvAbwj2sSaHB2I3GQO9sStJIkRK9j9zv66NGjTJ8+3bqKyGKxABeunViwYAHLly93TAuFaIP23Kiova/TOGQE/xwaj1ntwuSBajbF+tPPWUpyiN7H7qGnhoYG+vfvj5OTE35+fvz444/WbUOHDuXYsWMOaaDoGzpqErojK7+2ZE+FC/t1UVgUeGCYB8+N8bEORXWFzprEF31Tm6rHXiwzHhERwaZNm7BYLFgsFt566y0CAgIc1kjR+3X07Ucdae1REw8eMGJRYOEoL1Y6MEmU6Ct4ZNlaZv5hJY8sW0upvul5vp7Uf6LnsTtRTJgwgQMHDgDwxz/+kT179jBo0CCGDBlCVlYWDz30kMMaKXq/8soqPn7reXZtWunQSegroSgKK746R1rehTs9Ph3lQ/p1jq0Aa28C6KxJfNE32T30lJaWZv0+JiaG3bt3s3PnTs6fP098fLxNkT4h2uqXk86OnIRuL4ui8NihSl49Vo2TCv5ysy/3hnlYtztq6MfeBNDUDZKE6CjtvuBu1KhRjBo1qiPbIvqw9IdmwKoLH0YcOQndnj/oDRaFhw9UsOW7GlydIDPGn0mD+9nENHXHvLbOlTTVNnsTQEfevlWIS3XqldlCNOeXf6xXP+G4yei2/kGvbVSYva+cj07V4uGs4u04f8YFXX5flo4Y+mmqbfYmgM6axBd9k92Jor6+nj//+c9s27aN06dPU1dXZ7NdpVJhMBg6vIFCdKS2/EE/V2/hd383cODHenxdVWQlaLlB59pkbEcM/TTVNkkAojuwO1EsWbKE1157zXq/CFfXpn9hhOjO7P2Dbqg1M223ga/0DQzo58T2RC0j/Fya3W9HDP3IPIPoruxOFDt27CAtLU2uwBY9mj1/0IurzUzJ0fNtZSNDvNS8n6hliJdzi/MbHfHJX+YZRHdld6Korq7mxhtvdGRbhHC41v6gf1fZyJ05ek5Xmxnh68z2RC0D+l8oF94RE9ZX0jYhukqbrqP4/PPPHdkWIbpUoUnFhOwyTlebuVHnwoe366xJAuRaBdF3tXhGceLECev3KSkpzJ07FycnJxISEvDz87ssvrW71QnRFexZEnuwpI65R9wxmS2MD3JjY6w/ni62n6NkDkH0VS3ej8LPz8/mqlPlp6qcl16J2p57Zouu0Z1r5zvq3g2t3aNi9+laZu0tp8asMHmwOxvG+eOmvvxq61K98bI5hNauwZD7UfR+faFvWjyj+Otf/+rQ8gRCdIaWhoy2Hz9PyicVNCowObCRv8X44+zU9Hte5hBEX9ViopgxYwY5OTkMHjyYESNGNBlz9OhRTp48SVJSkkMaKHqfzq506u7myj+PFNFoNuOsVnPzDREAvP7vav5w0IgCPBzhySzf0maThBB9WYuT2Vu2bOH++++nf//+zcZ4enrywAMPkJWV1eGNE71Tp1c6VQAVKD/9C7CqoIrUn5LEkuu8eepGb+TkWYimtXhG8e677/K73/2uxUnqwYMHc8899/DOO+8wbdq0jm6f6IU6e/VQbX09/3XNhVv1KsCXfiN498tzqIAXbvLhvmGeDn19IXq6Fs8o/vWvf9lVFTYmJoavvvqqwxolerfOul3ppa+noOJoyE18p4vAWQUbxvlZk0SJvoKn125r9b4PQvRFLSYKk8mEr2/rY8e+vr6YTKYOa5To3TrrdqW/fL0BgVqOXD2OYt01uDnBW3EapoX+PKS6Ys1mysrPyY1/hGhCi0NPGo2GU6dOcdNNN7W4k9OnT6PRaDq0YaL36uzVQx4+3hSPnsrZM3V4u6jYHK8heoCbTUx5ZZV1hZ9cTCeErRbPKMaMGcM777T+yertt99mzJgxHdYoITqKsc7ClBwDe8/UoXV3YmeS9rIkAReGp5ROHA4ToidpMVHMmzeP/fv3k5aWRn19/WXbGxoaWLx4MZ988gkPPvigwxopREuau690yXkzt39URl5ZPcEeanbdrmWUpumqx+kPzSDA37vThsOE6ElaHHqKiooiIyODP/3pT2zdupXY2FgGDRoEwKlTp8jNzaW8vJyMjAwpGCi6TFPF+h5NfYApOXq+rzIT5uPMewkagj2bf7sHaH15fN7UXn+FrRDt0Wr12AcffJBRo0bx0ksv8cEHH1BTUwNAv379uOWWW3j00UeJjo52eEOFaM6ly21P1DiRlF3G2fMWRmlc2JagQeuubmUvHa9EX4HPT98/smytwy8sFMJR7CozfvPNN3PzzTdjsVisd7Hz9/dHre78Xz4hLvXLYn0V/TX86+oE6s5biA50ZXO8Bm9Xu4skd6gVazbzvz9974iy5EJ0ljb9Bjk5OaHT6dDpdO1KEn/+858ZP348gwYN4uqrryY5OZlvvvnGJkZRFJ555hmGDRvGgAEDmDhxIseOHbOJqaurY+HChYSGhhIUFMTdd99NcXGxTYzRaCQlJYWQkBBCQkJISUnBeElhtlOnTpGcnExQUBChoaEsWrSoybkY0b1dXG57zm8g/wyfQJ3alcRB7mxL0HZZkoALZzoT7l3EhHsXyUoq0aN16m/RgQMHuO+++8jJyWHHjh04Ozvzm9/8hoqKCmvM6tWrWbNmDc899xx79+5Fp9MxZcoUqqp+/iVLS0tj586dZGZmkp2dTVVVFcnJyZjNZmvM/fffT0FBAVu3biUrK4uCggLmzJlj3W42m0lOTsZkMpGdnU1mZiY7duwgPT29czpDdJgArS/x//17vhwaT6OTM9ND+7Ep1p9+zl1bk6OzLywUwlFaLDPuaCaTiZCQEN566y2SkpJQFIVhw4bxwAMPWG+5WlNTQ1hYGE899RSzZ8+msrKSoUOHsmbNGqZPnw5cuI5j5MiRZGVlERcXR2FhIaNHj2bXrl3WZbsHDx4kKSmJw4cPExYWxu7du5k+fTpHjhwhODgYuFDbav78+RQVFeHt7d01neJg3bkkcntLcr9dVM3DnxmxKPDAMA+eG+NjnbNoi47um/aUJe+uuvP7pqv1hb7puvNyLiQKi8Vivfr7hx9+oKSkxKZsSL9+/YiOjubQoUMA5Ofn09DQYBMTHBxMeHi4NSYvLw9PT09Gjx5tjRkzZgweHh42MeHh4dYkARAXF0ddXR35+fmOO2jRodYeNfHggQtJYuEoL1a2M0k4wsULCzf+eRGrn5jXY5OEEHbfM9sRHnvsMUaOHElUVBQAJSUlAOh0Ops4nU7H2bNnASgtLUWtVl92JbhOp6O0tNQao9FobO6loVKp0Gq1NjGXvo5Go0GtVltjmlJUVNSeQ+1Wuusx3PDTv/a0T1Hg1ZMuvHbKBYDUX9Uz3auE//yn5Ira0F37pjuQvmleT++b1s6IuixRPP7443zxxRfs2rXrsonx5u6g15JLY5qKtyempceh9Q7t7nrCaXJr7bMoCo8dquS1U9U4qeAvN/tyb5jHFb9uT+ibriJ907y+0DddMvSUlpbGtm3b2LFjh00J88DAQIDLPtHr9Xrrp/+AgADMZrN1mW5zMXq93lqSAS4kCYPBYBNz6esYDAbMZvNlZxqi+2iwKMz9tIJXj1Xj6gRvjPfvkCQhhGhepyeKxYsXk5WVxY4dO7jmmmtstg0ePJjAwEByc3Otj9XW1nLw4EHrfENkZCQuLi42McXFxdYJbLhwRbnJZCIvL88ak5eXR3V1tU1MYWGhzbLa3Nxc3NzciIyM7PgDF1estlFh1t5y3v2uBg9nFVtv0zBpcL+ubpYQvV6nDj0tWLCALVu2sGnTJnx9fa1zEh4eHnh6eqJSqZg3bx4vvvgiYWFhDB06lBdeeAEPDw/rTZF8fHyYOXMmS5cuRafT4efnR3p6OhEREcTExAAQHh5OfHw8qamprF69GkVRSE1NJTEx0XqKGBsby/Dhw5k7dy4ZGRlUVFSwdOlSZs2a1WtXPPVk5+ot/O7vBg78WI+vq4qsBC036Jqu2ySE6Fidmihee+01AO68806bxxcvXkxaWhoAjzzyCDU1NSxcuBCj0cj111/P9u3b8fL6eQ36ihUrUKvVzJ49m9raWsaOHcu6dets5jo2bNjA4sWLueuuuwBISkpi5cqV1u1qtZotW7awYMECJkyYgLu7O9OmTSMjI8Nhxy/ax1BrZtpuA1/pGxjQz4ntiVpG+Ll0dbOE6DO69DoK0fm688RbU9dRFFebmZKj59vKRoZ4qXk/UcsQL8d8vunOfdPVpG+a1xf6pkuXxwrRku8qG7kzR8/pajMj/JzZnqBlQH+pLyZEZ5NEIbqlAkM9Uz82UFZr4UadC+/epsXPzXbtRYm+ghVrNlNe2fOvfBaiO+vSK7OFaMrBkjru2KWnrNbC+CA33ku8PEnAz/ehaOo+183dzEgI0XaSKES3c1eOgXP1CpMHu7M5XoOnS9Nv00vvQ/HL6qwtJREhRNtIohDdTo1Z4d6w/vwtxh83dfNXybdUnbWlJCKEaBtJFKJbeP3f1TitOopq1VEejvDk5Zt9cXZquWzLxftQNHWfaynxLUTHkcls0eVWFVSx7MtzACy5zps//Nqz1dpe8HN11qakPzTjshLfQoj2kUQhuoyiKDz5j3Os/tqECnjhJh/uG+bZ7v3JKighHEOGnkSXMFsUHvncyOqvTTirYMM4vytKEiAT2EI4ipxRiE5XZ1aY80kF75+owV0Nb4zXkDjI/Yr3KxPYQjiGnFGITlXdYGHGHgPvn6jB20XF9gRthyQJkAlsIRxFzihEq6507P/i83+squOfQ+Moc/NH6+7EtgQNozQdVwE2/aEZ/OnF/+WL/H8DCn7eHpTqjTJPIcQVkjMK0aorHftfsWYz35fX8NmvLiQJj8bz7Lpd26FJAi6sgurn7kZ46CCGXz2YinPVMk8hRAeQRCFadaVj/6fPWzg8LAlTf388aiu56T85DPVxTJlwmacQouNJohCtupKx/2MVDXw+NJEad2+8qw3c8O9sBjqwAqzMUwjR8SRRiFa1dAV0S74sq+f2j8qoce5HYK2e6BN7GOLv4dCL39rbViFE82QyWzTr0knsFx9PsXtieP+ZOu75uwFTo0LiIHf+N+bX9HMe5eAWt3y1thCifeSMQjSrvZPYH/xQw2936zE1KkwP7cemWH/6ObdekkMI0T1JohDNas/E8NtF1czKLafeAg8M82DdWD9cWinuJ4To3iRRiGa1dWJ47VETDx4wYlFg4SgvVo7xsSYaIUTPJYlCNMveiWFFUVjx1TnS8ioBeDrKh/TrvO2qACuE6P5kMls0y56JYYui8NihSl49Vo2TCv5ysy/3hnl0UguFEJ1BEoVotwaLwkMHKtgyOZT1wKZ/nWXS4H5d3SwhRAeTRNHHtbeOU22jwux95Xx0qpYtPz0mSUKI3knmKPq49iyBPVdvYdpuPR+dqsXXVeYhhOjt5Iyij2vrElhDrZlpuw18pW9gQD8ntidqO6OZQoguJImij/P38eJMaTlOKlWrS2CLq81MydHzbWUjQ7zUvJ+oZYhX57+F5JanQnSuTh96+uyzz7j77rsZPnw4vr6+vPXWWzbb582bh6+vr81XfHy8TUxdXR0LFy4kNDSUoKAg7r77boqLi21ijEYjKSkphISEEBISQkpKCkaj0Sbm1KlTJCcnExQURGhoKIsWLaK+vt4xB95N2bsE9rvKRhI/LOPbykZG+Dmz63ZdlyQJkFueCtHZOv03vbq6mhEjRjBjxgzmzp3bZExMTAzr16+3/uzqanvfgrS0NLKzs8nMzMTPz4/09HSSk5PZv38/avWFyqT3338/p0+fZuvWrahUKubPn8+cOXPYsuXC1KvZbCY5ORk/Pz+ys7OpqKhg3rx5KIrC888/76Cj737sWQJbYKhn6scGymot3Khz4d3btPi5dd30lpQSF6JzdXqiSEhIICEhAYAHH3ywyRg3NzcCAwOb3FZZWcnGjRtZs2YN48ePB2D9+vWMHDmSffv2ERcXR2FhIXv27GHXrl2MHj0agFWrVpGUlERRURFhYWHs3buXY8eOceTIEYKDgwFYtmwZ8+fPZ8mSH+1ZswAAF9ZJREFUJXh7e3f0ofdIB0vqSN5j4Fy9wvggNzbG+uPp0rVrINoyXCaEuHLdctXTwYMHGTp0KNdffz3z58+nrKzMui0/P5+GhgZiY2OtjwUHBxMeHs6hQ4cAyMvLw9PT05okAMaMGYOHh4dNTHh4uDVJAMTFxVFXV0d+fr6jD7FH2H26lrtyLiSJyYPd2Ryv6fIkAVJKXIjO1u0ms+Pj45k0aRKDBw/m5MmTZGRkMHnyZPbt24ebmxulpaWo1Wo0Go3N83Q6HaWlpQCUlpai0WhsSkioVCq0Wq1NjE6ns9mHRqNBrVZbY5pSVFTUUYfaZew5ho/L1Cz91hWzomJyYCNpweWcPF7eZOwNbdhvR3loxs/zVpUVZVRWlLUQbb/e8P/rKNI3zevpfRMWFtbi9m6XKKZOnWr9PiIigsjISEaOHElOTg6TJ09u9nmKolyWGNoT09Lj0HqHdncXh95a8vq/q/lToREFeDjCk6dutK9u0y/32xNXJtnTN32V9E3z+kLfdP04QiuuuuoqgoKCOH78OAABAQGYzWYMBoNNnF6vt54hBAQEoNfrUX6qfAoXkoTBYLCJufTMwWAwYDabLzvT6EtWFVSRevBCklhynXerSaJEX2H9/pFlaynVX1hZJiuThOg9un2iMBgMnD171jq5HRkZiYuLC7m5udaY4uJiCgsLrXMSUVFRmEwm8vLyrDF5eXlUV1fbxBQWFtosq83NzcXNzY3IyMjOOLRuRVEUnjhcybIvz6ECXrzJhz+O8mr1TGLFms3W73+ZEGRlkhC9R6cPPZlMJuvZgcVi4fTp0xQUFODn54efnx/PPvsskydPJjAwkJMnT7J8+XJ0Oh133HEHAD4+PsycOZOlS5ei0+msy2MjIiKIiYkBIDw8nPj4eFJTU1m9ejWKopCamkpiYqL1FDE2Npbhw4czd+5cMjIyqKioYOnSpcyaNavPrXgyWxRSDxp589vzOKtg3Vg/poX2t+u55ZVVTLh3EXDhU8fFhHDpyiR3V1ceWba2Rw1FCSEu6PQziq+++oqxY8cyduxYampqeOaZZxg7diz/v717D6uqzvc4/obNVRQ3brYYNxmEUJC85N0eDEnESzleEsixZzim5NQzyoxI5qOpKCSlDp0hNKRyzMZSsbDxWmCH1KJznhxGI8bG9CjWBrZAsJPbZp8/PG5ni2xAkdv+vp6HP/ZaP9Ze6wvP+qzL77dWUlISCoWCb7/9lmeeeYZRo0axdOlS/Pz8OH78OH363O4CmZSUxMyZM4mJiSEiIgInJyf27t1rHEMBkJGRwdChQ5kzZw5z585l6NChJmMzFAoFH3zwAb169SIiIoKYmBhmzpzJxo0bO7Qena1Wb2DR5+X85Z+/4KCAPWGqVocENP9yozt7JllZIZeihOimrCoqKgwtNxM9xb/feNPVN7Iw5zo512pxtrVi7xMqJgywb9PySsoqSHrzr2grzJ8pLPxDCnV1DcbPdnY27N668v42pp1Zwk3JeyW1aZ4l1KbL9XoSHaOitpH5J7Tkl9bh6mDNgXAVw1R2Lf/iHVozshvMD5Lrjj2khLAkXf5mtmh/ml/0TD9SSn5pHZ5OCo5Od202JDRl5Sxbn87CP6SY9GpqK3OD5KSHlBBdm5xR9CCtOTIvrrFi/uFSfqjS49/XhoPhKjx7N/9vcGsnbm1lZdyJt+YM4k7mzjykh5QQXZucUfQgLR2ZF5bXs7jAnh+q9AxT2XJkuqvZkICO2Yk3d0NcCNE1SFD0IOZ26v9TWsf0I6WU1lkzwc2OQxGuuDoomluUUUfsxOXZTUJ0bXLpqQdp7obx59dqWfCZluoGA4+56NkX7oqjTeteYbr6hegmvZraW2tviAshOocERQ9yt536J5dv8B8nr1PXCPN9HYkboG11SIDsxIUQEhQ9yp079fcv6Hjx1HUaDbB4sBObx/XlX99rzSxBCCGakqDoodLPV7MqvxKA+GF9eHlEy89tEkKIu5Gg6GEMBgPJZ6tIOXvzRvamMX15Iah3J6+VEKI7k6DoQRoNBl76qpK3CnVYW8HGR+wo2r+bhZkP7ka0EKLnk+6xPUR9o4Hn88p5q1CHnTXsCu1H0aH9MuJZCHHfJCh6gJoGA8/mXOfDf93AycaKfVNUPDnQUUY8CyHahQRFN/dzXSPzTpRx5EoNSjsrPo5wZZK7AyAjnoUQ7UOCohvT1uiZdayML36qY4CjNYenqxmlvv1wPxnxLIRoD3Izu5sq1umZfayMf1Y24NNHwUdTXfHpY/rnvNtgucry0o5cTSFEDyBB0Q39q7KBWcfKuKrTE+hiQ1a4KwN6tfzcJiGEuBcSFN1MgbaOuce1lNY0Mlpty4dTXHGxlyuIQogHR4KiGzmjqSXyUy0/1xkIdbdn9+R+9LZtXUjcelfF/179EW/Ph+QtckKIVpND0U7S1jfHnbhaw5xjN0PiqYEO7H1C1eqQgNvvqqhv0MuYCiFEm0hQdJK2vP4z6+IvRH+q5YbewG/8e/H24/2wV7TtuU0ypkIIca8kKDpJa3fc73ynY9Hn5TQY4MWg3vznRCU21m1/uJ+MqRBC3CsJik7Smh33toIq4s5UYADWjHQmcbTzPT8B9taYClsbhYypEEK0idzM7iTm3hxnMBhY998/k3quGivg9fF9WTT4/p4Ae2tMxYULF/D397/PtRdCWBIJik7S3Jvj9I0G4s5U8Jd//oKNFWwPcWGeb69OWEMhhLhJgqILqdUbiP2vcj66dAMHBewKVTHVy6GzV0sIYeEkKLoIXX0jC3Ouk3OtFmdbK/Y+oWLCAPvOXi0hhOj4m9mnTp0iKiqKIUOGoFQq2bNnj8l8g8FAcnIygwcPZsCAAcyYMYPCwkKTNrW1tcTHx+Pr64u7uztRUVEUFxebtKmoqGDJkiV4e3vj7e3NkiVLqKgwHatw5coVIiMjcXd3x9fXl5UrV1JXV/dgNtyMitpGZh/TknOtFlcHaw5Nc73vkGjrOA0hhGhOhweFTqcjMDCQV199FUdHxybzU1NTSUtLY/PmzeTk5KBWq5k9ezZVVbe7j65atYpDhw6RmZnJ4cOHqaqqIjIyEr1eb2zz3HPPUVBQwL59+9i/fz8FBQXExsYa5+v1eiIjI6murubw4cNkZmaSnZ3N6tWrH2wB7qD5Rc/0I6Xkl9bh6aTg6HRXhqnsWv7FFrRlnIYQQpjT4ZeewsPDCQ8PB+B3v/udyTyDwUB6ejrLly9n1qxZAKSnp+Pv78/+/fuJiYmhsrKS3bt3k5aWRmhoKAA7duwgODiYkydPEhYWRlFREZ9++ilHjx5l7NixAGzbto1p06YZe/3k5ORQWFjIP/7xDzw9PQFYv349v//971mzZg3Ozs4PvBaXqhqYfayMH6r0+Pe14WC4Cs/e7fMnkQF2Qoj20qXGUVy+fBmNRsPkyZON0xwdHZkwYQJfffUVAGfPnqW+vt6kjaenJwEBAcY2+fn59O7d2xgSAOPGjcPJycmkTUBAgDEkAMLCwqitreXs2bMPdDsBCsvrmXa4lB+q9AxT2XJkumu7hQTIADshRPvpUjezNRoNAGq12mS6Wq3mxx9/BKCkpASFQoFKpWrSpqSkxNhGpVKZDE6zsrLC1dXVpM2d36NSqVAoFMY2d3PhwoV73LrbzldZs+y8PZUNVoxw1rPV/xfKr1RSft9Lvi16+lh2/PU4FVW/0LdPL6KnjzWue3tsQ08ltWme1KZ53b02LY2t6lJBccudo48NBkOLI5LvbHO39q1pY246tFzQlnx+rZYXv9RS3WBgqpcD7z7eD0ebexttbY4/MG70yCbTZcBd86Q2zZPaNM8SatOlLj25ubkBNDmiLysrMx799+/fH71ej1arNdumrKwMw/9feoGbIaHVak3a3Pk9Wq0WvV7f5EyjvXxy+QZPnyijusHAfF9H3pv8YEJCCCHaU5cKioEDB+Lm5kZubq5xWk1NDWfOnDHebxg+fDi2trYmbYqLiykqKjK2GTNmDNXV1eTn5xvb5Ofno9PpTNoUFRWZdKvNzc3F3t6e4cOHt/u2vX9Bx7O516lrhMWDndge4oLtPTzcTwghOlqHX3qqrq7m4sWLADQ2NnL16lUKCgpwcXHBy8uLpUuXsmXLFvz9/fHz8+P111/HycmJefPmAdC3b18WLlzI2rVrUavVuLi4sHr1aoKCgnj88ccBCAgI4IknniAuLo7U1FQMBgNxcXFMnTrVeIo4efJkhgwZwvPPP8/GjRspLy9n7dq1PPvss+3e4yn9fDWr8isBiB/Wh5dH9Lnnh/sJIURH6/Cg+Oabb3jyySeNn5OTk0lOTiY6Opr09HSWLVvGjRs3iI+Pp6KigkcffZSsrCz69LndaycpKQmFQkFMTAw1NTWEhISwfft2FIrb743OyMggISGBOXPmADBt2jRSUlKM8xUKBR988AErVqwgIiICBwcH5s2bx8aNG9ttWw0GA8lnq0g5e7Nr6qYxfXkh6P4e7ieEEB3NqqKiwtByM3EvLv7cwISPNNQ1whsTlfzG36mzV8kibrzdK6lN86Q2zbOE2nTJXk89ha+zDX8JVVGjN/CUT9NR6EII0R1IUDxg4fL0VyFEN9elej0JIYToeiQohBBCmCVBIYQQwiwJCiGEEGZJUAghhDBLgkIIIYRZEhRCCCHMkqAQQghhlgSFEEIIsyQohBBCmCUPBRRCCGGWnFEIIYQwS4JCCCGEWRIUQgghzJKgEEIIYZYEhRBCCLMkKLq5U6dOERUVxZAhQ1AqlezZs8dkvsFgIDk5mcGDBzNgwABmzJhBYWGhSZva2lri4+Px9fXF3d2dqKgoiouLO3IzHoitW7cSGhqKl5cXgwYNIjIykm+//dakjaXWJyMjgwkTJuDl5YWXlxdTpkzh2LFjxvmWWpe72bJlC0qlkvj4eOM0S6uPBEU3p9PpCAwM5NVXX8XRsenrVlNTU0lLS2Pz5s3k5OSgVquZPXs2VVVVxjarVq3i0KFDZGZmcvjwYaqqqoiMjESv13fkprS7L774gkWLFnHs2DGys7OxsbHh17/+NeXl5cY2llofd3d31q9fz+eff05ubi4hISEsWLCAc+fOAZZblzt9/fXX7Nq1i6CgIJPpllYfGUfRg3h4eJCSksKCBQuAm0c9gwcPZvHixaxYsQKAGzdu4O/vT2JiIjExMVRWVuLn50daWhrz588H4OrVqwQHB7N//37CwsI6bXvaW3V1Nd7e3uzZs4dp06ZJfe7g4+PDK6+8wm9/+1upC1BZWcmkSZNITU0lJSWFwMBAXnvtNYv8v5Ezih7s8uXLaDQaJk+ebJzm6OjIhAkT+OqrrwA4e/Ys9fX1Jm08PT0JCAgwtukpqquraWxsRKlUAlKfW/R6PQcOHECn0zFmzBipy/9bvnw5s2bNYtKkSSbTLbE+Np29AuLB0Wg0AKjVapPparWaH3/8EYCSkhIUCgUqlapJm5KSko5Z0Q7y0ksvERwczJgxYwCpz/nz5wkPD6empgYnJyfee+89goKCjDsyS60LwK5du7h48SI7duxoMs8S/28kKCyAlZWVyWeDwdBk2p1a06Y7efnll/nyyy85evQoCoXCZJ6l1sff35+8vDwqKyvJzs5m6dKlfPLJJ8b5llqXCxcusGHDBo4cOYKdnV2z7SypPnLpqQdzc3MDaHIEU1ZWZjwa6t+/P3q9Hq1W22yb7m7VqlUcOHCA7OxsfHx8jNMtvT52dnb4+voyYsQIXnnlFYKDg3nzzTctvi75+flotVrGjx+PSqVCpVJx6tQpdu7ciUqlol+/foBl1UeCogcbOHAgbm5u5ObmGqfV1NRw5swZxo4dC8Dw4cOxtbU1aVNcXExRUZGxTXeWkJDA/v37yc7O5uGHHzaZJ/Ux1djYSF1dncXXZcaMGZw+fZq8vDzjz4gRI5g7dy55eXn4+flZXH0UL7300rrOXglx76qrq/nuu+/QaDTs3r2bwMBAnJ2dqauro2/fvuj1erZt24afnx96vZ7Vq1ej0Wj405/+hL29PQ4ODvz0009kZGQwdOhQKisriYuLw9nZmfXr12Nt3X2PJVasWMHevXt599138fT0RKfTodPpgJtH01ZWVhZbn3Xr1mFnZ0djYyPFxcWkp6fz4Ycfsm7dOgYNGmSxdQFwcHBArVab/Ozbtw9vb28WLFhgkf83co+im/vmm2948sknjZ+Tk5NJTk4mOjqa9PR0li1bxo0bN4iPj6eiooJHH32UrKws+vTpY/ydpKQkFAoFMTEx1NTUEBISwvbt25tcy+9udu7cCcCsWbNMpickJLBq1SoAi62PRqNhyZIllJSU4OzsTFBQkEm3TUutS2tZWn1kHIUQQgizutf5jxBCiA4nQSGEEMIsCQohhBBmSVAIIYQwS4JCCCGEWRIUQgghzJKgEKKV9uzZg1KpNP54enoyceJE3nrrLRoaGtrlO/Ly8lAqleTl5XXJ5QnLJAPuhGijXbt24e7uTlVVFR999BErV66ktLSU1atX3/eyhw0bxokTJwgICGiHNRWifUhQCNFGwcHB+Pr6AjB58mQuXrzI9u3b7yso9Ho9BoMBZ2dnRo8e3V6rKkS7kEtPQtynkSNHUlVVRWlpKXDzjGPixIm4ubnh6+vLiy++aPL6VQClUkliYiLbtm3jkUceQa1Wc/78+bteKjIYDKSlpTFq1CjUajUBAQHEx8fz888/myyzrKyM5557Di8vL7y9vYmNjaWysrLJ+n722WeEh4fj7e2Nh4cHo0aNYvPmzQ+gMqKnkDMKIe7T5cuXUSgUODk5sW7dOv785z8TGxtLYmIi165dY9OmTRQWFnL8+HGT5/y8//77+Pj4kJiYiJOTEw899FCTnT9AYmIiW7duZfHixURERPDdd9+RlJTEuXPn+Nvf/mZ8wNzChQs5d+4ca9asYdCgQWRlZZGQkGCyrEuXLhEdHc2sWbNYuXIltra2XLx4kUuXLj3QGonuTYJCiDbS6/U0NDRQXV3NwYMHOXToEBEREZSWlvLGG2+QkJBgsoP28/MjIiKCI0eOMHPmTON0g8FAVlYWjo6OxmlFRUUm31VeXk5aWhrR0dG89tprAISFheHq6kpsbCxHjx5l+vTp5ObmcubMGTIzM5k7d66x3bx58yguLjYu7+9//zt1dXVs2bIFZ2dngCav+hTiTnLpSYg2Gj16NK6urvj4+PDHP/6Rp59+mrS0NE6ePEljYyPz58+noaHB+DNq1CicnZ05ffq0yXLCwsJMQuJuvv76a2pra4mMjDSZPnfuXGxsbDh16hRw82U7CoWCp556yqTdnDlzTD4HBwdja2vLokWL+Pjjj42Xy4QwR84ohGij9957Dw8PD3r37o2XlxcODg4Axp3uiBEj7vp7169fN/k8YMCAFr/r1r2NW2+du8XGxoZ+/foZ52s0GpRKJba2tibt+vfvb/LZ19eXAwcOkJqaSmxsLLW1tYwcOZL169fz2GOPtbg+wjJJUAjRRoGBgcZeT//u1isyDx48iFKpbDLfxcXF5HNr3p1863dKSkoYMmSIcXpDQwPXr183fqebmxsVFRXU19ebhMWdr+sECAkJISQkhNraWr788kuSk5OJjIykoKAAlUrV4joJyyNBIUQ7CQ0NxdramitXrhAaGtouyxw9ejT29vYcOHDA5F5CVlYWDQ0NTJw4EYAxY8ag1+vJzs423qO41a459vb2TJo0CZ1OxzPPPMPly5clKMRdSVAI0U5+9atfsXz5clauXMn333/PxIkTcXBw4OrVq5w8eZKFCxcSEhLSpmW6uLjwwgsvsHXrVnr16kV4eDhFRUVs2rSJ8ePHM3XqVOBmSI0fP564uDi0Wq2x11NhYaHJ8t5++21Onz7NlClT8PDwQKvVsm3bNh566CGTMxYh/p0EhRDtaO3atTz88MPs3LmTnTt3YmVlhYeHB5MmTWLQoEH3tMw1a9agUql45513yMzMpF+/fkRFRbF27VqTdy/v3r2bhIQENmzYgLW1NdOmTSMlJYUFCxYY2wwdOpQTJ06wYcMGSktLcXFxYdy4cWRkZLR4Y11YLnkVqhBCCLOke6wQQgizJCiEEEKYJUEhhBDCLAkKIYQQZklQCCGEMEuCQgghhFkSFEIIIcySoBBCCGGWBIUQQgiz/g8/m7cz/bgL1gAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lw_rmse(lw_reg_slope, lw_reg_intercept)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The proof of this statement requires abstract mathematics that is beyond the scope of this course. On the other hand, we do have a powerful tool – Python – that performs large numerical computations with ease. So we can use Python to confirm that the regression line minimizes the mean squared error." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Numerical Optimization ###\n", "First note that a line that minimizes the root mean squared error is also a line that minimizes the squared error. The square root makes no difference to the minimization. So we will save ourselves a step of computation and just minimize the mean squared error (mse).\n", "\n", "We are trying to predict the number of characters ($y$) based on the number of periods ($x$) in chapters of Little Women. If we use the line\n", "\n", "$$\n", "\\mbox{prediction} ~=~ ax + b\n", "$$\n", "\n", "it will have an mse that depends on the slope $a$ and the intercept $b$. The function `lw_mse` takes the slope and intercept as its arguments and returns the corresponding mse." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def lw_mse(any_slope, any_intercept):\n", " x = little_women.column('Periods')\n", " y = little_women.column('Characters')\n", " fitted = any_slope*x + any_intercept\n", " return np.mean((y - fitted) ** 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check that `lw_mse` gets the right answer for the root mean squared error of the regression line. Remember that `lw_mse` returns the mean squared error, so we have to take the square root to get the rmse." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2701.690785311856" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lw_mse(lw_reg_slope, lw_reg_intercept)**0.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's the same as the value we got by using `lw_rmse` earlier:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Root mean squared error: 2701.690785311856\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lw_rmse(lw_reg_slope, lw_reg_intercept)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can confirm that `lw_mse` returns the correct value for other slopes and intercepts too. For example, here is the rmse of the extremely bad line that we tried earlier." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16710.11983735375" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lw_mse(-100, 50000)**0.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here is the rmse for a line that is close to the regression line." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2715.5391063834586" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lw_mse(90, 4000)**0.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we experiment with different values, we can find a low-error slope and intercept through trial and error, but that would take a while. Fortunately, there is a Python function that does all the trial and error for us.\n", "\n", "The `minimize` function can be used to find the arguments of a function for which the function returns its minimum value. Python uses a similar trial-and-error approach, following the changes that lead to incrementally lower output values. \n", "\n", "The argument of `minimize` is a function that itself takes numerical arguments and returns a numerical value. For example, the function `lw_mse` takes a numerical slope and intercept as its arguments and returns the corresponding mse. \n", "\n", "The call `minimize(lw_mse)` returns an array consisting of the slope and the intercept that minimize the mse. These minimizing values are excellent approximations arrived at by intelligent trial-and-error, not exact values based on formulas." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 86.97784117, 4744.78484535])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "best = minimize(lw_mse)\n", "best" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These values are the same as the values we calculated earlier by using the `slope` and `intercept` functions. We see small deviations due to the inexact nature of `minimize`, but the values are essentially the same." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "slope from formula: 86.97784125829821\n", "slope from minimize: 86.97784116615884\n", "intercept from formula: 4744.784796574928\n", "intercept from minimize: 4744.784845352655\n" ] } ], "source": [ "print(\"slope from formula: \", lw_reg_slope)\n", "print(\"slope from minimize: \", best.item(0))\n", "print(\"intercept from formula: \", lw_reg_intercept)\n", "print(\"intercept from minimize: \", best.item(1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Least Squares Line\n", "\n", "Therefore, we have found not only that the regression line minimizes mean squared error, but also that minimizing mean squared error gives us the regression line. The regression line is the only line that minimizes mean squared error.\n", "\n", "That is why the regression line is sometimes called the \"least squares line.\"" ] } ], "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": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 1 }