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RegressionChart.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Grouped Regression Plots in Altair"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from altair import *\n",
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def make_data(N, rseed=42):\n",
" rng = np.random.RandomState(rseed)\n",
" x = 100 * rng.rand(N)\n",
" c = rng.randint(0, 3, N)\n",
" y = (c - 2) * x + (10 + 0.2 * x) * rng.randn(N)\n",
" return pd.DataFrame({'x': x, 'y': y, 'c': c})"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>c</th>\n",
" <th>x</th>\n",
" <th>y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>2</td>\n",
" <td>37.454012</td>\n",
" <td>29.849890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>2</td>\n",
" <td>95.071431</td>\n",
" <td>25.346573</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0</td>\n",
" <td>73.199394</td>\n",
" <td>-146.173473</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0</td>\n",
" <td>59.865848</td>\n",
" <td>-127.763754</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1</td>\n",
" <td>15.601864</td>\n",
" <td>-7.085604</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" c x y\n",
"0 2 37.454012 29.849890\n",
"1 2 95.071431 25.346573\n",
"2 0 73.199394 -146.173473\n",
"3 0 59.865848 -127.763754\n",
"4 1 15.601864 -7.085604"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = make_data(100)\n",
"data.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Specializing ``Chart``\n",
"\n",
"Here I'll specialize ``Chart`` and add a method which computes a regression plot:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import altair\n",
"from copy import deepcopy\n",
"\n",
"\n",
"def linear_regression(x, y):\n",
" \"\"\"Return the linear regression of y at x\"\"\"\n",
" p = np.polyfit(x, y, 1)\n",
" return np.polyval(p, x)\n",
"\n",
"\n",
"class Chart(altair.Chart):\n",
" @staticmethod\n",
" def _add_regression_column(group, regression_func, x, y, yfit):\n",
" group[yfit] = regression_func(group[x], group[y])\n",
" return group\n",
" \n",
" def regression_plot(self, func=linear_regression):\n",
" if not isinstance(self.data, pd.DataFrame):\n",
" raise ValueError(\"regress() requires data to be specified as pandas DataFrame\")\n",
"\n",
" points = self.mark_point()\n",
" \n",
" encoding = points.encoding.to_dict()\n",
" if any(enc.get('bin', None) for enc in encoding.values()):\n",
" raise ValueError(\"regress() cannot handle binned variables\")\n",
"\n",
" group_cols = [enc['field'] for key, enc in encoding.items()\n",
" if key not in ['x', 'y']]\n",
" x = encoding['x']['field']\n",
" y = encoding['y']['field']\n",
" yfit = y + '_fit'\n",
"\n",
" if group_cols:\n",
" groups = self.data.groupby(group_cols)\n",
" data = groups.apply(self._add_regression_column,\n",
" regression_func=func,\n",
" x=x, y=y, yfit=yfit)\n",
" else:\n",
" data = self._add_regression_column(self.data.copy(),\n",
" regression_func=func,\n",
" x='x', y='y', yfit='y_fit')\n",
"\n",
" lines = deepcopy(self).mark_line().encode(y=yfit)\n",
" lines.data = data\n",
"\n",
" return LayeredChart(data).set_layers(points, lines)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Global Regression"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div class=\"vega-embed\" id=\"afa5fcd9-5e3b-415e-b452-4a50ce26c9b4\"></div>\n",
"\n",
"<style>\n",
".vega-embed svg, .vega-embed canvas {\n",
" border: 1px dotted gray;\n",
"}\n",
"\n",
".vega-embed .vega-actions a {\n",
" margin-right: 6px;\n",
"}\n",
"</style>\n"
]
},
"metadata": {
"jupyter-vega": "#afa5fcd9-5e3b-415e-b452-4a50ce26c9b4"
},
"output_type": "display_data"
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{
"data": {
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"
},
"metadata": {
"jupyter-vega": "#afa5fcd9-5e3b-415e-b452-4a50ce26c9b4"
},
"output_type": "display_data"
}
],
"source": [
"Chart(data).encode(\n",
" x='x',\n",
" y='y',\n",
").regression_plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Grouped Regression"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
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" border: 1px dotted gray;\n",
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"data": {
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"var selector = \"#4583effa-6ea2-4450-be65-b87cb53cc5c6\";\n",
"var type = \"vega-lite\";\n",
"\n",
"var output_area = this;\n",
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" vega.render(selector, spec, type, output_area);\n",
"}, function (err) {\n",
" if (err.requireType !== 'scripterror') {\n",
" throw(err);\n",
" }\n",
"});\n"
]
},
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"
},
"metadata": {
"jupyter-vega": "#4583effa-6ea2-4450-be65-b87cb53cc5c6"
},
"output_type": "display_data"
}
],
"source": [
"Chart(data).encode(\n",
" x='x',\n",
" y='y',\n",
" color='c:N',\n",
").regression_plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cubic Regression"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div class=\"vega-embed\" id=\"e445abc6-78a5-47fc-80e7-f14653e1acbb\"></div>\n",
"\n",
"<style>\n",
".vega-embed svg, .vega-embed canvas {\n",
" border: 1px dotted gray;\n",
"}\n",
"\n",
".vega-embed .vega-actions a {\n",
" margin-right: 6px;\n",
"}\n",
"</style>\n"
]
},
"metadata": {
"jupyter-vega": "#e445abc6-78a5-47fc-80e7-f14653e1acbb"
},
"output_type": "display_data"
},
{
"data": {
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"
},
"metadata": {
"jupyter-vega": "#e445abc6-78a5-47fc-80e7-f14653e1acbb"
},
"output_type": "display_data"
}
],
"source": [
"def cubic_regression(x, y):\n",
" p = np.polyfit(x, y, 3)\n",
" return np.polyval(p, x)\n",
"\n",
"Chart(data).encode(\n",
" x='x',\n",
" y='y',\n",
" color='c:N',\n",
").regression_plot(cubic_regression)"
]
}
],
"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": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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