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working through regression
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‎chapters/02_regression/00_intro-to-regression.ipynb‎

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‎chapters/02_regression/01_fitting-with-least-squares.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"import matplotlib.pylab as plt"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"import scipy.optimize\n",
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"import pandas as pd"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## What does the following code do?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": true,
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"d = pd.read_csv(\"data/dataset_0.csv\")\n",
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"plt.plot(d.x,d.y,'o')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## What does the following code do?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"def linear(x,a,b):\n",
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" return a + b*x"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## What does the following code do?\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"def linear(x,a,b):\n",
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" return a + b*x\n",
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"\n",
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"def linear_r(param,x,y):\n",
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" return linear(x,param[0],param[1]) - y"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## What does the following code do?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"def linear_r(param,x,y): # copied from previous cell\n",
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" return linear(x,param[0],param[1]) - y # copied from previous cell\n",
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"\n",
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"param_guesses = [1,1]\n",
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"fit = scipy.optimize.least_squares(linear_r,param_guesses,\n",
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" args=(d.x,d.y))\n",
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"fit_a = fit.x[0]\n",
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"fit_b = fit.x[1]\n",
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"sum_of_square_residuals = fit.cost"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## What does the following code do?\n",
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"+ What the heck is `linspace`?\n",
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"+ What are we plotting?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"x_range = np.linspace(np.min(d.x),np.max(d.x),100)\n",
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"\n",
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"plt.plot(d.x,d.y,\"o\")\n",
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"plt.plot(x_range,linear(x_range,fit_a,fit_b))\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## Put together"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"def linear(x,a,b):\n",
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" \"\"\"Linear model of x using a (slope) and b (intercept)\"\"\"\n",
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" return a + b*x\n",
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"\n",
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"def linear_r(param,x,y):\n",
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" \"\"\"Residuals function for linear\"\"\"\n",
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" return linear(x,param[0],param[1]) - y\n",
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"\n",
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"# Read data\n",
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"d = pd.read_csv(\"data/dataset_0.csv\")\n",
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"plt.plot(d.x,d.y,'o')\n",
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"\n",
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"# Perform regression\n",
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"param_guesses = [1,1]\n",
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"fit = scipy.optimize.least_squares(linear_r,param_guesses,args=(d.x,d.y))\n",
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"fit_a = fit.x[0]\n",
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"fit_b = fit.x[1]\n",
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"sum_of_square_residuals = fit.cost\n",
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"\n",
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"# Plot result\n",
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"x_range = np.linspace(np.min(d.x),np.max(d.x),100)\n",
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"plt.plot(x_range,linear(x_range,fit_a,fit_b))\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"<h4>For your assigned model:</h4>\n",
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"<ul>\n",
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" <li>Write a function and residuals function</li>\n",
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" <li>Estimate the parameters of the model</li>\n",
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" <li>Plot the data and the model on the same graph</li>\n",
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" <li>Write the SSR and number of parameters on the board</li>\n",
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" <li>If you finish early: plot the residuals and decide if you like your model</li>\n",
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" <li>If you're still waiting: try to figure out which model best fits dataset_1.csv</li>\n",
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"</ul>\n",
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"<br/>\n",
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"\n",
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"<div style=\"font-size:30px;\" >\n",
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"<div class=\"row\">\n",
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" <div class=\"col-xs-6\">$y = a \\Big ( \\frac{bx}{1 + bx} \\Big )$</div>\n",
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" <div class=\"col-xs-6\">$y = a \\Big ( \\frac{bx^{c}}{1 + bx^{c}} \\Big )$</div>\n",
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"</div>\n",
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"\n",
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"<div class=\"row\">\n",
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" <div class=\"col-xs-6\">$y = a(1 - e^{-bx})$</div>\n",
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" <div class=\"col-xs-6\">$y = a + bx^{2} + cx^{3}$</div>\n",
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"</div>\n",
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"<div class=\"row\">\n",
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" <div class=\"col-xs-6\">$y = a + bx^{2} + cx^{3} + dx^{4}$</div>\n",
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" <div class=\"col-xs-6\">$y = asin(bx + c)$</div>\n",
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"</div>\n",
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"<div class=\"row\">\n",
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" <div class=\"col-xs-6\">$y = aln(x + b)$</div>\n",
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" <div class=\"col-xs-6\">$y = aln(bx + c)$</div>\n",
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"</div>\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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