{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "path_data = '../../../../data/'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "plt.style.use('fivethirtyeight')\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "\n", "def standard_units(any_numbers):\n", " \"Convert any array of numbers to standard units.\"\n", " return (any_numbers - np.mean(any_numbers))/np.std(any_numbers) \n", "\n", "def correlation(t, x, y):\n", " return np.mean(standard_units(t[x])*standard_units(t[y]))\n", "\n", "def slope(table, x, y):\n", " r = correlation(table, x, y)\n", " return r * np.std(table[y])/np.std(table[x])\n", "\n", "def intercept(table, x, y):\n", " a = slope(table, x, y)\n", " return np.mean(table[y]) - a * np.mean(table[x])\n", "\n", "def fit(table, x, y):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * table[x] + b\n", "\n", "def scatter_fit(table, x, y):\n", " #fig, ax = plt.subplots(figsize=(7,6))\n", " plt.scatter(table[x], \n", " table[y], \n", " color='darkblue',\n", " s=20)\n", " \n", " plt.plot(table[x], fit(table, x, y), lw=2, color='gold')\n", " plt.xlabel(x)\n", " plt.ylabel(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A Regression Model ###\n", "\n", "In brief, such models say that the underlying relation between the two variables is perfectly linear; this straight line is the *signal* that we would like to identify. However, we are not able to see the line clearly. What we see are points that are scattered around the line. In each of the points, the signal has been contaminated by *random noise*. Our inferential goal, therefore, is to separate the signal from the noise.\n", "\n", "In greater detail, the regression model specifies that the points in the scatter plot are generated at random as follows.\n", "\n", "- The relation between $x$ and $y$ is perfectly linear. We cannot see this \"true line\" but it exists.\n", "- The scatter plot is created by taking points on the line and pushing them off the line vertically, either above or below, as follows:\n", " - For each $x$, find the corresponding point on the true line (that's the signal), and then generate the noise or error.\n", " - The errors are drawn at random with replacement from a population of errors that has a normal distribution with mean 0.\n", " - Create a point whose horizontal coordinate is $x$ and whose vertical coordinate is \"the height of the true line at $x$, plus the error\".\n", "- Finally, erase the true line from the scatter, and display just the points created." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based on this scatter plot, how should we estimate the true line? The best line that we can put through a scatter plot is the regression line. So the regression line is a natural estimate of the true line. \n", "\n", "The simulation below shows how close the regression line is to the true line. The first panel shows how the scatter plot is generated from the true line. The second shows the scatter plot that we see. The third shows the regression line through the plot. The fourth shows both the regression line and the true line.\n", "\n", "To run the simulation, call the function `draw_and_compare` with three arguments: the slope of the true line, the intercept of the true line, and the sample size.\n", "\n", "Run the simulation a few times, with different values for the slope and intercept of the true line, and varying sample sizes. Because all the points are generated according to the model, you will see that the regression line is a good estimate of the true line if the sample size is moderately large." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "\n", "def draw_and_compare(true_slope, true_int, sample_size):\n", " x = np.random.normal(50, 5, sample_size)\n", " xlims = np.array([np.min(x), np.max(x)])\n", " eps = np.random.normal(0, 6, sample_size)\n", " y = (true_slope*x + true_int) + eps\n", " tyche = pd.DataFrame({'x':x,'y':y})\n", "\n", " plt.figure(figsize=(6, 16))\n", " \n", " plt.subplot(4, 1, 1)\n", " plt.scatter(tyche['x'], tyche['y'], s=20)\n", " plt.plot(xlims, true_slope*xlims + true_int, lw=2, color='green')\n", " plt.title('True Line, and Points Created')\n", "\n", "#---\n", " plt.subplot(4, 1, 2)\n", " plt.scatter(tyche['x'], tyche['y'], s=20)\n", " plt.title('What We Get to See')\n", " \n", "#---\n", " plt.subplot(4, 1, 3)\n", " scatter_fit(tyche, 'x', 'y')\n", " plt.xlabel(\"\")\n", " plt.ylabel(\"\")\n", " plt.title('Regression Line: Estimate of True Line')\n", "#---\n", " plt.subplot(4, 1, 4)\n", " scatter_fit(tyche, 'x', 'y')\n", " \n", " xlims = np.array([np.min(tyche['x']), np.max(tyche['x'])])\n", " plt.plot(xlims, true_slope*xlims + true_int, lw=2, color='green')\n", " plt.ylabel(\"\")\n", " plt.title(\"Regression Line and True Line\")\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The true line,\n", "# the points created,\n", "# and our estimate of the true line.\n", "# Arguments: true slope, true intercept, number of points\n", "\n", "draw_and_compare(4, -5, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In reality, of course, we will never see the true line. What the simulation shows that if the regression model looks plausible, and if we have a large sample, then the regression line is a good approximation to the true 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": "3.6.12" } }, "nbformat": 4, "nbformat_minor": 1 }