{
"cells": [
{
"cell_type": "markdown",
"id": "565fd595",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Linear regression: prediction error and more"
]
},
{
"cell_type": "markdown",
"id": "658ba253",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"##### Libraries"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "51c0f716",
"metadata": {
"slideshow": {
"slide_type": "skip"
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},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/anaconda3/lib/python3.9/site-packages/scipy/__init__.py:146: UserWarning: A NumPy version >=1.16.5 and <1.23.0 is required for this version of SciPy (detected version 1.23.1\n",
" warnings.warn(f\"A NumPy version >={np_minversion} and <{np_maxversion}\"\n"
]
}
],
"source": [
"## Imports\n",
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import statsmodels.api as sm\n",
"import statsmodels.formula.api as smf\n",
"import seaborn as sns\n",
"import scipy.stats as ss"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e53866de",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina' # makes figs nicer!"
]
},
{
"cell_type": "markdown",
"id": "0e698b4b",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Goals of this lecture\n",
" \n",
"- Extracting model **predictions**.\n",
"- Basic model evaluation: \n",
" - Visualizing $\\hat{Y}$ vs. $Y$.\n",
" - $RSS$: residual sum of squares. \n",
" - $S_{Y|X}$: standard error of the estimate. \n",
" - Using $S_{Y|X}$ to calculate **standard error** for our coefficients.\n",
" - $R^2$: coefficient of determination. \n",
"- Homoscedasticity. "
]
},
{
"cell_type": "markdown",
"id": "559a9a83",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Models as *predictors*"
]
},
{
"cell_type": "markdown",
"id": "f3f1f507",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Modeling our data\n",
"\n",
"> A **statistical model** is a mathematical model representing a \"data-generating process\".\n",
"\n",
"This means we can use a model to **generate predictions** for some value of $X$. \n",
"\n",
"$\\Large \\hat{Y} = f(X, \\beta)$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "67cfbaab",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
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