{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Way number eight of looking at the correlation coefficient\n", "\n", "This is a notebook to accompany the blog post [\"Way number eight of looking at the correlation coefficient\"](http://composition.al/blog/2019/01/31/way-number-eight-of-looking-at-the-correlation-coefficient/). Read the post for additional context!" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from datascience import *\n", "from datetime import *\n", "import matplotlib\n", "%matplotlib inline\n", "import matplotlib.pyplot as plots\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import pandas as pd\n", "import math" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Recap from last time\n", "\n", "As [before](http://composition.al/blog/2018/08/31/understanding-the-regression-line-with-standard-units/), we're using the [datascience](http://data8.org/datascience/) package, and everything else we're using is pretty standard.\n", "\n", "And, as before, here's the data we'll be working with, [converted to standard units](https://www.inferentialthinking.com/chapters/14/2/Variability#standard-units) and plotted:" ] }, { "cell_type": "code", "execution_count": 2, "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", "
Date Height (standard units) Weight (standard units)
07/28/2017 -1.26135 -1.3158
08/07/2017 -1.08691 -1.13054
08/25/2017 -0.912464 -0.808628
09/25/2017 -0.228116 -0.399485
11/28/2017 0.107349 0.254728
01/26/2018 0.617255 0.728253
04/27/2018 1.12716 1.2537
07/30/2018 1.63707 1.41777
" ], "text/plain": [ "Date | Height (standard units) | Weight (standard units)\n", "07/28/2017 | -1.26135 | -1.3158\n", "08/07/2017 | -1.08691 | -1.13054\n", "08/25/2017 | -0.912464 | -0.808628\n", "09/25/2017 | -0.228116 | -0.399485\n", "11/28/2017 | 0.107349 | 0.254728\n", "01/26/2018 | 0.617255 | 0.728253\n", "04/27/2018 | 1.12716 | 1.2537\n", "07/30/2018 | 1.63707 | 1.41777" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "heightweight = Table().with_columns([\n", " 'Date', ['07/28/2017', '08/07/2017', '08/25/2017', '09/25/2017', '11/28/2017', '01/26/2018', '04/27/2018', '07/30/2018'],\n", " 'Height (cm)', [ 53.3, 54.6, 55.9, 61, 63.5, 67.3, 71.1, 74.9],\n", " 'Weight (kg)', [ 4.204, 4.65, 5.425, 6.41, 7.985, 9.125, 10.39, 10.785],\n", " ])\n", "def standard_units(nums):\n", " return (nums - np.mean(nums)) / np.std(nums)\n", "\n", "heightweight_standard = Table().with_columns(\n", " 'Date', heightweight.column('Date'),\n", " 'Height (standard units)', standard_units(heightweight.column('Height (cm)')),\n", " 'Weight (standard units)', standard_units(heightweight.column('Weight (kg)')))\n", "heightweight_standard" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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