Day11.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8b1cf4b2",
   "metadata": {},
   "source": [
    "# Quiz\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0df6e547",
   "metadata": {},
   "source": [
    "# Regression\n",
    "\n",
    "Regression allows us to:\n",
    "* determine the *nature* of a relationship between one (or more!) independent variables and a dependent variable\n",
    "* determine the *strength* of the relationship\n",
    "\n",
    "Regression *fits* a function to a dataset.\n",
    "\n",
    "**Regression is *not* the same as interpolation**: we don't want to fit so closely that we exactly pass through each data point, but rather fit so that we generalize over the data. Why is this?\n",
    "* because the data sets we have are not *all* the data, but a *sample* of the data, and other samples may be somewhat different\n",
    "* because we want to be able to *explain* relationships between variables\n",
    "\n",
    "Both of these require some generalization/abstraction away from the actual data.\n",
    "\n",
    "Okay, so we need three things:\n",
    "1. a function\n",
    "2. a method for making the function \"fit\" the data\n",
    "3. a measure of how \"good\" the fit is"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "bb149e5c",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "\n",
    "There are lots of types of regression. Today we will look at the most basic: linear regression.\n",
    "\n",
    "For linear regression, the function we fit looks like:\n",
    "\n",
    "$\\hat{y_i} = b + m x_i$\n",
    "\n",
    "The $m$ is the *slope* (or a *weight* for $x_i$).\n",
    "\n",
    "The $b$ is the *bias* (offset, intercept). It says where the function will cross the y axis.\n",
    "\n",
    "The $x_i$ is the value of the *independent variable* (feature) for the $i$ th data point.\n",
    "\n",
    "The $\\hat{y_i}$ we want to be as close as possible to $y_i$, the value of the *dependent variable* (label) for the $i$ th data point. For linear regression, $y_i$ s should be quantitative.\n",
    "\n",
    "Notice  that this function tries to calculate one variable ($y_i$) as a function of one other variable ($x_i$). Next week, we will look at functions that calculate $y_i$ as a function of multiple other variables.\n",
    "\n",
    "**Question**: What type of function is this? Does it fit:\n",
    "* An upside down U shape curve?\n",
    "* A line?\n",
    "* An S shape curve?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c6f44154",
   "metadata": {},
   "source": [
    "## What does it mean to *fit* a function? \n",
    "\n",
    "Now let's talk about methods for making the function \"fit\" the data. We know $x_i$, and we know $y_i$. We do *not* know the values for $b$ or $m$; that's what we need to figure out. In order to do that, we need a notion of \"goodness of fit\"."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "38df7d93",
   "metadata": {},
   "source": [
    "## How do we measure how \"good\" the fit is?\n",
    "\n",
    "If we have a function and a set of data points, how well does the function fit the data? \n",
    "\n",
    "The \"bit left over\" or the \"distance\", which we call the *residual*, is often calculated as: $r_i = y_i - \\hat{y_i}$. Look at the picture: if the diagonal line is the function we fit to the data, the length of each vertical line is a residual.\n",
    "\n",
    "<img src=\"https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2017/04/residuals.png\" alt=\"drawing\" width=\"400\"/>\n",
    "\n",
    "*Image from https://statisticsbyjim.com/regression/mean-squared-error-mse/*\n",
    "\n",
    "And how can we combine these residuals? We could:\n",
    "* Take the average, median, min or max of the distances\n",
    "* Take the average, median, min or max of the absolute distances\n",
    "* Take the sum of the absolute distances\n",
    "\n",
    "**Question**: What is not great about each of these?\n",
    "* Think about data points that fall *above* or *below* the line we fit.\n",
    "* Think about small and large data sets.\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "30c291b0",
   "metadata": {},
   "source": [
    "What we will do is take the mean of the sum of the square of the distances (MSSE, or *mean sum of squared error*):\n",
    "\n",
    "$MSSE = 1 / N \\sum_{i=1}^N (r_i)^2 = 1/N \\sum_{i=1}^N (y_i - \\hat{y}_i)^2$\n",
    "\n",
    "What is good about this measure of goodness of fit?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "25d7b781",
   "metadata": {},
   "source": [
    "## Now in python\n",
    "\n",
    "Let's load and look at our data. (These first three cells have been seen often before.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "39ed5ca6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1cc074ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "# For today we only care about price and year\n",
    "data = np.array(np.genfromtxt('data/vehiclesNumeric.csv', delimiter=',', skip_header=1, dtype=int, encoding=\"utf-8\", usecols=[1,2]))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "436978be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min, max, mean, std per variable\n",
      "              0            1\n",
      "0      0.000000  1999.000000\n",
      "1  55000.000000  2021.000000\n",
      "2   7978.281507  2012.381887\n",
      "3   5542.906703     3.997048\n",
      "shape\n",
      "((3158, 2), dtype('int64'))\n"
     ]
    }
   ],
   "source": [
    "def getSummaryStatistics(data):\n",
    "    print(\"min, max, mean, std per variable\")\n",
    "    return pd.DataFrame([data.min(axis=0), data.max(axis=0), data.mean(axis=0), data.std(axis=0)])\n",
    "\n",
    "def getShapeType(data):\n",
    "    print(\"shape\")\n",
    "    return (data.shape, data.dtype)\n",
    "\n",
    "print(getSummaryStatistics(data))\n",
    "print(getShapeType(data))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ba4d912b",
   "metadata": {},
   "source": [
    "We don't need to transform this data, since we only have one independent variable."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a01395d5",
   "metadata": {},
   "source": [
    "**Team exercise**: in your teams, implement linear_regression and msse. Assume that $x$, $y$ and $\\hat{y}$ are numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1d03163c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression(x, m, b):\n",
    "    ??\n",
    "\n",
    "def msse(y, yhat):\n",
    "    ??\n",
    "    return r\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a7284e02",
   "metadata": {},
   "source": [
    "What happens if we set the slope to 0 and the intercept to the mean value for price?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "df651c1c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30723814.716510456\n"
     ]
    }
   ],
   "source": [
    "# x is model year\n",
    "x = data[:, 1]\n",
    "\n",
    "# y is price\n",
    "y = data[:, 0]\n",
    "\n",
    "# calculate yhat\n",
    "yhat = linear_regression(x, 0, y.mean())\n",
    "print(msse(y, yhat))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f3c777f1",
   "metadata": {},
   "source": [
    "Let's plot the line we fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9d9e89d0",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotxyyhat(x, y, yhat):\n",
    "    plt.plot(x, y, 'o', label='data')\n",
    "    plt.plot(x, yhat, label='least squares fit, $y = mx + b$')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.legend(framealpha=1, shadow=True)\n",
    "    plt.grid(alpha=0.25)\n",
    "    plt.show()\n",
    "\n",
    "plotxyyhat(x, y, yhat)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "871d77ef",
   "metadata": {},
   "source": [
    "Can we do better than just guessing the slope and intercept? Come back on Monday!"
   ]
  }
 ],
 "metadata": {
  "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": "3.10.4"
  },
  "vscode": {
   "interpreter": {
    "hash": "3ad933181bd8a04b432d3370b9dc3b0662ad032c4dfaa4e4f1596c548f763858"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}