{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Understanding the regression line with standard units\n", "\n", "This is a notebook to accompany the blog post [\"Understanding the regression line with standard units\"](http://composition.al/blog/2018/08/31/understanding-the-regression-line-with-standard-units/). 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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're using the [datascience](http://data8.org/datascience/) package that the Data 8X course uses. Everything else we're using here is pretty standard.\n", "\n", "To start with, let's make a table of the height and weight data we'll be working with. For now, dates are just strings, but we'll fix that later!" ] }, { "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 (cm) Weight (kg)
07/28/2017 53.3 4.204
08/07/2017 54.6 4.65
08/25/2017 55.9 5.425
09/25/2017 61 6.41
11/28/2017 63.5 7.985
01/26/2018 67.3 9.125
04/27/2018 71.1 10.39
07/30/2018 74.9 10.785
" ], "text/plain": [ "Date | Height (cm) | Weight (kg)\n", "07/28/2017 | 53.3 | 4.204\n", "08/07/2017 | 54.6 | 4.65\n", "08/25/2017 | 55.9 | 5.425\n", "09/25/2017 | 61 | 6.41\n", "11/28/2017 | 63.5 | 7.985\n", "01/26/2018 | 67.3 | 9.125\n", "04/27/2018 | 71.1 | 10.39\n", "07/30/2018 | 74.9 | 10.785" ] }, "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", "heightweight" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can plot weight as a function of height." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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rSQaFAhiR9B2SIN0O9EfEeN2rNDMrmEqzKn0a+DRAepzzt0lG1V8LvJkkTPdLuhPYHhH/u/7lmpkVQ7X3MJo8zrkVkklCSML07cDvAr8DODzNbN6Y1ZR0klaS9D4nHy8BRoHv1b40m4uGR0YZGNpHd2cH7W3L8y7HrG4qhqekl/DMsFxJctvhbwNXpc8/iIhKl2/aPLH9zvvYtHkr4+MTtLa20Ne7njWrV+VdllldqNzguaTHSc7n/CnJ5Zd3AHdExM7GlVdeT09P9Pf3512GpYZHRjn74o0sXrSQZUuXsH/sAAcPHWbbtX3ugdqcIunuiOiZablKVxgdTzLhxwPA/eljV23Ks2YzMLSP8fEJli1dAsCypUs4Mj7BwNC+nCszq49K4XkCcBHwCHABSe9zn6RvSLpc0tr0vkNmdHd20Nrawv6xAwDsHzvAgtYWujs7cq7MrD7KhmdEDETEDRHxZxHxSpL7C50P3A2cCdxMEqZ3SdrcmHKtqNrbltPXu56Dhw4zuHeYg4cO09e73rvs1rTKHvOc8YPS6cD7SU5VIiJKJ0muKx/zLCaPtttcV+0xz6pOVZLUApzK06PurwGOJZldaYDkiiMz2tuWOzRtXqg0MchreDoszwCWk4TlbuBrpJdoemYlM5uPKvU8J3uTPwNuSF/fHhEecTezea9SeP5Xkp7l440qxsxsrqg0MciXGlmImdlcUu0N4MzMbAqHp5lZBg5PM7MMChOekjok3SDpQUkPSDoj75rMzMqZ1XyedfYp4GsR8XuSFgG+bt7MCqsQ4SmpjeRk/IsAIuIQcCjPmszMKinKbvsLgEHgWkk/kLRF0jGlC0naIKlfUv/g4GDjqzQzSxUlPBeQXDt/VUT8FvAUyaQjzxARV0dET0T0dHV1NbpGM7NfKUp47gZ2R8Rd6esbSMLUzKyQChGeEfFL4FFJp6RNa4Ef51iSmVlFhRgwSr0H+Hw60v4z4OKc6zEzK6sw4RkR9wIzTkBqZlYEhdhtNzObaxyeZmYZODzNzDJweJqZZeDwNDPLwOFpZpaBw9PMLAOHp5lZBg5PM7MMHJ5mZhk4PM3MMnB4mpll4PCss+GRUXbu2s3wyGjepZhZDRVmVqVmtP3O+9i0eSvj4xO0trbQ17ueNatX5V2WmdWAe551MjwyyqbNW1m8aCErjmtn8aKFbLxii3ugZk3C4VknA0P7GB+fYNnSJQAsW7qEI+MTDAzty7kyM6sFh2eddHd20Nrawv6xAwDsHzvAgtYWujs7cq7MzGrB4Vkn7W3L6etdz8FDhxncO8zBQ4fp611Pe9vyvEszsxrwgFEdrVm9im3X9jEwtI/uzg4Hp1kTcXjWWXvbcoemWRPybruZWQYOTzOzDByeZmYZODzNzDJweJqZZeDwNDPLwOFpZpaBw9PMLIPCnCQv6WHgP4Bx4EhE9ORbkZlZeYUJz9TrI2JP3kWYmc3Eu+1mZhkUKTwDuFXS3ZI2TLeApA2S+iX1Dw4ONrg8M7OnFSk8Xx0RpwJnAZdIWlO6QERcHRE9EdHT1dXV+ArNzFKFCc+I+EX6PADcCJyWb0VmZuUVIjwlHSPpWZN/A28CduRblZlZeUUZbT8euFESJDV9ISK+lm9JZmblFSI8I+JnwCvyrsPMrFqF2G03M5trHJ5mZhk4PM3MMnB4mpll4PCswvDIKDt37WZ4ZDTvUsysIAox2l5k2++8j02btzI+PkFrawt9vetZs3pV3mWZWc7c86xgeGSUTZu3snjRQlYc187iRQvZeMUW90DNzOFZycDQPsbHJ1i2dAkAy5Yu4cj4BAND+3KuzMzy5vCsoLuzg9bWFvaPHQBg/9gBFrS20N3ZkXNlZpY3h2cF7W3L6etdz8FDhxncO8zBQ4fp611Pe9vyvEszs5x5wGgGa1avYtu1fQwM7aO7s8PBaWaAw7Mq7W3LHZpm9gzebTczy8DhaWaWgcPTzCwDh6eZWQYOTzOzDByeZmYZODzNzDJweJqZZeDwNDPLYN6Epyc0NrNamheXZ3pCYzOrtabveXpCYzOrh6YPT09obGb10PTh6QmNzawemj48PaGxmdXDvBgw8oTGZlZrhQpPSa1AP/BYRJxTy+/2hMZmVktF222/FHgg7yLMzGZSmPCU9BzgbGBL3rWYmc2kMOEJ/C3QC0zkXYiZ2UwKEZ6SzgEGIuLuGZbbIKlfUv/g4GCDqjMz+3WFCE/g1cBbJD0MfAn4HUmfK10oIq6OiJ6I6Onq6mp0jWZmv1KI8IyID0TEcyLiZOAdwDcj4oKcyzIzK6sQ4WlmNtcU6jxPgIj4FvCtnMswM6tIEZF3DZlIGgQeybmMFcCenGtohPmyneBtbUaz3c7nRcSMgypzNjyLQFJ/RPTkXUe9zZftBG9rM6rXdvqYp5lZBg5PM7MMHJ5H5+q8C2iQ+bKd4G1tRnXZTh/zNDPLwD1PM7MMHJ5VkvSwpB9JuldSf9p2uaTH0rZ7Jb057zprQVKHpBskPSjpAUlnSDpO0m2SdqbPx+Zd59Eqs51N95tKOmXK9twraUTSZU36m5bb1pr/rt5tr1J63X1PROyZ0nY5MBoRH8+rrnqQdD1wR0RskbQIWAZsBPZGxEclvR84NiL+Z66FHqUy23kZTfibTkonHH8MWA1cQpP9plOVbOvF1Ph3dc/TnkFSG7AG2AoQEYciYh/wVuD6dLHrgXPzqbA2Kmxns1sL/DQiHqHJftNpTN3WmnN4Vi+AWyXdLWnDlPb/LumHkq5pht0e4AXAIHCtpB9I2iLpGOD4iHgcIH3uzrPIGii3ndB8v+lU7wC+mP7dbL9pqanbCjX+XR2e1Xt1RJwKnAVcImkNcBXwQuCVwOPAlTnWVysLgFOBqyLit4CngPfnW1JdlNvOZvxNAUgPTbwF+EretdTbNNta89/V4VmliPhF+jwA3AicFhFPRMR4REwA/wCclmeNNbIb2B0Rd6WvbyAJmScknQiQPg/kVF+tTLudTfqbTjoLuCcinkhfN9tvOtUztrUev6vDswqSjpH0rMm/gTcBOyb/w0utA3bkUV8tRcQvgUclnZI2rQV+DNwEXJi2XQj8Sw7l1Uy57WzG33SK83nmbmxT/aYlnrGt9fhdPdpeBUkvIOltQrK794WI+Iikz5LsBgTwMPCnk8eQ5jJJryS5Ed8i4GckI5UtwD8CK4GfA2+LiL25FVkDZbbz72jO33QZ8CjwgogYTts6abLfFMpua83/rTo8zcwy8G67mVkGDk8zswwcnmZmGTg8zcwycHiamWXg8LSqSbpIUkh60TTvLUjfuzzD914uKdNpH5K+JenbVSx3rqQ/n+V3/2dJ+yU9O0ttWUh6b3oJof9tFpx/ICuCLcAZdV7HucCswhPYDFwTEY/VoZ5y/p7kGvMLZ1rQ8uXwtNxFxO6IuDPvOqaSdCrwepJrohsmIsaAzwB/0cj12uw5PK2uJD1f0uclDUo6mE5Eu65kmV/bbZfUJemL6WS2T0q6VtJb0kMDr5tmPW+QdE+6m71D0rlT3ruOpCf37PTzkc7PWsk7gR9GxP3TrOud6brG0tq2S3pV+t7J6fe/S9LfSPqlpP+Q9DlJyyS9SNItkkYlPSRpuh7ml4CXTX6nFZPD07JoTY9x/uoBtJYuJOm5wF3AK4D3ksxycw/wT5LeMsM6vkoyucMHSKYWOwz8nzLLvhD4FPAJ4DySWXNumHJs9sPAv5FMQXdG+lg3zfdMdSZwxzTb9HGSG4rdA7wduAC4neQSx6k+AJxEEtofBH6fZJf8RmBbuv4fkkyJ9xsln70XGElrsKKKCD/8qOoBXERybXClx+VTlt9KElidJd9zG3DvlNeXJ/8p/ur1m9LvenvJ525K2183pe1bJMH64ilt3cA4sHFK23UksyhVs53Hp+t5Z0n7i9Lv/USFz56cfvabJe1fTdsvmNJ2LHAE+NA033MHcGvev7kf5R8Lji56bZ5aRzKl21StQOlxyzNJenzDae900i3AZkltETEyzfefThJSN5a03wD87jTL74yInZMvImJA0gC/3hus1knp82BJ+xtI9taquZXtzSWvH0yfb5lsiIgn0zqfO83nB4GXVLEey4nD07LYEREPTW0oCcdJ3cAfpY/pdJLsnpY6EXgyIg6XtD8xzbIA080EdBBYUmb5mUx+7mBJe2f6XPo/juk8WfL6UIX26eocA5ZWsR7LicPT6mmIZPfzY2Xe/0WZ9seBYyUtLAnQ42tZXAVD6XPprRomb/73bOAnda7huCnrswJyeFo9fY1kcOb+SE7BqdadJIcB1pHMNznpbUdRy0Gq78k9DBwguc/RVF8HJoANwPuOopZqPB/4fp3XYUfB4Wn19EGSALhd0v8lCaVjgZeTTFT7x9N9KCJuTa8aulrSCuAh4PdIRu0hCbDZ+jFwnKT/BvQDByLiR2XWf0jSXZTcqiEifirpk8Cfp3cWuInk2OxpwIMR8eUMdf0aSR0kxzub8vbHzcLhaXUTET+X1EMymt4HdJHsEu/g6VvelnMeyalJHyMJqJuA/0Uyaj6coZwtJANRfUAH8AjJyHg5XyYZ1DomIp6abIyIv5D0EPBuktOQniI55ejWDDWVczbJsdDSATMrEM8kb3OGpE+TnC51XESUDubUel1tJAND746Iz9VzXdOs+2ZgT0T8YSPXa7PjnqcVkqSLgHbgfpJ7DJ0JvAvYXO/gBIiIEUkfA3olfT4a1MtI76v0epJDG1ZgDk8rqqeAy0iuHloM7AI2kkzW0SifIBm4OpHyZwbU2gnAxaWnglnxeLfdzCwDX9tuZpaBw9PMLAOHp5lZBg5PM7MMHJ5mZhk4PM3MMvj/b+rX0a3oKv4AAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heightweight.scatter('Height (cm)', 'Weight (kg)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look at that! Those dots aren't too far from being a straight line. It looks as though height and weight are more or less linearly related! We'll come back to that in a moment, but first, let's convert them to standard units." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Converting to standard units\n", "\n", "A value in standard units is _how many standard deviations above the mean_ it is. So, to convert a data point to standard units, we need the mean and the standard deviation of the data set that it came from. Then we subtract the mean from it, and then divide that by the standard deviation The `standard_units` function below, which comes [from the Data 8 textbook](https://www.inferentialthinking.com/chapters/14/2/Variability#standard-units), does this for a whole array of numbers at once." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def standard_units(nums):\n", " return (nums - np.mean(nums)) / np.std(nums)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can create a version of the `heightweight` table that's in standard units. " ] }, { "cell_type": "code", "execution_count": 5, "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": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "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": "markdown", "metadata": {}, "source": [ "And we can plot this data, just like we did with the data in original units." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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G+BiwEHgHKdmeCiwCfgI8ALy+oHhuAw6WdKCkscAJwFVVba7K4oBUT/dGj9ea2XCXN9m+GTgLuDx7fGtEXJJN97oTOLKIYLIx2FOBHwD3At+IiFWSzpL0xqzZcmC6pNXAh4HTiji2mVkz5R2znQ2sioh+SduAp1Tsuxi4BPhAEQFFxDXANVXbzqi4vxk4rohjmZmVJW/PtgeYlN1/BHhexb4ZwIQigzIzazd5e7YrgBcA1wL/BXxS0p8A24GPkMZuzcysjrzJ9hzSUAKkcovPJI3hdpIS8XuKD83MrH3kXUG2EliZ3f8/4M1ZjYJxEbGhifGZmbWFXGO2ks6Q9LTKbRGxJSI2SNpX0hn1ftfMzPKfIPs4aYFBLU/L9puZWR15k229VWMAe7PrNcnMzKxC3TFbSQuBV1Zsepek6pViE4DXAauKD83MrH00OkH2cuCfsvsBnFSjzVZS+cP3FxyXmVlbqTuMEBGfiIiOiOggDSMcNvC44jY+Ig6JiJ+XF7KZ2ciTd+rXcKt7a2Y2ouSd+vXiyvFaSdMlfV3SXZL+NbucjZmZ1ZG3x3oO6QKLA5YBRwG/Ad4NnF5wXGZmbSVvsn0O2QoySWNIdWQ/FBFvBpYAf9Wc8MzM2kPeZDsJGFiWeyipxOL3sse/5Mm6CWZmVkPeZPs7niyr+Frg7ojozh7vDWwsOjAzs3aSt+rX14Gl2UKHo9h5ee4hwP0Fx2Vm1lbyJtszgc3AYcDZwHkV+54HfLPYsMzM2kveebb9wD/X2XdMoRGZmbUhL1YwMytB3WQr6Q5Jx0pqVPGrsv3+kj4naXFx4ZmZtYdGPdv/AL4M/E7SZyS9SdIzJE2WNE7SPtnKsg9KugF4GHgW8O0S4jYzG1HqjtlGxKclXQQsAt5JulR5VDUTqZbtd4AjIuLmZgVqZjaSNTxBFhG9wKeBT0s6ADicdGWG8aTLm/8a+EVEuHi4mVkDead+ERGPAI80MRYzs7bl2QhmZiVwsjUzK4GTrbVU74Y+7n+oi94Nfa0Oxaypco/ZmhXt5hV3smTZcvr7d9DZ2cHSxYtYMH9uq8Myawr3bK0lejf0sWTZcsaNHcOMaVMYN3YMp597kXu41rbyXhbnYkkH1tn3dEkXFxuWtbvunvX09+9g4oTxAEycMJ7t/Tvo7lnf4sjMmiNvz/ZEYGadfTOAdxQSjY0as6ZPpbOzg42bNgOwcdNm9ursYNb0qS2OzKw5BjOMUL16bMA+wKYCYrFRZMrkSSxdvIgtW7exZl0vW7ZuY+niRUyZPKnVoZk1Rd0TZJKOBY6t2PQJSWurmk0AXgbc3oTYrM0tmD+Xqy9ZSnfPemZNn+pEa22t0WyE2aRECqlX+3xSHYRKW4CfAR8tPjQbDaZMnuQka6NCo0I0nwU+CyDpIeCYiLizrMDMzNpJ3is11JyJUCRJ04ArgDmkco3HR8QfarTrB+7KHv5vRLyx2bGZmQ1V7kUNkjpIlzGfTar6tZOIuGyIsZwG3BARZ0s6LXv8jzXabYqI5w/xWGZmpcqVbCU9l1QU/BmkGrbVAhhqsj0aWJjd/wpwE7WTrZnZiJO3Z/v5rO3xpK/wzahf+9SIeAwgIh6TNKtOu/GSVgLbgbMjouaVISSdDJwMMHv27CaEa2aWX95kewhwYkT891AOJul60rzcaksG8TSzI+JRSQcBN0q6KyIeqG4UERcCFwLMmzev3hxhM7NS5E22a4GtQz1YRLyq3j5Jj0vaN+vV7gt013mOR7OfD0q6CXgBsEuyNTMbTvKuIPsM8F5JnU2M5SqeXPb7DtJ1zXYiaW9J47L7M4CXAPc0MSYzs0I0WkF2VtWm5wD3SPohsK5qX0TEx4cYy9nANyS9E/hf4LgsjnnAKRGxCPhT4EuSdpD+ozg7IpxszWzYU0Tt4cwsoeUVEdHMXu+QzJs3L1auXNnqMMyszUi6PSLm5WnbaAWZa92amRXECdXMrAROtmZmJch7pYYdkvrr3LZL6pH0Q0mvbnbAZmYjUd6e7SeBR4A1wKXAOaQltWuALuA/SFdyuFbS64sP08xsZMu7qGEz8BDw2ojYPLBR0gTgWlLSPQS4Gjgd+F7BcZqZjWh5e7anAJ+pTLQAEbGJtODhlIjYAVwE+FrUZmZV8ibbWcCYOvvGAtOz+2upXRXMzGxUy5tsVwJnZjULniDpacDHs/0ATwceLS48M7P2kHfM9gPADcBDkn5OKhIzCzgc2Aj8ddbumcB/Fh2kmdlIl/eyOL+U9EzgI8B84C+Ax4BPA+dFRE/W7oxmBWpmNpLlvixOllBPb2IsZmZtyyvIzMxK0KjE4o3AeyLi19n9RiIijig2NDOz9tFoGKFyClcH6aKOedqamVmVRiUWX1Fxf2Ep0ZiZtSmP2ZqZlSB3spW0n6TzJK2U9JCkP8+2f1DS/OaFaGY28uUtsfhnwF3A35BWiM0mLdOFtGrsA02JzsysTeTt2X4auBc4EHgTO58Q+xlwWMFxjVq9G/q4/6Euejf0tToUMytQ3kUNLwXeFhF9NS5n/jiwT7FhjU43r7iTJcuW09+/g87ODpYuXsSC+S6iZtYO8vZsG11pdwawqYBYRrXeDX0sWbaccWPHMGPaFMaNHcPp517kHq5Zm8ibbH8BnFRn3/HAT4sJZ/Tq7llPf/8OJk4YD8DECePZ3r+D7p71LY7MzIqQdxjhk8D1kq4jVfUK4FWSPgAcCyxoUnyjxqzpU+ns7GDjps1MnDCejZs2s1dnB7OmT211aGZWgFw924i4GTiGdILsYtIJsrOBlwHHRMStTYtwlJgyeRJLFy9iy9ZtrFnXy5at21i6eBFTJk9qdWhmVgBFNFqFW+MXUqnFWUBPRNzXlKgKNm/evFi5cuXuGw4DvRv66O5Zz6zpU51ozYY5SbdHxLw8bRsVonluRNxTvT0iVgOrhxCfNTBl8iQnWbM21GjM9m5Ja4EfA7dktztisF1hMzNrmGzfRxqTfRnpJFgAGyT9lJR4bwZWRkR/06M0MxvhGlX9ugC4AJ4Yp305adbBy4CjSMl3o6QVwM0R8anmh2tmNjLlvQbZwDjtckhFaUjJ93jgDcArASdbM7M6cl+DDEDSbFLvduD2LKAP+HnxoZmZtY+GyVbSs9g5uc4mXcb8J8AXsp//ExGNlvOamY16jaZ+PUaaT/sAaTnuWcCPI+L+kmIzM2sbjVaQPZVUYOZeYFV2e6iMoMzM2k2jZLsPcCLwW+CvSb3b9ZJukHSmpCMkTSwhRjOzEa9uso2I7oi4MiLeHxHPB6YDbwNuB44EriUl31slLRtqIJKOk7RK0g5JdZe/STpS0n2SVks6bajHNTMrQ+5rkEVEb0R8NyIWR8RhpBNm1wDzgA8XEMvdpKtA3FKvQVa4/ALgtcBzgbdJem4BxzYza6pcU78kdQCH8OSshJcCe5Oqf3XTIEHmFRH3Zsdq1OxQYHVEPJi1vRw4GtilhoOZ2XDSaDbCS3kyuR4OTCIl1y7g+2RLdkuu/LUf8EjF4y6g5pV9JZ0MnAwwe/bs5kdmZtZAo57tQG/1QeDK7PEtEbHHMxIkXU/t65UtiYjv5HmKGttqFsaJiAuBCyGVWMwdpJlZEzRKtn9F6rk+VtTBIuJVQ3yKLuCAisf7ky6tbmY2rDWajXB5kYm2ILcBB0s6UNJY4ATgqhbHZGa2W7lnIzSbpGMldZHGh6+W9INs+9MkXQMQEduBU4EfkBZbfCMiVrUqZjOzvAZViKaZIuJbwLdqbH+UVNJx4PE1pClnZmYjxrDp2ZqZtTMnWzOzEjjZmpmVwMm2CXo39HH/Q130buhrdShmNkwMmxNk7eLmFXeyZNly+vt30NnZwdLFi1gwf26rwzKzFnPPtkC9G/pYsmw548aOYca0KYwbO4bTz73IPVwzc7ItUnfPevr7dzBxwngAJk4Yz/b+HXT3rG9xZGbWak62BZo1fSqdnR1s3LQZgI2bNrNXZwezpk9tcWRm1mpOtgWaMnkSSxcvYsvWbaxZ18uWrdtYungRUyZPanVoZtZiPkFWsAXz53L1JUvp7lnPrOlTnWjNDHCybYopkyc5yZrZTjyMYGZWAidbM7MSONmamZXAydbMrAROtmZmJXCyNTMrgZOtmVkJnGzNzErgZGtmVgIn2zpcANzMiuTlujW4ALiZFc092youAG5mzeBkW8UFwM2sGZxsq7gAuJk1g5NtFRcAN7Nm8AmyGlwA3MyK5mRbhwuAm1mRPIxgZlYCJ1szsxI42ZqZlcDJ1sysBE62ZmYlcLI1MyuBk62ZWQmcbM3MSqCIaHUMTSdpDfDbVsdRZQawttVB5DSSYoWRFe9IihVGVrxlxPr0iJiZp+GoSLbDkaSVETGv1XHkMZJihZEV70iKFUZWvMMtVg8jmJmVwMnWzKwETratc2GrAxiEkRQrjKx4R1KsMLLiHVaxeszWzKwE7tmamZXAybYkko6TtErSDkl1z5BKOlLSfZJWSzqtzBgrYpgm6YeS7s9+7l2nXb+kO7LbVSXH2PB9kjRO0hXZ/lslzSkzvhrx7C7eEyWtqXg/F7UiziyWiyV1S7q7zn5J+lz2Wn4l6ZCyY6yIZXexLpTUW/G+nlF2jE+ICN9KuAF/CjwbuAmYV6dNJ/AAcBAwFrgTeG4LYj0XOC27fxpwTp12fS16L3f7PgHvAb6Y3T8BuKKFn32eeE8Ezm9VjFWxLAAOAe6us/8o4FpAwGHArcM41oXA91r9nkaEe7ZliYh7I+K+3TQ7FFgdEQ9GxFbgcuDo5ke3i6OBr2T3vwIc04IYGsnzPlW+hiuBIySpxBgrDZfPNZeIuAVY16DJ0cBlkawApkrat5zodpYj1mHDyXZ42Q94pOJxV7atbE+NiMcAsp+z6rQbL2mlpBWSykzIed6nJ9pExHagF5heSnS7yvu5vjn7Wn6lpAPKCW2PDJe/07wOl3SnpGsl/VmrgvA1yAok6Xpgnxq7lkTEd/I8RY1tTZku0ijWQTzN7Ih4VNJBwI2S7oqIB4qJsKE871Np72UOeWL5LvD1iNgi6RRSr/yVTY9szwyn93Z3fklaUtsn6Sjg28DBrQjEybZAEfGqIT5FF1DZo9kfeHSIz1lTo1glPS5p34h4LPt62F3nOR7Nfj4o6SbgBaSxyWbL8z4NtOmStBcwhdZ93dxtvBHRU/Hwy8A5JcS1p0r7Ox2qiNhQcf8aSZ+XNCMiSq/v4GGE4eU24GBJB0oaSzqxU+pZ/sxVwDuy++8AdumVS9pb0rjs/gzgJcA9JcWX532qfA1vAW6M7IxJC+w23qoxzzcC95YY32BdBfxtNivhMKB3YNhpuJG0z8BYvaRDSTmvp/FvNUmrz9CNlhtwLKlHsAV4HPhBtv1pwDUV7Y4CfkPqIS5pUazTgRuA+7Of07Lt84CLsvsvBu4inVm/C3hnyTHu8j4BZwFvzO6PB74JrAZ+ARzU4s9/d/H+C7Aqez9/BDynhbF+HXgM2Jb9zb4TOAU4Jdsv4ILstdxFndk1wyTWUyve1xXAi1sVq1eQmZmVwMMIZmYlcLI1MyuBk62ZWQmcbM3MSuBka2ZWAifbYS6rBhWSnllj317ZvjP34HnPlLRHU1Ek3STpJznaHSPpw4N87hdK2igp9/LP7D36u8Ecp0hDeS/34FiXSnq4jGNVHXen1yhparZt0BW/JH0oW5Y8qvLPqHqxtpOLgMObfIxjgEElW2AZcHFE/G4Qv3Mi0LJkO0pU/71MBT5Oqrg1WF8k1dt4x+4athMn21EqIroiVWwaNrJe0iuAL7Q6llaRNKaF1cnqKvLvJSI2AZcB/1DE840UTrZtKFsW+rWsGPWWrGjysVVtdvnqK2mmpK9L2iDpD5IukfTGbKhiYY3jvErSL7Ov/XdXVv6SdCmp57Jf9vuR4+vv3wO/iohVVcf5K0n/I6kvKwR9l6R3ZftuAl4OvKTiODdVvJ4vSfpNFuMjkv6zeohi4L2QdLCkq7Pj/FbSGdVfdSW9QNKPJW2W9DtJH6NGYRZJp0r6uaR1ktYrVUZ7XVWbOdlx3yPpXEmPklYYTs32H5G9v5slPTDwmnen4nlPrNq+sPqzHBgSavRZVr5HA88PPJTt+nLF+35itv81kn6WfVZ9SkXTq4t2Xw6PeI2BAAAGdUlEQVQ8V9KL87ymduBCNCNHp1JBlZ22VTdSKs13K6l4zIeANcBbgf+SdExENKq18N/AXwAfJS1zfTPw73XaPgP4LGmZ6VrgI8CVkp4TEauBTwIzgReR1vpDSiSNHAlcXfV6Xgp8Ffgc8P9IHYTnkCUkUpHwr5Lei4FkNFB8ZBqwOXs9a0hLoz8C/DSLc3PV8b8FXAJ8BngD8AlSKcFLslhmADcCvyf9R7Ili2l2jdcyh/TV+2HSv7M3AN+TdFREXFvVdgmpfsLJ2evYLOlPgWuAlaRaCuOAM4FJQH+N4w3F7j7Lao8BbyL9vfwLT9Z5eECpAtxVpBrCZwFbSVW2Dqp6jjtIn9ORwM8KfTXDVavWCfuW70Yaj4zd3M6saL+clFimVz3PD4E7Kh6fmT7+Jx6/Onuu46t+76ps+8KKbTeR1qIfXLFtFikJnF6x7VKgK+frfGp2nL+v2v4PwLrd/O5NwE9yHKOTVK0qgGOr3wvgpKr2dwHXVTz+Z1LymF2x7SmkBBUNjttBSrjXAd+p2D4nO+4vyS6+WrHva9nzPqVi2wHZ8R/ezesceN4Tq7YvHMJnWf33MnCMRVXHeEu2fXKOz+PHle9vu988jDByHEvqJVbeDqvR7khSj6hXabbCXlmP+AfA8yRNrvP8h5H+gX2ravuVddrfHxH3DzyIiG5Sb7pWLy+Pp2U/11Rtvw3YW9JXJb1e0lQGQdK7lQpH9wHbgf/Ndj27RvOrqx7fzc6v53BgRUQMPAcR8UdSLdrq475Q0vckPZ4ddxvwl3WO++3Isk/Vsa7Jnn/gWI8AP63x+0NV5Gd5B+m1Xi7pLZLqFZ6HJ79tjApOtiPH3RGxsvIG3F6j3Szgb0l/8JW3Zdn+elcr2Bf4Q0Rsq9r+eJ32tWrDbiFV29oTA7+301BDRNwMHEfq1X0LWCPpeklzd/eEkt4HfB64nvS191Ce/A+qVpzVr6n69exL7fdjp23ZUM4NpGGM95EqpL0I+H6d49YqT5jrWAUp7LOMNOzwGlJu+Q/g90oX3Hx5jeabgAmDPcZI5THb9tND+npWr/h0vSLPj5F6kGOqEu5TiwyugYEao7tcyTciriSNIU4ifRU+B/i+pP0jYkeD5zwBuCEiPjKwQdKBQ4jxMWq/H9XbjiQVKz8+Iroqjj2xzvPWmqOb91i1DIxFj63aXsplgSLiR8CPlOodv4Q0dnu1pDmxc9HuaaShklHBPdv2831gLrCquiec3eqdpFpBGtM8tmr7cUOIZQv5ey4Pk5JE9YmUJ0REX0R8D/gSqec3kDzqHWciqVdf6aSc8dTyc+AwVVwfTNJTSCe/qo9L5bElPYuUeAZzrKOy5x94jgNyPsfjpPfkz6u2v65G2z018HdU9/ONiC0RcSPpas1PAar/ozsQ2N1FUNuGe7bt5wxSsexbJJ1PSmJ7k/7hHRQRNSf/R8R1SqvCLszOuq8mnex4XtakUQ+ynnuAaZLeTTqrvjki7qpz/K2SbiV91X+CpLNIvbkfkXrl+wPvJ53sGxjfvQd4j6S3kgpa/1+kKxl/H/hHSaeT3pNXZq9pT32GNPvhOqVVewOzETZVtbueNE57maRPk/5j+ARpvDhvB+dTpP/orpO0jNRL/QQ5hhEiIiRdAbxT0m9ICe11pG8FRXmc9G3kBEm/Av5Img52HOny4teQZnLMIM0GeZQ0Bg6kFWjAs4B/LTCmYc092zaTnbyZR6pMv5Q0C+ELpLmoN+7m199ESlDnAN8gjdl9LNvXuwfhXESaT7mUlOx2OZFU5QrglZW9OdI0tjmkRPfDLLab2bmXdg5pjPQi0gm1L2Xbz8ruf4g03juXNJ64R7KvwEeQvvp+hXS1gu8DF1e1WwW8HXg6aTbHYuA04JZBHOte0tUdJpLel7OBfyO9zjw+QJqadWb2++NJ48eFyIZvFpH+I7+e9L6/gfR39xTSlLDrgPNJSfiVkRYzDHgdaWZF9QnZtuUrNVhDki4gTT+b1mAIoqhjTSZd2uQ9EfHVZh7LWkvStcDaiPibVsdSFg8j2BOyFUBTSNdsGks60XMKsKzZiRbSlVAlnQMslvS1GtOhrA1Iej5pWXb1mHJbc7K1Sn8EPkhaUTSO9PXvdJ6cNlaG80gn6vZlmF4e24ZsH9ICklqr09qWhxHMzErgE2RmZiVwsjUzK4GTrZlZCZxszcxK4GRrZlYCJ1szsxL8f6g3g6YmS39jAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heightweight_standard.scatter('Height (standard units)', 'Weight (standard units)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data points on our plot are exactly the same. Only the axes have changed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The correlation coefficient\n", "\n", "Now that we've got standard units, though, it's easy to compute the correlation coefficient $r$. First, we need to take the product of our $x$ and $y$ values -- in this case, height and weight -- for each data point. We'll add a new column to our table that has these products." ] }, { "cell_type": "code", "execution_count": 7, "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) Product of standardized height and weight
07/28/2017 -1.26135 -1.3158 1.65968
08/07/2017 -1.08691 -1.13054 1.22879
08/25/2017 -0.912464 -0.808628 0.737844
09/25/2017 -0.228116 -0.399485 0.091129
11/28/2017 0.107349 0.254728 0.0273447
01/26/2018 0.617255 0.728253 0.449518
04/27/2018 1.12716 1.2537 1.41312
07/30/2018 1.63707 1.41777 2.32099
" ], "text/plain": [ "Date | Height (standard units) | Weight (standard units) | Product of standardized height and weight\n", "07/28/2017 | -1.26135 | -1.3158 | 1.65968\n", "08/07/2017 | -1.08691 | -1.13054 | 1.22879\n", "08/25/2017 | -0.912464 | -0.808628 | 0.737844\n", "09/25/2017 | -0.228116 | -0.399485 | 0.091129\n", "11/28/2017 | 0.107349 | 0.254728 | 0.0273447\n", "01/26/2018 | 0.617255 | 0.728253 | 0.449518\n", "04/27/2018 | 1.12716 | 1.2537 | 1.41312\n", "07/30/2018 | 1.63707 | 1.41777 | 2.32099" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "heightweight_product = heightweight_standard.with_column(\n", " 'Product of standardized height and weight',\n", " heightweight_standard.column('Height (standard units)') * heightweight_standard.column('Weight (standard units)'))\n", "heightweight_product" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute $r$, we just need to take the mean of the product column." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9910523777994954" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = np.mean(heightweight_product.column('Product of standardized height and weight'))\n", "r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wow. $r$ is very close to 1, which means that our data has an almost perfect linear correlation.\n", "\n", "What does \"almost perfect\" look like? Now that we have $r$, we can plot the regression line. (To be specific, we're plotting a segment of the regression line that goes from -2 to 2 on the $x$-axis, but we could plot a longer segment if we wanted to.)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heightweight_standard.scatter('Height (standard units)', 'Weight (standard units)', label=\"data\")\n", "x = np.array(range(-2, 3)) \n", "y = r * x # <-- the regression equation!\n", "plots.plot(x, y, label=\"regression line\", linewidth=1.5) \n", "plots.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since $r$ is so close to 1, the regression line is awfully close to $y = x$, a perfect linear correlation. Let's plot that line, too." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heightweight_standard.scatter('Height (standard units)', 'Weight (standard units)', label=\"data\")\n", "x = np.array(range(-2, 3)) \n", "y = r * x # <-- the regression equation\n", "plots.plot(x, y, label=\"regression line\", linewidth=1.5) \n", "y = x # <-- linear correlation\n", "plots.plot(x, y, label=\"linear correlation\", linewidth=1.5) \n", "plots.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The slope of the actual regression line is just sliiiiightly smaller than the slope of the line $y = x$. That is, the regression line is slightly higher than the red line on the left side of the plot, and slightly lower on the right side. If we scale up the plot size and tweak the line width and range of the axes, we can see the separation between the two lines a bit more clearly." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "original_dpi = plots.rcParams['figure.dpi']\n", "plots.rcParams['figure.dpi'] = plots.rcParams['figure.dpi'] * 1.5\n", "heightweight_standard.scatter('Height (standard units)', 'Weight (standard units)', label=\"data\")\n", "x = np.array(range(-2, 101)) \n", "y = r * x # <-- the regression equation\n", "plots.plot(x, y, label=\"regression line\", linewidth=0.5) \n", "y = x # <-- linear correlation\n", "plots.plot(x, y, label=\"linear correlation\", linewidth=0.5) \n", "plots.legend()\n", "plots.rcParams['figure.dpi'] = original_dpi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Secret Bonus Content™\n", "\n", "We've seen that the relationship between height and weight in this data set is very well captured by a straight line. But what about the relationship between height and time, or weight and time?\n", "\n", "Let's go back to our original table and look at the date column. To make dates easier to work with, let's convert them to Python date objects instead of strings." ] }, { "cell_type": "code", "execution_count": 12, "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 (cm) Weight (kg)
2017-07-28 53.3 4.204
2017-08-07 54.6 4.65
2017-08-25 55.9 5.425
2017-09-25 61 6.41
2017-11-28 63.5 7.985
2018-01-26 67.3 9.125
2018-04-27 71.1 10.39
2018-07-30 74.9 10.785
" ], "text/plain": [ "Date | Height (cm) | Weight (kg)\n", "2017-07-28 | 53.3 | 4.204\n", "2017-08-07 | 54.6 | 4.65\n", "2017-08-25 | 55.9 | 5.425\n", "2017-09-25 | 61 | 6.41\n", "2017-11-28 | 63.5 | 7.985\n", "2018-01-26 | 67.3 | 9.125\n", "2018-04-27 | 71.1 | 10.39\n", "2018-07-30 | 74.9 | 10.785" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "heightweight_dates = heightweight.with_columns(\n", " 'Date',\n", " [datetime.strptime(date, \"%m/%d/%Y\").date() for date in heightweight.column(0)])\n", "heightweight_dates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now compute the number of days since birth for each row in our data set. Sylvia was born on July 24, 2017, so we'll define that date to be her `birthday` and work from there." ] }, { "cell_type": "code", "execution_count": 13, "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 (cm) Weight (kg) Days since birth
2017-07-28 53.3 4.204 4
2017-08-07 54.6 4.65 14
2017-08-25 55.9 5.425 32
2017-09-25 61 6.41 63
2017-11-28 63.5 7.985 127
2018-01-26 67.3 9.125 186
2018-04-27 71.1 10.39 277
2018-07-30 74.9 10.785 371
" ], "text/plain": [ "Date | Height (cm) | Weight (kg) | Days since birth\n", "2017-07-28 | 53.3 | 4.204 | 4\n", "2017-08-07 | 54.6 | 4.65 | 14\n", "2017-08-25 | 55.9 | 5.425 | 32\n", "2017-09-25 | 61 | 6.41 | 63\n", "2017-11-28 | 63.5 | 7.985 | 127\n", "2018-01-26 | 67.3 | 9.125 | 186\n", "2018-04-27 | 71.1 | 10.39 | 277\n", "2018-07-30 | 74.9 | 10.785 | 371" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "birthday = date(2017,7,24)\n", "days_since_birth = [(date - birthday).days for date in heightweight_dates.column('Date')]\n", "heightweight_with_days = heightweight_dates.with_columns('Days since birth', days_since_birth)\n", "heightweight_with_days" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we can easily plot the relationship between days since birth and height, and the relationship between days since birth and weight." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ay4D1wNKI+F2lCmx0XT29DAwM0jxrJgDNs2by+MAgXT29Na7MzEZT8qhKEbGddH8iK6OO9jaamqawe89emmfNZPeevUxtmkJHe1utSzOzUXhUpRprbZlN54rl7Nt/gO5H+ti3/wCdK5bT2jK71qWZ2SiK7nlK+vg4vici4h/LUM+ktGzpIq5f10lXTy8d7W0OTrMJYLRm+wUjTAuefHVR4XSH50FobZnt0DSbQEZrtk8b9phFCs6lI8ybXtkyzczqy2hD0g0Uvpf+sMM5MHyemdlk4w4jM7Mcqh6ektokXSPpbkl3SXqppDmSbpK0NXs+pNp1mZmNRy32PC8EboiI5wNHA3eRrla6OSKeB9ycvTczq1ujnaq0cNikpuz5cElPufwlIu4ba2WSWkhXJp2efWY/sF/SycArs8UuA24hjRtqZlaXRjtV6R5Gvunbd4os31RkeqGFpBGY1kk6Grgd+DBwaETsAIiIHZI6SvguM7OaGS08z6jQ+o4BzomI2yRdyDia6JLOAs4COOKIIypQnplZaUY7VemyCqxvO7A9Im7L3l9DCs+HJc3P9jrnA11FaroEuARgyZIlvhWymdVMVTuMIuIh4LeSjsomnQD8CvguT9wH6TTS/ZLMzOpWyaMqldE5wBWSppPuwnkGKcS/KelM4DfA22tQl5lZyaoenhGxEVgywqwTql2LmVlevsLIzCwHh6eZWQ4OTzOzHByeZmY5ODzNzHJweJqZ5eDwNDPLweFpZpaDw9PMLAeHp5lZDg5PM7McHJ5mZjk4PM3McnB4mpnl4PA0M8vB4WlmloPD08wsB4enmVkODk8zsxwcnmZmOTg8zcxycHiameXg8DQzy8HhaWaWg8PTzCwHh6eZWQ4OTzOzHByeZmY5ODzNzHJweJqZ5eDwNDPLweFpZpaDw9PMLAeHp5lZDg5PM7McHJ5mZjk4PM3McnB4mpnl4PA0M8vB4ZlDX/8utt6/nb7+XbUuxcxqZGqtC5hobl2/iZWr1zIwMEhT0xQ6Vyxn2dJFtS7LzKrMe57j0Ne/i5Wr1zJj+jTmzmllxvRpnL9qjfdAzSYhh+c4dPX0MjAwSPOsmQA0z5rJ4wODdPX01rgyM6s2h+c4dLS30dQ0hd179gKwe89epjZNoaO9rcaVmVm1OTzHobVlNp0rlrNv/wG6H+lj3/4DdK5YTmvL7FqXZmZV5g6jcVq2dBHXr+ukq6eXjvY2B6fZJOXwzKG1ZbZD02ySc7PdzCwHh6eZWQ5VD09J2yT9QtJGSRuyaRdIejCbtlHSG6pdl5nZeNTqmOfxEbFz2LQvRMRna1KNmdk4udluZpZDLcIzgBsl3S7prILpZ0u6U9Klkg4Z6YOSzpK0QdKG7u7u6lRrZjaCWoTnyyLiGOBE4IOSlgEXAc8BFgM7gM+N9MGIuCQilkTEknnz5pWtII+SZGbjVfVjnhHxu+y5S9K1wLER8eOh+ZK+DHyvWvV4lCQzy6Oqe56Snibp6UOvgdcCmyXNL1jsLcDmatTjUZLMLK9q73keClwraWjdX4+IGyRdLmkx6XjoNuAD1ShmpFGSHtuzj66eXl9BZGajqmp4RsR9wNEjTH9vNesYUjhKUvOsmR4lycxKNqlPVfIoSWaW16QfGMSjJJlZHpM+PMGjJJnZ+E3qZruZWV4OTzOzHByeZmY5ODzNzHJweJqZ5eDwNDPLweFpZpbDpAlPDztnZuU0KU6S97BzZlZuDb/n6WHnzKwSGj48Rxp27vGBQbp6emtcmZlNZA0fnoXDzgEeds7MyqLhw9PDzplZJUyKDiMPO2dm5TYpwhM87JyZlVfDN9vNzCrB4WlmloPD08wsB4enmVkODk8zsxwcnmZmOTg8zcxycHiameWgiKh1DblI6gYeKGHRucDOCpdTinqpA1zLSOqlDqifWuqlDqhuLc+OiHljLTRhw7NUkjZExBLX8QTXUr91QP3UUi91QH3VMsTNdjOzHByeZmY5TIbwvKTWBWTqpQ5wLSOplzqgfmqplzqgvmoBJsExTzOzSpgMe55mZmXXsOEp6fWStki6R9K5NVj/Nkm/kLRR0oZs2hxJN0namj0fUqF1XyqpS9LmgmkjrlvJl7LtdKekYypcxwWSHsy2y0ZJbyiYd15WxxZJrytjHc+S9CNJd0n6paQPZ9NrsU2K1VKL7TJT0s8kbcpq+WQ2/UhJt2Xb5SpJ07PpM7L392TzF1S4jq9Iur9gmyzOplfs9zMuEdFwD6AJuBdYCEwHNgF/XOUatgFzh01bBZybvT4X+D8VWvcy4Bhg81jrBt4A/AAQcBxwW4XruAD4+xGW/ePs9zQDODL7/TWVqY75wDHZ66cDv87WV4ttUqyWWmwXAbOz19OA27Kf95vAqdn0i4G/yl7/NXBx9vpU4KoK1/EV4JQRlq/Y72c8j0bd8zwWuCci7ouI/cCVwMk1rglSDZdlry8D3lyJlUTEj4FHSlz3ycBXI1kPtEmaX8E6ijkZuDIi9kXE/cA9pN9jOerYERF3ZK9/D9wFHE5ttkmxWoqp5HaJiBi6B/e07BHAq4BrsunDt8vQ9roGOEGSKlhHMRX7/YxHo4bn4cBvC95vZ/Q/0EoI4EZJt0s6K5t2aETsgPSPCOioYj3F1l2LbXV21ty6tODQRVXqyJqaLyHt3dR0mwyrBWqwXSQ1SdoIdAE3kfZseyPi8RHW94dasvl9QHsl6oiIoW3yz9k2+YKkGcPrGKHGqmnU8Bzpf8Nqn1bwsog4BjgR+KCkZVVef6mqva0uAp4DLAZ2AJ+rVh2SZgPfAj4SEf2jLVqDWmqyXSJiICIWA88k7dG+YJT1VayW4XVIehFwHvB84E+AOcA/VLqO8WjU8NwOPKvg/TOB31WzgIj4XfbcBVxL+sN8eKh5kT13VbGkYuuu6raKiIezfyiDwJd5ogla0TokTSOF1RUR8e1sck22yUi11Gq7DImIXuAW0jHENklDN4csXN8fasnmt1L6YZnx1vH67BBHRMQ+YB1V3iZjadTw/DnwvKzXcDrp4PZ3q7VySU+T9PSh18Brgc1ZDadli50GXFetmkZZ93eB92U9mMcBfUNN2UoYdmzqLaTtMlTHqVmP7pHA84CflWmdAtYCd0XE5wtmVX2bFKulRttlnqS27PUs4NWkY7A/Ak7JFhu+XYa21ynADyPrwalAHXcX/Mcm0nHXwm1Stb/ZomrRS1WNB6lH7tekYzgrq7zuhaQe0k3AL4fWTzo+dDOwNXueU6H1f4PU9DtA+l/6zGLrJjWB/iXbTr8AllS4jsuz9dxJ+kcwv2D5lVkdW4ATy1jHn5GadXcCG7PHG2q0TYrVUovtsgj4n2ydm4GPF/z9/ozUOXU1MCObPjN7f082f2GF6/hhtk02A1/jiR75iv1+xvPwFUZmZjk0arPdzKyiHJ5mZjk4PM3McnB4mpnl4PA0M8vB4TlJSDpdUhQ8HlMa+elaSe+QNOH+FiQtyH6W02tdy3DZiEDbS1hu6PeyoIRlFyiNvrRwhHnbJH0tX7WWx4T7B2MH7e3AS0nnFn4M2Ec6H/PG7ATliWQH6We5vtaFHITrST9DKSd5LwA+QToP02ps6tiLWIPZGBH3FLy/XNLVpJOfVwHn1Kas8Yt02d76WtdxMCKiG+gebZnsCptp1anISuU9TyMivkW6BO/9kpqHpkv6pKQ7JPVJ2inph9nlcEPzD5O0X9mAvoWy5uVuPTHA8Osk/TT7rl1KA/t+fLS6su+/TNLvJO2TtEPS9yR1ZPOf0mwfai5Leomkn2Q1bJX0lyN8/5GSLpf0UPb990m6cNgyr5B0s6TfZ4c6/iMbtKIkkv5U0s8l7c2a1ucMm/+UZvtQE1zSX0i6G9gPvJF02STATQWHX1457PtOVRpo+TFJGyT9Wam12vg4PG3I90kD7hbeG/tw4Auk64pPJw2c8WNJiwAi4iHgO8AHCr9IUhPpUsxvRsSj2TG67wL3A+8ETgI+DzxtjJouJzVpPwq8BvgQ6TLP5tE+BLQAXydd0ncyaayDiyQdX1DjkaRLDJeRmsInAp8E5hYs80bSZZu7gD8H3k0awPgnkgoHphitjqt4YkzMW4AvlXiM9njgb7OaXg/cB3wwm/ch0nZ5KXBHwWdeDvwd6XDMO0mDgn9v6LpxK7NaXBPqR/UfpPAL4LlF5r8um//OIvObSId5tgAXFkx/Zfa5lxdMOymbdlz2/pTsfcs4a94FfGiU+Quy7z29YNpXsmnHF0ybAewELimY9tXs+58xyvffA9w8bFpL9l1fHKP2oTpOHTb9JuABnrj54tDvZUHBMtuA3cBhwz47tK1fPcL6tgGPAocUTFuSLf/uWv/9NeLDe542ZGiMxD8MdiDp1Ur32+kBHicN8PFHwFFDy0TELcCvePLe5weAOyON8g1p8IsDwJWSThlqdpfg58BHJX1Y0ouzY3+l2B0RQ01cIh0b3QocUbDMa4HvRTZ04HCSnkcaX/MKSVOHHqRQ+2/SHutYBkhDzxW6MqtjrMF710fasx+P/46IRwve/yJ7PmKkhe3gODxtyFAzdAeA0k21vk/aOzuTNM7jn5BGipo57LMXAadIapf0bFIz8+KhmZE6qF5H+nu7HHhI6QZirxijpneSmvsrSCPuPCjp4yWcVvXoCNP2Dau7nXQIoJihgF9LCv7Cx5sobQT1RyPiwLBpD2fPY4VnniHWnjS2ZvafBjz192Vl4N52G/JGYC9we/b+baS9zbcWBkDWAdQ77LNfBT5NaoIeAuwBrihcINsT/JHSrRReBnwKuF7SgojYOVJBkQaS/iBpJP6jSGNJfpLUO31R7p802cnoAdaTPZ8H/OcI8/eXsI5DJE0bFqCHZs8PjvFZD3dW5xyehqS3ko5TXhgRu7PJzaRmZ2Ez/lWkJuD9hZ+PiH5JV5Ca67OBr0eR21xke0M/VLoNxXWkO0KOGJ7DPrcFOD/rNS+5t3sUNwJvlTQ/Rh5IdwvpOOILI+IzOdfRRPpP6MqCaacCv2Hs8BzJ0J7kRDsftyE5PCefxZLmkm7JfASpCfp2UkfGeQXL3QB8BPiKpHWkY50fo/g/+n/lieOeFxfOyAJvGekwwG9JPdrnkW6dsJkRSGol7fFdAdxNai6fTNqzvbHkn7a4T5D2tn8qqZPUOXQ46fYPfx4RIemDwHVKdyP4JinkDwX+FPhNPHlU+pH8HliVbe+twLtIo6SfHlmPzjj9mtQa+AtJj5DCdEuku3BalTk8J5+rs+e9pFOP7iDtDV1T+A86Iv5D0odIp8u8jRRy7wP+90hfGhF3Svo10B/ZrXULbCKdCvRp0rHER4D/At4TEXuK1Lk3q+39wLOBQdLe4Hsi4qBvXxIR2yQtBf4pq+vppP8YritY5vtKN+5bCawh7fE9RDox/6oSVtNP2rYXAi8mHe/8cERcNuqnitfcI+ls0o3QbiXt2R5POgXKqswjyVtZSPoj0h7i+yNiba3rMas0h6cdFEnPBJ5L6sh5Luk80mJ7k2YNw6cq2cFaTrpR16Gkk7EdnDYpeM/TzCwH73mameXg8DQzy8HhaWaWg8PTzCwHh6eZWQ4OTzOzHP4/dlI0TAWpdQYAAAAASUVORK5CYII=\n", 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heightweight_with_days.scatter('Days since birth', 'Height (cm)')\n", "heightweight_with_days.scatter('Days since birth', 'Weight (kg)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How linear are these relationships? We can find out by computing $r$ for each relationship." ] }, { "cell_type": "code", "execution_count": 15, "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) Days since birth (standard units) Product of standardized height and days since birth Product of standardized weight and days since birth
2017-07-28 -1.26135 -1.3158 -1.03738 1.3085 1.36498
2017-08-07 -1.08691 -1.13054 -0.957736 1.04097 1.08276
2017-08-25 -0.912464 -0.808628 -0.814374 0.743087 0.658526
2017-09-25 -0.228116 -0.399485 -0.567474 0.12945 0.226697
2017-11-28 0.107349 0.254728 -0.0577429 -0.00619863 -0.0147087
2018-01-26 0.617255 0.728253 0.412165 0.254411 0.30016
2018-04-27 1.12716 1.2537 1.13694 1.28151 1.42538
2018-07-30 1.63707 1.41777 1.88561 3.08686 2.67336
" ], "text/plain": [ "Date | Height (standard units) | Weight (standard units) | Days since birth (standard units) | Product of standardized height and days since birth | Product of standardized weight and days since birth\n", "2017-07-28 | -1.26135 | -1.3158 | -1.03738 | 1.3085 | 1.36498\n", "2017-08-07 | -1.08691 | -1.13054 | -0.957736 | 1.04097 | 1.08276\n", "2017-08-25 | -0.912464 | -0.808628 | -0.814374 | 0.743087 | 0.658526\n", "2017-09-25 | -0.228116 | -0.399485 | -0.567474 | 0.12945 | 0.226697\n", "2017-11-28 | 0.107349 | 0.254728 | -0.0577429 | -0.00619863 | -0.0147087\n", "2018-01-26 | 0.617255 | 0.728253 | 0.412165 | 0.254411 | 0.30016\n", "2018-04-27 | 1.12716 | 1.2537 | 1.13694 | 1.28151 | 1.42538\n", "2018-07-30 | 1.63707 | 1.41777 | 1.88561 | 3.08686 | 2.67336" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "heightweight_with_days_standard = Table().with_columns(\n", " \"Date\", heightweight_with_days.column('Date'),\n", " \"Height (standard units)\", standard_units(heightweight_with_days.column('Height (cm)')),\n", " \"Weight (standard units)\", standard_units(heightweight_with_days.column('Weight (kg)')),\n", " \"Days since birth (standard units)\", standard_units(heightweight_with_days.column('Days since birth'))\n", ")\n", "heightweight_with_days_product = heightweight_with_days_standard.with_columns(\n", " \"Product of standardized height and days since birth\",\n", " heightweight_with_days_standard.column('Height (standard units)') * heightweight_with_days_standard.column('Days since birth (standard units)'),\n", " \"Product of standardized weight and days since birth\",\n", " heightweight_with_days_standard.column('Weight (standard units)') * heightweight_with_days_standard.column('Days since birth (standard units)'))\n", "heightweight_with_days_product" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "r_days_height: 0.9798241135426988\n", "r_days_weight: 0.9646449280709019\n" ] } ], "source": [ "r_days_height = np.mean(heightweight_with_days_product.column('Product of standardized height and days since birth'))\n", "print(\"r_days_height:\", r_days_height)\n", "r_days_weight = np.mean(heightweight_with_days_product.column('Product of standardized weight and days since birth'))\n", "print(\"r_days_weight:\", r_days_weight)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both of these values for $r$ are pretty close to 1, although a little less so than the relationship between height and weight. Let's plot the regression lines:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heightweight_with_days_standard.scatter(\"Days since birth (standard units)\", \"Height (standard units)\", label=\"data\")\n", "x = np.array(range(-2, 3)) \n", "y = r_days_height * x # <-- the regression equation\n", "plots.plot(x, y, label=\"regression line\", linewidth=1.5) \n", "y = x # <-- linear correlation\n", "plots.plot(x, y, label=\"linear correlation\", linewidth=1.5) \n", "plots.legend()\n", "\n", "heightweight_with_days_standard.scatter(\"Days since birth (standard units)\", \"Weight (standard units)\", label=\"data\")\n", "x = np.array(range(-2, 3)) \n", "y = r_days_weight * x # <-- the regression equation\n", "plots.plot(x, y, label=\"regression line\", linewidth=1.5) \n", "y = x # <-- linear correlation\n", "plots.plot(x, y, label=\"linear correlation\", linewidth=1.5)\n", "plots.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although $r$ is pretty close to 1 in each case, the shapes of the scatter plots look to me like the data would be better modeled by a curved line, especially the second one. Maybe the next part of the course will talk about those." ] } ], "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }