{
"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": [
"
"
]
},
"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": [
"
"
]
},
"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",
"
Date
Height (standard units)
Weight (standard units)
Product of standardized height and weight
\n",
"
\n",
" \n",
" \n",
"
\n",
"
07/28/2017
-1.26135
-1.3158
1.65968
\n",
"
\n",
"
\n",
"
08/07/2017
-1.08691
-1.13054
1.22879
\n",
"
\n",
"
\n",
"
08/25/2017
-0.912464
-0.808628
0.737844
\n",
"
\n",
"
\n",
"
09/25/2017
-0.228116
-0.399485
0.091129
\n",
"
\n",
"
\n",
"
11/28/2017
0.107349
0.254728
0.0273447
\n",
"
\n",
"
\n",
"
01/26/2018
0.617255
0.728253
0.449518
\n",
"
\n",
"
\n",
"
04/27/2018
1.12716
1.2537
1.41312
\n",
"
\n",
"
\n",
"
07/30/2018
1.63707
1.41777
2.32099
\n",
"
\n",
" \n",
"
"
],
"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": {
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DzKxs5k8eU+KpTkvK11m/SuvdCMaYUurztb8xYvoy2jSozqxhPYpMtOB5Waqc3DySUw4FOly/8SnZisgNIjIk3+umIvKziBwRkbkiUrbu0TDGBMRnq/dw38zlnN+oJu/F9aBWlYo+vS9Qy1IFk68t2yeB/JNHvozTpzsO6AWM9m9Yxpiy5qMVSTw4awVdmtRi+tAe1IiO8vm9gViWKth8Ha57DrAaQEQqA9cCA1X1PyKyAXgc+GtgQjTGlHbvJ+7ibx+sJrZ5HSYOjqFKxeLPFODvZamCzdczjsa58g9wgfu+L93Xm3AGOhhjzClmJOxk1EdrubhVXcYNiKFyxcjTPlbNGtVKXZI9ztduhB3ARe7zG4Blqprqvq6PM9DBGGNOMuXH7Yz6aC1/aFOf8QNLlmhLO19btu8CL4nITUAn4E/59vUE1vs7MGNM6TZu8VbGLNhI73Zn8ka/LlSsUL5vfvIp2arqayJyAGduhNdVNf/0h9VxpkU0xpRxqYfTfOozffObLYz9YhPXdWjAq3d0IiqyfCda8H0imibA+6o6w8Pu+3GG7RpjyjBfRnCpKq8u3MxrizZzU+dGjL21AxUs0QK+99luBzp72deB/62aYIwpg1IPpzFq7EQqVYyibu2aVKoYxRMvTjhpjgJV5cUvNvHaos3c1rUxL93W0RJtPr5+JwpbfjYKZzYwY0wZVdQILlXlufkbePvbrfTv0YQXbulAZIStWp2f124EEamFM43icY1EpEWBYpWBQcBvAYjNGBMm8o/gOj43wfERXHl5yuhP1zHt550MvqAZT/+xLe7EfCafwlq2DwFbgM2AAnPd5/kfq3Fm+hoX2DCNMaHkbQRX9WpVGfXxGqb9vJPhvVpYoi2E11m/RKQjzm1eAkwCngO2FiiWCaxX1dWBDNIfbNYvY0ou/90I1apVZeTc1XywPIn7L2vJX65qXS4Tra+zfnntRlDVVcAq92AKzLfVEIwp346P4MrJzePP76/kk5V7eOSK1jx0hceVqUw+vt5nOzXQgRhjSofs3Dwemr2CBWt+Y+TV53LvpS1DHVKpUNgFsq+Be1V1o/u8MKqql/s3NGNMuMnMyeX+mSv4av0+nrzuPOIuLnjN3HhTWMs2f+dLBM5FMl/KGmPKoIzsXP703jK+2bSfZ25ox8CezUIdUqlSWJ/tZfmeXxqUaIwxYelYVi7DpiXy49YD/PPm9vTr3iTUIZU6xZ9U0hhTrhzNzGHo1KUkbD/I2Fs7cmvXxqEOqVTyOdmKSATQHWiCM7/tSQpMTmOMKQOOZGQzZPJSVuw6xKt3dOKGTo1CHVKp5etENG2Bj3FWbPDUP6uAJVtjypDUY9kMmrSEtbtTeaNfZ65tb/NNlYSvLdu33LK3A2twBjMEhIhMAq4HklX1fA/7BXgNZ2medGCwqi4PVDzGlEe/H81iwKQENv12hLfu7MJV7c4KdUilnq/JtgtOUvswkMG4pgD/xntL+RqglfvoAbztfjXG+MGBtEzumpDAtgNHGTcghsva1A91SGWCr7N+HQCyAhnIcaq6GDhYSJEbgGnqiAdqiYh9vjHGD5IPZ9BvXDw7Uo4ycZAlWn/yNdm+AtwnIuGwgFAjYFe+10nuNmNMCfyWmkHfcfHsPnSMyYO7c3GreqEOqUzxtRuhHnAusF5EvuLUlqeq6tN+jcw7bxfoTi0oMhwYDtCkid0XaIw3uw8do//4eFLSsph6d3e6Natd9JtMsfiabJ/M99zTjBMKBCvZJgFn53vdGNjjqaCqjsOd/jEmJqawEXDGlFu/pqTTb3w8hzOymT60O52bnBHqkMokn7oRVDWiiEcwuxfmAQPFEQukqureINZvTJmx/cBR7hj3M0ezcpg1LNYSbQCF3QgyEZkFXArUFZEknBZzFICqvgMswLntawvOrV9DQhOpMaXbluQj9B+fQE6eMjMulrYNa4Q6pDIt7JKtqvYrYr8C9wUpHGPKpE2/HeHOCfGAMHt4LK3PrB7qkMo8X0eQ5VH4rF8EuSvBGHOa1u5OZcDEBCpWiGDmsFjOqVct1CGVC762bJ/h1GRbB7gKqIQzEMEYE+ZW7TrEgIkJVI+OYuawHjStUzXUIZUbvq7UMNrTdve+20+BVD/GZIwJgGU7DzJ40lJqVY1iZlwsZ9euEuqQyhVfBzV4pKq5OPMmPOyfcIwxgZCwLYWBE5dQt3ol5gzvaYk2BPxxgawSYHdAGxOmftxygLipiTSsFc2sYbHUr3HKDKkmCHy9QOZp+FVF4HzgecDWCDcmDH33y36GT0ukWZ2qvBfXg3rVK4U6pHLL15btDjzfjSDAVuxWLGPCzsL1+7h3xnJa1q/Ge3E9qF21YqhDKtd8TbZ3c2qyzQB2AkvdvltjTJj4fO1e7p+5grYNazDt7u7UqmKJNtR8vRthSoDjMMb4yaer9vDwnJV0bFyTKXd3p0Z0VKhDMpTwbgRjTPCkHk5j8/YkUg+neS3z4fIkHpq9gq5Nz2Da0B6WaMNI2A3XNcac6rv4VYwaO5Hc3DwiIyMYMzKOXj06nFTm/aW7+NuHq+nZog4TBsVQpaL9eYcTa9kaE+ZSD6cxauxEKlWMom7tmlSqGMUTL044qYU7PX4nIz9YzcWt6jFpcDdLtGHIkq0xYS455RC5uXlUqezcH1ulcjQ5uXkkpxwCYNIP2/n7x2u5vE19xg3oSnSUTVMSjizZGhPm6tepRWRkBOnHMgBIP5ZBhcgI6tepxbvfbeWZz9ZzdbuzePsuS7ThzJKtMWGuZo1qjBkZR2ZWNvsPppKZlc2YkXFMW7qXf/53I3/s2JA3+nemYgX7cw5nXjt2RGRSMY6jqjrUD/EYYzzo1aMD8yePITnlEPVq12RSwh5e//oXbu7ciBdv7UCFSEu04a6wXvQ/cPJAhlpATSAHSMGZYrECzoxfvwcqQGOMo2aNatSoXpXnP9/Iu99t4/aYxvzz5g5ERnhaA9WEG6//DlW1mao2V9XmwAAgDegLVFbVBkBloJ+7/a5gBGtMeaaqPPvZBt79bht3xTbheUu0pYqv94e8DPxTVd8/vsEdojtHROoCrwLdAxCfMQbIy1OenreO6fE7GXJhM566vi0ilmhLE1+TbXucBRY92Ywz+5cxJgDy8pQnPlrD7KW7GHFJCx67uo0l2lLI117134DbvezrC+zzTzjGmPxy85S/zl3F7KW7eOAPLS3RlmK+tmxfBV4RkQbAf3CS65k4Cbg3tlKDMX6Xk5vHI++v4tNVe/jzla158PJWoQ7JlIBPLVtVfQ0YhtOdMAmY735tBwxT1Tf8FZCIXC0im0Rki4g85mH/YBHZLyIr3Uecv+o2Jlxk5eTxwKwVfLpqD49d08YSbRng8wBqVZ3o3nvbGGgA7AWSVLXQJc6Lw11A8k3gSiAJWCoi81R1fYGic1T1fn/Va0w4yczJ5b4Zy1m4IZm/X9+WoRc1D3VIxg+KbNmKSEURWS4iV6ljl6oucb/6LdG6ugNbVHWbqmYBs4Eb/FyHMWErIzuX4dOWsXBDMs/e0M4SbRlSZLJ1k15znMEMgdYI2JXvdZK7raBbRGS1iMwVkbODEJcxAZeelcPQqUtZvHk/z9/cngE9m4U6JONHvt6N8BVwVSADcXm6zFqw9fwp0ExVOwALgaleDyYyXEQSRSRx//79fgzTGP9Ky8xh8OSl/Lw1hZdu7Ujf7p7WWDWlma99tm8A74lIBeBjnP7ak5Kgqm7zQzxJQP6WamNgT4F6UvK9HA+84O1gqjoOGAcQExPj7y4PY/zicEY2QyYvZeWuQ7zatzN9OjYMdUgmAHxNtt+5X/8MPOKljD/mdlsKtBKR5sBunHt4++cvICINVHWv+7IPsMEP9RoTEqnp2QyclMC6PYf5d7/OXNO+QahDMgHia7IdEtAoXKqaIyL3A1/gJO9JqrpORJ4BElV1HvCgiPTB6UM+CAwORmzG+NvBo1kMmJjA5n1pvHNXV65oe2aoQzIBJP6/oSA8xcTEaGJiYqjDMAaAA2mZ3DUhgW0HjjJuQFcuPbd+qEMyp0lElqlqTFHlbKEiY4Is+XAG/SckkPR7OpMHd+PClnVDHZIJAp+TrYjUx5lS8VwgusBumzzcGB/sTT1G//EJ7DucwZQh3YltUSfUIZkg8SnZisi5QDxOP2pV4ABQ2339O84E4saYQiT9nk7/8Qn8fjSL6UO707Vp7VCHZILI1/tsxwJLcCafEeAanMnD44B04KaARGdMGbEz5Sh3vBvPofQspsf1sERbDvnajdANuAfIdF9HqGoOMCnf5OGXBSA+Y0q9bfvT6D8+gYycXGYOi+X8RjVDHZIJAV9bttWAg6qah9NlkL9HPxEnGRtjCti87wh3jIsnOzeP2cMt0ZZnvibbHcBZ7vNNwG359l0PHPJjTMaUCRv2HqbvuHgAZg+Ppc1ZNUIckQml4syNcKX7/GVgiDvn7DrgIZy5bY0p01IPp7F5exKph9OKLLt2dyr9xscTFRnBnOGxtDqzehAiNOHM1z7bx4FKAKr6vogcA+4AqgCv4cxRYEyZ9V38KkaNnUhubh6RkRGMGRlHrx4dPJZduesQAycmUD06ipnDetC0TtUgR2vCkY0gM6YIqYfTuG7IE1SqGEWVytGkH8sgMyub+ZPHULNGtZPKJu44yODJS6ldtSIzh/Wg8RlVQhS1CRZfR5D52o1gTLmVnHKI3Nw8qlR2xvJUqRxNTm4eySknX6qI35bCwElLqF+9EnNGxFqiNSfx2o0gIl8X4ziqqpf7IR5jwk79OrWIjIwg/VjGiZZthcgI6tepdaLMD5sPEDdtKWefUYUZcT2oX6PgIEtT3hXWso3AGcBw/NEGuBRohjOgoZn7+lw8T/ptTJlQs0Y1xoyMIzMrm/0HU8nMymbMyLgTXQjfbErm7qlLaVanKrOGx1qiNR55bdmq6qXHn4vIjTgXwmJVdUm+7T2AOe4+Y8qsXj06MH/yGJJTDlG/Tq0Tifar9fu4b8ZyWp1ZjfeG9uCMqhVDHKkJV77ejfAs8Pf8iRZAVRNEZDTwHPCJn2MzJqzUrFHtpAti/12zlwdmraBdo5pMG9KdmlWiQhidCXe+JttWgLdFvJKBlv4Jx5jS4ZOVu/nz+6vodHYtpgzpRvVoS7SmcL7ejbAdGOFl3wicEWbGlAtzlyXxyJyVdG16BtPu7m6J1vjE15btP4AZIrIWmAvsw5kB7FacC2d3BiY8Y8LL7CW/8vhHa7jgnDqMHxhDlYo2/77xjU+/Kao6W0QO4CTdx4EoIBtngcbeqroocCEaEx6m/7yDv3+yjkta1+PdAV2JjvLHGqemvPD537KqLgQWikgEzqxfB9xZwIwp8yb+sJ1nP1vPFeedyZt3dqZSBUu0pniK/RnITbDJAYjFmLD09rdbeeHzjVxz/lm81rczFSvYwEtTfMVZg6wFcDvQBFuDzJQTry/azMtf/UKfjg15+faOVIi0RGtOj69rkN0A/Afn7oVk/rdiw3HlYzYbU26oKi9/9QtvfL2Fm7s0YuytHYmMsIGS5vT5+m/6OeBboIGqNlTV5gUeLfwVkIhc7c6Vu0VEHvOwv5KIzHH3J4hIM3/VbQw4ifb5/27kja+30Lfb2bxkidb4ga/JtgXwkqp6G9jgFyISCbyJs6BkW6CfiLQtUGwo8LuqtgReAV4IZEymfFFVnvlsPe8u3saA2KaMuak9EZZojR/4mmw3AsFY4L47sEVVt6lqFjAbuKFAmRuAqe7zucDlImJ/DabE8vKUJz9ey+QfdzD0ouY8c0M7S7TGb3xNtiOBJ9yLZIHUCNiV73WSu81jGXeF31S8/CMQkeEikigiifv3B7RRbkq53DzlsQ9XMyPhV+655ByevO487H+48Sdf70YYjZPQNojIZuBggf2qqpf4IR5Pv90FL775UsbZqDoOGAfOSg0lC82UVTm5eTw6dzUfrdjNg5e34pErWlmiNX7na7LNxVlVN9CSgLPzvW4M7PFSJklEKgA1OTX5G+OT7Nw8Hpmzks9W7+WvV7Xm/j+0CnVIpozydbjupQGO47ilQCsRaQ7sBvoC/QuUmQcMAn7GmZvhay0vC6kZv8rKyeOBWcv5Yt0+nri2DcN7nRPqkEwZFlazaKggjigJAAAgAElEQVRqjojcD3wBRAKTVHWdiDwDJKrqPGAiMF1EtuC0aPuGLmJTWmVk53LfjOUs2pjM039sy5ALm4c6JFPGFSvZisgZOHPbnrLuh6ou9kdAqroAWFBg21P5nmcAt/mjLlM+ZWTnMmxaIt9vPsBzN57PXbFNQx2SKQd8HUEWDUzCGa7r7cqBzcxhwl56Vg5xUxP5eVsKL97Sgdu7nV30m4zxA19v/fo7zuKOg3CS7f1AHPADsBW4PhDBGeNPaZk5DJ60lPhtKbx8e0dLtCaofE22twDP4AwyAEhQ1cnu7V6rgKsDEZwx/nI4I5uBExNY9uvvvNa3Mzd1bhzqkEw542uybQKsU9VcnEnDq+bbNwm4w9+BGeMvh9KzuGtCAmt2p/Jm/y78sWPDUIdkyiFfk20KcHxZ0V1Ax3z76gKV/RmUMf5y8GgW/ccnsHHvEd65qytXn39WqEMy5ZSvdyPEA52B/wIfAM+KSHUgB/gLTt+tMWFl/5FM7pqQwI6Uo4wfFMMlreuFOiRTjvmabF/A6UoAZ7rFljh9uJE4ifhe/4dmzOnbdziD/uPj2XMog8mDu3FBy7qhDsmUc76OIEsEEt3nR4BbRKQSUElVDwcwPmOKbc+hY/QfH8/+I5lMvbs73ZvXDnVIxvjWZysiT4nISVcVVDVTVQ+LSAMRecrbe40Jpl0H07lj3M+kpGUxbWgPS7QmbPh6gexpnElhPGno7jcmpHamHOWOd38mNT2b9+J60LXpGaEOyZgTfO2zLWy+uTM4dU0yY4Jq6/40+o+PJysnj1nDY2nXsGaoQzLmJF6TrYhcCvwh36YRIlJwpFhl4Dpgnf9DM8Y3v+w7Qv/xCYAye3hPzj2reqhDMuYUhbVsLwGedJ8rMMRDmSxgPfCgn+Myxifr9xzmrokJVIgQZg7rScv61Yp+kzEh4LXPVlX/oaoRqhqB040Qe/x1vke0qnZR1Z+DF7IxjjVJqfQbH0+lChHMGWGJ1oQ3X2/98vVCmjFBseLX3xk4aQk1oqOYPTyWs2tXCXVIxhTK11u/LsjfXysidURkloisEZGX3CXIjQmKpTsOMmDiEmpXrcj79/S0RGtKBV9brC8AXfO9HgtcC/wC/Al4ws9xGePRz1tTGDRpCfVrVGLO8J40quV5Wo7Uw2ls3p5E6uG0IEdojGe+3vrVBngeQESicNb+elhVJ4nIw8AI4NnAhGiM4/vN+xk2LZGzz6jCjGE9qF/9lAVDAPgufhWjxk4kNzePyMgIxoyMo1ePDkGO1piT+dqyrQYcH5bbHWeKxc/c18v537wJxgTENxuTGTo1kWZ1qjJ7eKzXRJt6OI1RYydSqWIUdWvXpFLFKJ54cYK1cE3I+Zpsd/O/aRWvAdaqarL7+gwg3d+BGXPcl+t+Y/j0RFqfWY1Zw2KpU62S17LJKYfIzc2jSmUnGVepHE1Obh7JKYeCFa4xHvmabGcBY0RkLvBn4L18+7oAm/0dmDEA81fv5d4Zy2nXsCYz4mI5o2rFQsvXr1OLyMgI0o9lAJB+LIMKkRHUr1MrGOEa45WvyXY0zkWySjh9ty/n29cR+I9/wzIGPlm5mwdmLafT2bWYPrQ7NStHFfmemjWqMWZkHJlZ2ew/mEpmVjZjRsZRs4bdg2tCS1Q11DEAICK1gTlAM2AHcLuq/u6hXC6wxn35q6r28eX4MTExmpiY6J9gTcD9J3EXIz9YTY/mtZk4qBtVK/l6LdeRejiN5JRD1K9TyxKtCSgRWaaqMUWVC6fBCo8Bi1S1FbDIfe3JMVXt5D58SrSmdJmZ8CuPzl3NRS3rMnlw92InWnBauK2aN7ZEa8KG12QrIitF5CYRKWzGr/zlG4vI6yIy8jRjuQGY6j6fCtx4mscxpdi0n3fwxEdruOzceowfGEPlijZexpQNhbVspwPjgd0i8oqI3Cwi54hIDRGpJCJnuSPLHhaRRTgf/VsDH59mLGeq6l4A92t9L+WiRSRRROJFpNCELCLD3bKJ+/fvP82wTLBM+H4bT32yjivbnsk7A7oSHWWJ1pQdhfbZikhNIA4YijOwoWBhwZnL9hPgbVX9rtDKRBYCnpY3HQVMVdVa+cr+rqqnzP4sIg1VdY+ItAC+Bi5X1a2F1QvWZxvu3vxmC2O/2MR17Rvwat9OREWGUw+XMd752mdbaGeYqqYC/wL+JSJnAz1xVmaIxlnefCOwRFV9mjxcVa8oJOB9ItJAVfeKSAMg2VM5Vd3jft0mIt/irPpbZLI14UlVeW3RZl5duJkbOjXkX7d1pIIlWlMG+XzlQVV3AbsCGMs8YBDOrWWDcFrLJxGRM4B0Vc0UkbrAhcCLAYzJBJCq8tKXm3jzm63c2rUxL9zSgcgIny4RGFPqhFMT4nngShHZDFzJ/+ZiiBGRCW6Z84BEEVkFfAM8r6rrQxKtKRFVZcyCDbz5zVb6dW/Ci5ZoTRlX/HtqAkRVU4DLPWxPxOk3RlV/AtoHOTTjZ6rKPz5dz5SfdjCoZ1NG92mHjze9GFNqhU2yNeVDXp4y6uO1zFryK3EXNWfUdedZojXlgiVbEzS5ecrfPljN3GVJ3HvpOTza+1xLtKbcsGRrgiInN4+//mcVH6/cw8NXtOKhy1tZojXliq/L4kwSkeZe9jUVkUn+DcuUJdm5eTw0eyUfr9zDo73P5eErWluiNeWOr3cjDAbqedlXF+dWLWNOkZmTy30zljN/zV5GXXse913WMtQhGRMSxelG8DbU7CzgmB9iMWVMRnYu985Yztcbkxn9x7YMvtDjhyNjygWvyVZEbgJuyrfpHyJyoECxysDFwLIAxGZKsWNZuQyfnsj3mw8w5qb29O9hKyeZ8q2wlm0TnEQKTqu2E848CPllAj8Bj/s/NFNapWflMHRKIvHbU3jx1g7cHnN2qEMyJuS8JltVfQ14DUBEtgM3quqqYAVmSqcjGdncPWUpy3b+ziu3d+LGzo1CHZIxYcGnPltVtc42U6TUY9kMmrSENbtTeaNfF67r0CDUIRkTNny+QCYiETjLmDfBmfXrJKo6zY9xmTBT1DIzh9KzGDBxCRt/O8xbd3ahdztPM2kaU375lGxFpC3OpODn4MxhW5AClmzLqO/iVzFq7ERyc/OIjIxgzMg4evXocGJ/Slomd01cwtb9abw7oCt/aHNmCKM1Jjz5ep/tWziJ+XacScSbF3i0CEh0JuRSD6cxauxEKlWMom7tmlSqGMUTL04g9XAaAMlHMug3Pp5t+9OYMDDGEq0xXvjajdAFGKyqHwYyGBN+klMOkZubR5XKTs9RlcrRHD2WSXLKIY5pBfpPiGfvoQwmD+nGBefUDXG0xoQvX1u2B4CsQAZiwlP9OrWIjIwg/VgGAOnHMqgQGUFuhWjuGPcz+1IzmHp3d0u0xhTB12T7CnCfiNgKfOVMzRrVGDMyjsysbPYfTCUzK5tH7htM3MzVHDyaxfS4HnRvXjvUYRoT9gobQfZMgU1tgPUi8hVwsMA+VdWn/R2cCQ+9enRg/uQxJKccIkMqMWLWao5m5TIzLpb2jWuGOjxjSoXC+myf9LK9lYdtCliyLcNq1qjG/gwYOj6enDxl1rBY2jasEeqwjCk1ChtBFk7rk5kQ2/TbEe6cEA8Is4fH0vrM6qEOyZhSxRKqKdK6Pan0HfczEWKJ1pjTZSs1mEKtTjrEgIlLqFoxkpnDYmlWt2qoQzKmVPJ1pYY8Ecn18sgRkRQR+UpErgp0wCZ4lv/6O3eOT6B6dAXmjOhpidaYEvC1G+FZYBewH5gCvABMdV8nAdNxVnL4r4hcfzqBiMhtIrLOTewxhZS7WkQ2icgWEXnsdOoyRVuy/SADJiRQp1pF3h/Rk7NrVwl1SMaUar52I2QA24FrVDXj+EYRqQz8FyfpdgHmA08An51GLGuBm4F3vRVw7/N9E7gSJ8kvFZF5qrr+NOozXvy05QBDpybSoFY0s4bFcmaNU+YdMsYUk68t23uAV/InWgBVPYYz4OEeVc0DJgAdPLy/SKq6QVU3FVGsO7BFVbepahYwG7jhdOozni3+ZT9Dpizl7NqVmTO8pyVaY/zE12RbH4jysq8iUMd9fgDPs4L5SyOc7ozjktxtHonIcBFJFJHE/fv3BzCssuHrjfuIm5pIi3rVmDUslnrVK4U6JGPKDF+TbSIwWkROmg1aRBriDGZIdDc1BfZ4O4iILBSRtR4evrZOvU3v6JGqjlPVGFWNqVfP2+LABuDztb8xYvoy2jSozqxhPahTzRKtMf7ka5/tQ8AiYLuI/Awk47R2ewLpwF1uuZbATG8HUdUrTj9UwGnJ5l/QqjGFJHfjm89W7+Gh2Svp0LgmU+/uTo1obx9ijDGny6eWraoux0mkLwN5QHv367+AVqq60i33VIDnSFgKtBKR5iJSEegLzAtgfWXeRyuSeHDWCro0qcX0oT0s0RoTID4PalDVFJw7DQLCXTr9DZxbyOaLyEpV7e12VUxQ1WtVNUdE7ge+ACKBSaq6LlAxlXXvJ+7ibx+sJrZ5HSYOjqFKRRvjYkyghM1fl6p+BHzkYfse4Np8rxcAC4IYWpk0I2Enoz5aS9fG1XjllvMs0RoTYIVNsfg1cK+qbnSfF0ZV9XL/hmYCZcqP2xn96Xqijyaze9EX3PrNB6esK2aM8a/C+mzzX/mPcF97e9iENqXEuMVbnUSbto+GB9ZR74zqp6wrZozxv8KmWLws3/NLgxKNCag3v9nC2C82cUmLmmxa8DlVazvz0eZfV8zTMuXGmJKzFmk5oKq88tUvjP1iEzd1bsTLt3ekQqScsq5Y/Tq1QhypMWWXz8lWRBqJyMvuiKztInK+u/1hEekRuBBNSagqL36xidcWbea2ro156baO1KlV/ZR1xcaMjLNWrTEB5NMlaBFpB3wP5AI/A51xhumCM2qsO9A/EAGa06eqPDd/AxN/2E7/Hk147obziYhwuuLzrytWv04tS7TGBJiv9/v8C9gA9MaZASz/suY/4Uy5aMJIXp4y+tN1TPt5J4MvaMbTf2yLyMmjnWvWqGZJ1pgg8TXZXgT0U9U0D8uZ7wPO8m9YpiTy8pRRH69h1pJdDO/VgsevaXNKojXGBJevyTavkH11gWN+iMX4QW6eMnLuaj5YnsT9l7XkL1e1tkRrTBjw9QLZEmCIl323Az/6JxxTEjm5efz5/ZV8sDyJR65ozV97n2uJ1pgw4WvL9llgoYh8iTOrlwJXiMhDwE1ArwDFZ3yUnZvHQ7NXsGDNb4y8+lzuvbRlqEMyxuTj66xf3wE3As2BSTijxp4HLgZuVNWEgEVoipSZk8uf3lvOgjW/8dcrzuHKptE2GsyYMFOcWb/m48zG1RJnLtsUH5axMQGWkZ3LPe8t49tN+xnQoRaz336LGbl5REZG2HwHxoQRry1bEWnrabuqblHVnyzRht6xrFzipiby3S/7eeqa1nzzwRwqVYyibu2aNt+BMWGmsG6EtSKSLCIfiMhDItJZ7GpL2DiamcOQKUv4cesBxt7akYubVCY3N48qlZ0FGqtUjiYnN4/klEMhjtQYA4V3IzyA0yd7Mc5FMAUOi8iPwGLgOyBRVXMDHqU5yZGMbIZMXsqKXYd49Y5O3NCpEamH04iMjCD9WAZVKkfbfAfGhBmvLVtVfVNV+6pqI6A1MBxnCZq2OBfHfgIOichXIvJkUKI1pKZnc9fEJazcdYg3+nXmhk7O4sI1a1Sz+Q6MCWOi6nVxWu9vEmkEXIJzj+0fAVS14MiysBITE6OJiYlFFwxjvx/NYsCkBDb9doQ3+3fhqnanDtxLPZxm8x0YE0QiskxVY4oqV6y1UESkCc49tccfrYE0nMlpTAAdSMvkrgkJbDtwlHEDYrisTX2P5Wy+A2PCU6HJVkRac3JybYKzjPkPwNvu1xWqWthwXlNCyYczuHNCArt+T2fioBgublUv1CEZY4qpsDXI9uLcT7sVZzjuM8D3qro5SLEZ4LfUDPqPj+e3wxlMHtydnufUCXVIxpjTUFjL9kwgHWdqxXXuY3swgjKOpN/T6T8+gYNHs5h2d3dimtUOdUjGmNNU2H22ZwGDgZ3AXTit20MiskhERovI5SJSxV+BiMhtIrJORPJExGtns4jsEJE1IrJSREr3Fa9C/JqSzh3vxvN7ehbTh1qiNaa0K2zBx2RgrvtARGri9NteDFwNPOFuXwEsVtVHSxjLWuBm4F0fyl6mqgdKWF/Y2n7gKP3Hx3MsO5dZw2I5v1HNUIdkjCmh4syNkAp86j4QkVjgMZxbv2KAEiVbVd3gHrckhyn1tiQfod/4BHLzlJlxsbRtWCPUIRlj/MDXNcgigC78766Ei4AzcGb/SsYZURYsCnwpIgq8q6rjvBUUkeE4gzFo0qRJkMI7fRt/O8yd4xMQEWYPj6X1mdVDHZIxxk8KuxvhIv6XXHsC1XCSaxLwOe6Q3eJMSCMiC/G8hM4oVf3Ex8NcqKp7RKQ+8JWIbFRVj8neTcTjwBnU4GucobB2dyoDJiZQsUIEM4fFck49u1fWmLKksJbt8QS2DaffdjFO3+xp35Ggqlec7nvzHWOP+zVZRD7CWdk3mC1rv1u16xADJiZQPTqKmcN60LRO1VCHZIzxs8KSbX+cluveYAVTFBGpCkSo6hH3+VU49/+WWst2HmTwpKXUqhrFzLhYzq7ttxs8jDFhpLCJaGYHM9GKyE0ikoTTZTFfRL5wtzcUkQVusTOBH0RkFc66aPNV9fNgxehvCdtSGDBxCXWrV2LO8J6WaI0pw4o1N0IgqepHwEcetu8BrnWfbwM6Bjm0gPhxywGGTl1Ko1qVmTUslvo1okMdkjEmgMIm2ZYn325KZsT0ZTSrU5X34npQr3qlUIdkjAkwS7ZBtnD9Pu6dsZyW9avxXlwPaletGOqQjDFB4NPqusY/Pl+7l3veW0abBtWZOcwSrTHlibVsg2Teqj08MmclHRvXZMrd3akRHRXqkIwxQWTJNgg+WJbEo3NXEdOsNpMGd6NaJfu2G1Pe2F99gM1Z+iuPfbiGni3qMGFQDFUq2rfcmPLI/vIDaHr8Tv7+8Vp6ta7HuAFdiY4K62XajDEBZMk2QCb9sJ1nPlvP5W3q8+adXSzRGlPOWbINgHe+28rz/93I1e3O4vV+nalYwW76MKa8s2TrZ68v2szLX/3C9R0a8ModnYiKtERrjLFk6zeqystf/cIbX2/h5s6NePHWDlSwRGuMcVmy9QNV5fnPN/Lud9u4PaYx/7y5A5ER5XvFCWPMySzZlpCq8sxn65n84w7uim3CM33OJ8ISrTGmAEu2JZCXpzw1by3vxf/KkAub8dT1bcv9GmrGGM8s2Z6mvDzl8Q/XMCdxFyN6teCxa9pYojXGeGXJ9jTk5imPzl3Fh8t388AfWvLnK1tbojXGFMqSbTFl5+bx5/dX8emqPfz5ytY8eHmrUIdkjCkFLNkWQ1ZOHg/OWsHn637jsWvacM8l54Q6JGNMKWHJ1keZObncN2M5Czck8/fr2zL0ouahDskYU4pYsvVBRnYuI6Yv47tf9vPsDe0Y0LNZqEMyxpQylmyLkJ6Vw7Bpify0NYXnb25P3+5NQh2SMaYUsmRbiLTMHO6espTEHQd56daO3NK1cahDMsaUUmEzeF9ExorIRhFZLSIfiUgtL+WuFpFNIrJFRB4LVDyHM7IZODGBZTt/59W+nS3RGmNKJGySLfAVcL6qdgB+AR4vWEBEIoE3gWuAtkA/EWnr70BS07MZMCGB1Ump/LtfZ/p0bOjvKowx5UzYJFtV/VJVc9yX8YCnpmR3YIuqblPVLGA2cIO/Y3n9681s2HuEt+/qyjXtG/j78MaYcihc+2zvBuZ42N4I2JXvdRLQw9+VP9r7XK5tfxZdm9b296GNMeVUUJOtiCwEzvKwa5SqfuKWGQXkADM8HcLDNi2kvuHAcIAmTXy/iyA6KtISrTHGr4KabFX1isL2i8gg4HrgclX1lESTgLPzvW4M7CmkvnHAOICYmBivSdkYYwItbPpsReRq4G9AH1VN91JsKdBKRJqLSEWgLzAvWDEaY8zpCptkC/wbqA58JSIrReQdABFpKCILANwLaPcDXwAbgPdVdV2oAjbGGF+FzQUyVW3pZfse4Np8rxcAC4IVlzHG+EM4tWyNMabMsmRrjDFBYMnWGGOCwJKtMcYEgSVbY4wJAku2xhgTBOJ5oFbZIyL7gZ3FeEtd4ECAwrH6w7fu8l5/eT73062/qarWK6pQuUm2xSUiiaoaY/WXr7rLe/3l+dwDXb91IxhjTBBYsjXGmCCwZOvdOKu/XNZd3usvz+ce0Pqtz9YYY4LAWrbGGBMElmxdoV7dV0RuE5F1IpInIl6vhorIDhFZ405DmRiC+v1+/iJSW0S+EpHN7tczvJTLdc97pYiUeB7jos5FRCqJyBx3f4KINCtpncWoe7CI7M93vnH+qts9/iQRSRaRtV72i4i87sa3WkS6BLHuS0UkNd+5P+Wvut3jny0i34jIBvd3/iEPZfx//qpqD6cr5Sqggvv8BeAFD2Uiga1AC6AisApo66f6zwPOBb4FYgoptwOoG4DzL7L+QJ0/8CLwmPv8MU/fe3dfmh/Pt8hzAe4F3nGf9wXmBLHuwcC//f1zznf8XkAXYK2X/dcC/8VZiioWSAhi3ZcCnwXw3BsAXdzn1XFW8y74/ff7+VvL1qUhXt1XVTeo6iZ/HCuA9Qfq/G8AprrPpwI3+uGYRfHlXPLHNRe4XEQ8rYMXiLoDSlUXAwcLKXIDME0d8UAtEfHLUtM+1B1QqrpXVZe7z4/gLETQqEAxv5+/JVvP7sb5r1aQp9V9C/6QAk2BL0VkmbugZTAF6vzPVNW94PwhAPW9lIsWkUQRiReRkiZkX87lRBn3H3EqUKeE9fpaN8At7kfYuSJytof9gRTq3/WeIrJKRP4rIu0CVYnbNdQZSCiwy+/nHzYrNQRDsFf3PZ36fXChqu4Rkfo4SwhtdFsKwaj/tM+/sLp9eb+riXvuLYCvRWSNqm4txvtPCsnDtoLnUqKfdwnr/hSYpaqZInIPTgv7D36o21eBOndfLMcZApsmItcCHwOt/F2JiFQDPgAeVtXDBXd7eEuJzr9cJVsN8uq+xa3fx2Pscb8mi8hHOB9JfUq2fqj/tM+/sLpFZJ+INFDVve5HtWQvxzh+7ttE5FucFsnpJltfzuV4mSQRqQDUxD8ff4usW1VT8r0cj3MdIZhK9LteEvkTn6ouEJG3RKSuqvptzgQRicJJtDNU9UMPRfx+/taN4JJSsLqviFQVkerHn+Nc1PN4RTdAAnX+84BB7vNBwCmtbBE5Q0Qquc/rAhcC60tQpy/nkj+uW4GvvfwT9nvdBfoH++D0KwbTPGCge1U+Fkg93tUTaCJy1vG+cRHpjpOnUgp/V7GOL8BEYIOqvuylmP/PP1BX/ErbA9iC00ez0n0cvwrdEFiQr9y1OFcvt+J8/PZX/Tfh/DfNBPYBXxSsH+fq9Sr3sS7Y9Qfq/HH6QRcBm92vtd3tMcAE9/kFwBr33NcAQ/1Q7ynnAjyD8w8XIBr4j/u7sQRo4cfvd1F1/9P9Ga8CvgHa+Pn3fRawF8h2f+5DgXuAe9z9ArzpxreGQu6QCUDd9+c793jgAj+f+0U4XQKr8/29Xxvo87cRZMYYEwTWjWCMMUFgydYYY4LAkq0xxgSBJVtjjAkCS7bGGBMElmzDnDv7k4pISw/7Krj7Rp/GcUeLyGndiiIi34rIDz6Uu1FE/lzMY3cVkXQR8XlopPs9urs49fhTSb6Xp1HXFBHZEYy6CtR70jmKSC13W7FnwxKRR9xhyOUq/5SrkzUnmQD0DHAdNwLFSrbAWGCSqu4uxnsG48xnYQKn4O9LLeBpnNm7iusdnPkvBhVVsCyxZFtOqWqSOrMZhQ23lXQZ8HaoYwkVEYny08xifuXP3xdVPQZMA/7qj+OVFpZsyyB3GOgMcSafznQnYL6pQJlTPvqKSD0RmSUih0XkdxGZLCJ93K6KSz3Uc4WILHc/9q/NPxOXiEzBabk0ct+vPnz8HQasVtV1BerpLyIrRCRNnEml14jICHfft8AlwIX56vk23/m8KyK/uDHuEpGZBbsojn8vRKSViMx369kpIk8V/KgrIp1F5HsRyRCR3SLydzxMWiIi94vIzyJyUEQOiTNT2XUFyjRz671XRF4UkT04I/hqufsvd7+/GSKy9fg5FyXfcQcX2H5pwZ/l8S6hwn6W+b9Hx48PbHd3jc/3fR/s7u8tIj+5P6s0cSZJLzgB+GygrYhc4Ms5lQXlaiKaUi5SnMlQTtpWsJA4U/El4Ezm8giwH7gD+EBEblTVwuYy+BBoDzyOM0T1FuANL2XPAV7DGVZ6APgLMFdE2qjqFuBZoB7QDWdsPziJpDBXA/MLnM9FwHvA68CjOA2ENrgJCWeC7/dwvhfHk9HxiUxqAxnu+ezHGXr8F+BHN86MAvV/BEwGXgH+CPwDZwj3ZDeWusDXwG84/0gy3ZiaeDiXZjgfvXfg/J39EfhMRK5V1YLTd47CmS9huHseGSJyHrAASMSZO6ESMBqoBuR6qK8kivpZFrQXuBnn9+Wf/G9eh63izMg2D2f+32eALJwZu1oUOMZKnJ/T1cBPfj2bcOXPMcf28P8Dpz9Si3iMzld+Ik5iqVPgOF8BK/O9Hu38+E+8vso91u0F3jfP3X5pvm3f4oxrb5VvW32cJPBEvm1TgCQfz/NMt55hBbb/FThYxHu/BX7woY5InJmcFLip4PcCGFKg/Brgy3yv/w8neTTJt60qToLSQuqNwEm4XwKf5NvezK13Oe7iq/n2zXCPWzXftrPd+ncUcZ7Hjzu4wPZLS/CzLPj7cryOuAJ13Opur+HDz+P7/N/fsv6wboTS4yacVmL+R6yHclfjtIhSxblboYLbIv4C6CgiNbwcPxbnD+yjAtvneim/WVU3H3+hqsk4rWlPrTxfNGTYIXUAAASlSURBVHS/7i+wfSlwhoi8JyLXi5e14bwRkT+JMwl1Gs48xb+6u871UHx+gddrOfl8egLxqnr8GKjqUZy5ZwvW21VEPhORfW692cCVXur9WN3sU6CuBe7xj9e1C/jRw/tLyp8/y5U45zpbRG4VZ95lb45/2igXLNmWHmtVNTH/A1jmoVx9YCDOL3z+x1h3v7eVBhoAv6tqdoHt+7yU9zSvaybOTFmn4/j7TupqUNXvgNtwWnUfAftFZKGIdCjqgCLyAPAWsBDnY293/vcPylOcBc+p4Pk0wPP346RtblfOIpxujAdwZizrBnzupV5PU/f5VJef+O1nqU63Q2+c3DId+E2cxTIv8VD8GFC5uHWUVtZnW/ak4Hw88zbZtLcJkPfitCCjCiTcM/0ZXCGOz1d6ysq6qjoXpw+xGs5H4ReAz0WksarmFXLMvsAiVf3L/7d37qBRRUEY/qaJkoBisFBQTCxSiVpYCHaxEUMKhaggFqKFWvhoVATFBAmG+CoiEgmCokWsfYQYErRRWyUKYmEhimAjKhqbsfjvxs31brJu1htZ54NAOHv3nLM3m7lz/plzptBgZs2zmON7su9Hum0TOmh8m7u/LRq7vkS/WTm65Y6VRUGLrku1V6Okz4y4+xgwZjp/eAPSbu+aWZNPPQC8EUkl/wXh2dYeQ8BqYDztCSc/pYJUT5CmuSXV3jGLuUxQvufyBhmJdCBlEnf/4u53gH7k+RWMR6lx6pFXX8zuMueTxWNgvRXVAzMd4t6eMS7FY5tZCzI8fzLW5qT/Qh/Ly+zjA7onq1LtbRnXVkrhe1Ty7+vuE+4+iqonNwDpB10zMGdFTvMmPNva4xQ66PqRmfUhI7YI/eOtdPfM5H93HzbtCruaRN1fo2DHmuSS6TzIUrwAGs1sP4qqf3f35yXG/2FmT9FSfxIz60Le3BjyypcBB1Gwr6DvvgAOmNl2dNjzZ1el4CHgmJmdQPekNflMlXIRZT8Mm3btFbIRvqWuG0E67Q0zO48eDJ1ILy7XwTmDHnTDZtaLvNROypAR3N3NbBDYY2avkEFrQ6uCavEBrUZ2mNkz4CtKB+tApcrvoUyOxSgb5B1FVUUS7b0FOFfFOf3ThGdbYyTBm3XolPtulIVwBeWijs7w9q3IQPUAt5FmdzJ57VMF0xlA+ZTdyNj9FkhKMQi0FntzKI2tCRm6B8ncHjLVS+tBGukACqj1J+1dye9HkN67GumJFZEsgTeipe91dJL/EHAtdd04sBNYgbI5jgLHKbNWXNLHS1Q9oB7dl7PAJfQ5y+EQSs06nbx/PtKPq0Ii3+xFD/IRdN/b0feuAaWEDQN9yAi3ujYzFGhDmRXpgGzNEpUagmkxs8so/axxGgmiWmMtQGVSDrj7zb85VjC3mNl94KO775rrueRFyAjBJMkOoIWo/lMdCvTsA3r/tqEFVVU1sx7gqJndykiHCmoAM1uLtmWnNeWaJoxtUMxX4DDaUTQPLf9O8CttLA8uoEDdUnIqnR3kzhK0gSRrd1rNEjJCEARBDkSALAiCIAfC2AZBEORAGNsgCIIcCGMbBEGQA2FsgyAIciCMbRAEQQ78BMHPTzBoZasGAAAAAElFTkSuQmCC\n",
"text/plain": [
"
"
]
},
"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",
"text/plain": [
"
"
]
},
"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",
"
Date
Height (cm)
Weight (kg)
\n",
"
\n",
" \n",
" \n",
"
\n",
"
2017-07-28
53.3
4.204
\n",
"
\n",
"
\n",
"
2017-08-07
54.6
4.65
\n",
"
\n",
"
\n",
"
2017-08-25
55.9
5.425
\n",
"
\n",
"
\n",
"
2017-09-25
61
6.41
\n",
"
\n",
"
\n",
"
2017-11-28
63.5
7.985
\n",
"
\n",
"
\n",
"
2018-01-26
67.3
9.125
\n",
"
\n",
"
\n",
"
2018-04-27
71.1
10.39
\n",
"
\n",
"
\n",
"
2018-07-30
74.9
10.785
\n",
"
\n",
" \n",
"
"
],
"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",
"
Date
Height (cm)
Weight (kg)
Days since birth
\n",
"
\n",
" \n",
" \n",
"
\n",
"
2017-07-28
53.3
4.204
4
\n",
"
\n",
"
\n",
"
2017-08-07
54.6
4.65
14
\n",
"
\n",
"
\n",
"
2017-08-25
55.9
5.425
32
\n",
"
\n",
"
\n",
"
2017-09-25
61
6.41
63
\n",
"
\n",
"
\n",
"
2017-11-28
63.5
7.985
127
\n",
"
\n",
"
\n",
"
2018-01-26
67.3
9.125
186
\n",
"
\n",
"
\n",
"
2018-04-27
71.1
10.39
277
\n",
"
\n",
"
\n",
"
2018-07-30
74.9
10.785
371
\n",
"
\n",
" \n",
"
"
],
"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": {
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\n",
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