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OLS regression tutorial with statsmodels in Python
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environment.yml
channels:
- conda-forge
dependencies:
- statsmodels
- numpy
- matplotlib
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regression_example.ipynb
{
"metadata": {
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3-final"
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Regression Tutorial\n",
"\n",
"This is a Jupyter notebook. If you open it on mybinder.org, you can play around with it in the browser freely without changing the underlying notebook. If you're already on mybinder.org, try running the code cell below!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"print(['Hello World! ']*10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports\n",
"\n",
"Imports belong at the top of your code. If you add new modules here while coding in a Jupyter notebook, make sure to re-run the cell. \n",
"\n",
"Aside: It is good practice to periodically \"Restart kernel\" and \"Run all cells\" (options at the top). This makes sure your notebook runs fresh from start to finish. Sometimes cells get moved around while you're playing in the notebook and this can cause code in those cells to be run too early or too late. Your notebook should always run from top to bottom so make sure to restart the kernal and run from the beginning often!"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import statsmodels.api as sm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Getting data\n",
"\n",
"Often the first thing you want to do is bring data into Python from some data source (text file, database, online link, etc). That usually goes here, but in this case I simulate my own data for this example. For help on importing data into Python, there is a good cheat sheet [here](https://www.datacamp.com/community/blog/importing-data-python-cheat-sheet).\n",
"\n",
"Basically this is where you wrangle your data into \"X\" and \"y\" arrays to plot / use for the regression."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# Simulate a linear relationship y = mx + b\n",
"m = 2 # Slope\n",
"b = 5 # y-intercept\n",
"X = np.linspace(-1, 1, 100) # X values\n",
"y_ideal = m * X + b # the perfect line, y=m*X+b\n",
"\n",
"# Add some Gaussian noise to simulate random observations\n",
"random_seed = np.random.seed(22) # comment this out to randomize each time\n",
"noise = np.random.normal(0, 1, 100) # Gaussian(mean, stdev, npts)\n",
"y = y_ideal + noise\n",
"\n",
"# Visualize the simulated observations\n",
"plt.plot(X, y, 'o')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Data cleaning\n",
"\n",
"Here is where you can play around with plotting the data, cleaning it to remove outliers / null values, etc. This is usually an iterative process that doesn't make it into the final notebook, expect in a few lines that clean or transform the data. These lines usually go right after the data is imported my data so that everything is nicely formatted for the analysis."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Analysis\n",
"\n",
"Let's break down the regression. Here we use a module called `statsmodels` which has documentation [here](https://www.statsmodels.org/stable/gettingstarted.html). The `statsmodels` modeule is a little overkill for our simple linear regression, but it provides a whole host of output statistics and fitting parameters so we don't have to re-invent the wheel computing each one. See the full `statsmodels` regression documentation [here](https://www.statsmodels.org/stable/regression.html).\n",
"\n",
"Statsmodels contains a function called `.OLS()` for doing Ordinary Least Squares regression. One nuance of how statemodels is set up is that it always requires at least two \"models\", in our case the \"target\" linear model, and the \"comparison\" constant model (also called the \"intercept\", this is the flat line with no slope). The constant model is the \"mean\" model, saying that we don't need a sloped line to fit this data, it's just a constant that runs through the sample mean. We can add a constant model with `sm.add_constant()`."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "[[ 1. -1. ]\n [ 1. -0.97979798]\n [ 1. -0.95959596]\n [ 1. -0.93939394]\n [ 1. -0.91919192]]\n"
}
],
"source": [
"X_ols = sm.add_constant(X)\n",
"print(X_ols[:5])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `sm.add_constant` adds a column of ones to our X data. One way to think about this is to note what happens to our linear equation when we plug in all 1's for X: \n",
"\n",
"$y = mx + b$\n",
"\n",
"$y = m(1) + b$\n",
"\n",
"$y = c$\n",
"\n",
"So now statsmodels has the input it likes of at least 2 columns, now we have to build the model (input the x and y values to OLS), and then we need to fit the model with `.fit()`."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
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"text/plain": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n OLS Regression Results \n==============================================================================\nDep. Variable: y R-squared: 0.575\nModel: OLS Adj. R-squared: 0.570\nMethod: Least Squares F-statistic: 132.5\nDate: Fri, 21 Aug 2020 Prob (F-statistic): 6.70e-20\nTime: 14:11:14 Log-Likelihood: -140.32\nNo. Observations: 100 AIC: 284.6\nDf Residuals: 98 BIC: 289.8\nDf Model: 1 \nCovariance Type: nonrobust \n==============================================================================\n coef std err t P>|t| [0.025 0.975]\n------------------------------------------------------------------------------\nconst 4.9463 0.099 49.745 0.000 4.749 5.144\nx1 1.9624 0.171 11.509 0.000 1.624 2.301\n==============================================================================\nOmnibus: 0.690 Durbin-Watson: 2.520\nProb(Omnibus): 0.708 Jarque-Bera (JB): 0.300\nSkew: -0.084 Prob(JB): 0.861\nKurtosis: 3.208 Cond. No. 1.71\n==============================================================================\n\nWarnings:\n[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n\"\"\"",
"text/html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n <th>Dep. Variable:</th> <td>y</td> <th> R-squared: </th> <td> 0.575</td>\n</tr>\n<tr>\n <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.570</td>\n</tr>\n<tr>\n <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 132.5</td>\n</tr>\n<tr>\n <th>Date:</th> <td>Fri, 21 Aug 2020</td> <th> Prob (F-statistic):</th> <td>6.70e-20</td>\n</tr>\n<tr>\n <th>Time:</th> <td>14:11:14</td> <th> Log-Likelihood: </th> <td> -140.32</td>\n</tr>\n<tr>\n <th>No. Observations:</th> <td> 100</td> <th> AIC: </th> <td> 284.6</td>\n</tr>\n<tr>\n <th>Df Residuals:</th> <td> 98</td> <th> BIC: </th> <td> 289.8</td>\n</tr>\n<tr>\n <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n</tr>\n<tr>\n <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[0.025</th> <th>0.975]</th> \n</tr>\n<tr>\n <th>const</th> <td> 4.9463</td> <td> 0.099</td> <td> 49.745</td> <td> 0.000</td> <td> 4.749</td> <td> 5.144</td>\n</tr>\n<tr>\n <th>x1</th> <td> 1.9624</td> <td> 0.171</td> <td> 11.509</td> <td> 0.000</td> <td> 1.624</td> <td> 2.301</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n <th>Omnibus:</th> <td> 0.690</td> <th> Durbin-Watson: </th> <td> 2.520</td>\n</tr>\n<tr>\n <th>Prob(Omnibus):</th> <td> 0.708</td> <th> Jarque-Bera (JB): </th> <td> 0.300</td>\n</tr>\n<tr>\n <th>Skew:</th> <td>-0.084</td> <th> Prob(JB): </th> <td> 0.861</td>\n</tr>\n<tr>\n <th>Kurtosis:</th> <td> 3.208</td> <th> Cond. No. </th> <td> 1.71</td>\n</tr>\n</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
},
"metadata": {},
"execution_count": 4
}
],
"source": [
"model = sm.OLS(y, X_ols) # note y first, then X with 2 columns\n",
"result = model.fit()\n",
"result.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This comes with a huge number of statistics, but the most important for linear regression are the R-squared value at the top and the `P>|t|` value for our `x1` model in the middle section.\n",
"\n",
"The R-squared value tells you how much variation in y is explained by X. A value of 0.641 means that 64.1% of the variation in y is explained by X.\n",
"\n",
"In the section that starts with `coef`, we see a number of columns. \n",
"\n",
"- `coef`: the coefficient (\"fit parameter\") of each model. The coef for const is the y-intercept (\"b\" in y=m*x+b), while the coef for x1 is the slope (\"m\" in y=mx+b).\n",
"- 'std err`: the standard error in each coefficient.\n",
"- `P>|t|`: the p-value for the t-test for significance of each parameter (if p < 0.05 then the parameter is significant to a 95% confidence level).\n",
"- `[0.025 0.975]`: the 95% confidence intervals (if the coef falls into the interval, it is significant to a 95% confidence level).\n",
"\n",
"\n",
"Since we see that both p-values are < 0.05 and both coefficient fall within the 95% confidence interval, we can say that the linear regression is significant to a 95% conficence level.\n",
"\n",
"We can access all of the values in this table and more directly from the `result` object. You can see a full list of things you can get out by running `dir(result)` or checking out the documentation [here](https://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.RegressionResults.html)."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "slope: m=1.962 +/- 0.171\nintercept: b=4.946 +/- 0.099\n"
}
],
"source": [
"b_coef, m_coef = result.params # params has the fit coefficients\n",
"b_err, m_err = result.bse # bse has the standard error\n",
"print(f'slope: m={m_coef:.3f} +/- {m_err:.3f}')\n",
"print(f'intercept: b={b_coef:.3f} +/- {b_err:.3f}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also get the R-squared and precise pvalue since it was too small to see in the table above. For regression, you want to check the pvalue of the x1 model which tells you if the \"slope\" model performs better than the \"constant\" model (your null hypothesis is \"The constant model performs better\" and if your p<alpha you reject the null and say \"My slope model performs better than the constant model at 1-alpha significance!\" Generally we set alpha=0.05, corresponding to 95% confidence). \n",
"\n",
"Aside: Variables be can quickly inserted into text in a \"format-string\" or \"f-string\", (put an f in front of the string like so: `f''`). Variable names in curly braces `{}` will be put into the string at that position. If that variable contains a number, you can include short format codes so that it doesn't print a million decimal points. The float formatter `f` rounds to the number of decimals (e.g. `:.3f` rounds to 3 places). The scientific notation formatter `e` takes the number of significant places and displays the number in scientific notation (e.g. `:.2e` will print a number of form 0.12e3)."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "Regression R-squared: R^2 = 0.575\nRegression p-value: p(>|t|) = 6.70e-20\n"
}
],
"source": [
"print(f'Regression R-squared: R^2 = {result.rsquared:.3f}')\n",
"print(f'Regression p-value: p(>|t|) = {result.pvalues[1]:.2e}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our p-value is < 0.05, so we can reject the null at 95% significance and say we do indeed have a line rather than a uncorrelated cluster of points. You can go back to the top, crank up the Gaussian noise and re-run the notebook until the p-value is no longer significant! Note how this also changes the R-squared value in the table above."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotting results\n",
"\n",
"Here is where you can easily spend the majority of your time: making things pretty. This [Medium article](https://towardsdatascience.com/an-introduction-to-making-scientific-publication-plots-with-python-ea19dfa7f51e) is a nice guide to ploting publication quality figures in matplotlib.\n",
"\n",
"One thing to make Python plots look more consistent and properly formatted off the bat is to use the `rcParams` feature which allows you to change the global settings of all your plots in one convenient place (see [this link](https://matplotlib.org/tutorials/introductory/customizing.html) for an exhaustive list of tunable plot params). You can also choose a style which sets a bunch of these parameters for you by default. You can find a good summary of styles [here](https://tonysyu.github.io/raw_content/matplotlib-style-gallery/gallery.html). Below we use `seaborn-paper`.\n",
"\n",
"One last note on plotting is if you know the dimensions you need your figure to be, set that explicitly with \"figsize\" first, that way you can adjust the point / font sizes accordingly and have the final figure be scaled correctly in your manuscript / presentation, etc."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"plt.style.use('seaborn-paper')\n",
"plt.rcParams.update({\n",
" 'figure.figsize': (5, 5), # Set figsize in inches\n",
" 'font.family': 'serif',\n",
" 'font.size': 12, \n",
" 'axes.titlesize': 14,\n",
" 'axes.grid': False,\n",
" 'lines.linewidth': 2\n",
"})\n",
"\n",
"# You have 3 options for plotting: quick, on a figure, on a set of axes\n",
"# These are mostly interchangeable but each gives you more control than the last\n",
"\n",
"# Quick:\n",
"# plt.plot(X, y)\n",
"\n",
"# On a figure object:\n",
"# f = plt.figure()\n",
"# f.plot(X, y)\n",
"\n",
"# On axes:\n",
"# f, ax = plt.subplots()\n",
"# ax.plot(X, y)\n",
"\n",
"# Since I often want subplots, I default to the last one for all plotting\n",
"f, ax = plt.subplots()\n",
"ax.set_title('Simulated observations')\n",
"ax.set_xlabel('X values')\n",
"ax.set_ylabel('y values')\n",
"\n",
"# Let's plot the original data points and the regression line\n",
"ax.plot(X, y, 'o')\n",
"y_regress = m_coef * X + b_coef\n",
"ax.plot(X, y_regress, '-')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also get prediction and confidence intervals from our OLS result from `statsmodels`. We first have to run `result.get_prediction()` and then choose an alpha significance level to make the intervals (confidence is 1-alpha, so alpha=0.05 corresponds to 95% confidence).\n",
"\n",
"The `predictions.conf_int()` method results 2 columns, the lower and upper confidence or prediction (set `obs=True` / `obs=False` respectively). As a quick one liner, we can do `predictions.conf_int().T` to take the transpose and save the two rows to two variables for the lower and upper array of the interval. Here we get the 95% confidence and prediction intervals and plot them on the same plot from above."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x7f979e4f8dd8>"
},
"metadata": {},
"execution_count": 8
},
{
"output_type": "display_data",
"data": {
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"predictions = result.get_prediction()\n",
"conf_low, conf_upp = predictions.conf_int(alpha=0.05, obs=True).T\n",
"pred_low, pred_upp = predictions.conf_int(alpha=0.05, obs=False).T\n",
"\n",
"# Plot setup\n",
"f, ax = plt.subplots()\n",
"ax.set_title('Simulated observations')\n",
"ax.set_xlabel('X values')\n",
"ax.set_ylabel('y values')\n",
"\n",
"# Plot the data\n",
"ax.plot(X, y, 'o', 'observations')\n",
"y_regress = m_coef * X + b_coef\n",
"ax.plot(X, y_regress, '-', label='regression')\n",
"\n",
"# Plot the intervals\n",
"ax.plot(X, conf_low, label='95% conf lower')\n",
"ax.plot(X, conf_upp, label='95% conf upper')\n",
"ax.plot(X, pred_low, label='prediction lower')\n",
"ax.plot(X, pred_upp, label='prediction upper')\n",
"ax.legend() # legend gets populated with the labels of each .plot() call"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's usually clear enough to plot the prediction and confidence intervals with the same style and not label each individually. We can do that like by specifying the same linestyle and color for each and only labelling one of the pair of lines for each interval."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x7f979e495c18>"
},
"metadata": {},
"execution_count": 9
},
{
"output_type": "display_data",
"data": {
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"predictions = result.get_prediction()\n",
"conf_low, conf_upp = predictions.conf_int(alpha=0.05, obs=True).T\n",
"pred_low, pred_upp = predictions.conf_int(alpha=0.05, obs=False).T\n",
"\n",
"# Plot setup\n",
"f, ax = plt.subplots()\n",
"ax.set_title('Simulated observations')\n",
"ax.set_xlabel('X values')\n",
"ax.set_ylabel('y values')\n",
"\n",
"# Plot the data\n",
"ax.plot(X, y, 'o', label='observations')\n",
"y_regress = m_coef * X + b_coef\n",
"ax.plot(X, y_regress, '-', label='regression')\n",
"\n",
"# Plot the intervals\n",
"ax.plot(X, conf_low, '--', color='red', label='95% conf lower')\n",
"ax.plot(X, conf_upp, '--', color='red')\n",
"ax.plot(X, pred_low, ':', color='green', label='prediction ')\n",
"ax.plot(X, pred_upp, ':', color='green')\n",
"ax.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Putting it all together\n",
"\n",
"Here's all the copy/pastable code. Feel free to play around with the different parameters!"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "Regression slope: m = 1.962 +/- 0.171\nRegression intercept: b = 4.946 +/- 0.099\nRegression R-squared: R^2 = 0.575\nRegression p-value: p(>|t|) = 6.70e-20\n"
},
{
"output_type": "execute_result",
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x7f979cb58f60>"
},
"metadata": {},
"execution_count": 11
},
{
"output_type": "display_data",
"data": {
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# Imports\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import statsmodels.api as sm\n",
"\n",
"# Simulated linear data\n",
"b = 5\n",
"X = np.linspace(-1, 1, 100)\n",
"y_ideal = m * X + b\n",
"random_seed = np.random.seed(22) \n",
"noise = np.random.normal(0, 1, 100)\n",
"y = y_ideal + noise\n",
"\n",
"# Regression\n",
"X_ols = sm.add_constant(X)\n",
"model = sm.OLS(y, X_ols)\n",
"result = model.fit()\n",
"# result.summary() # get tabulated regression results\n",
"b_coef, m_coef = result.params\n",
"b_err, m_err = result.bse\n",
"print(f'Regression slope: m = {m_coef:.3f} +/- {m_err:.3f}')\n",
"print(f'Regression intercept: b = {b_coef:.3f} +/- {b_err:.3f}')\n",
"print(f'Regression R-squared: R^2 = {result.rsquared:.3f}')\n",
"print(f'Regression p-value: p(>|t|) = {result.pvalues[1]:.2e}')\n",
"\n",
"# Plot setup\n",
"plt.style.use('seaborn-paper')\n",
"plt.rcParams.update({\n",
" 'figure.figsize': (5, 5), # Set figsize in inches\n",
" 'font.family': 'serif',\n",
" 'font.size': 12, \n",
" 'axes.titlesize': 14,\n",
" 'axes.grid': False,\n",
" 'lines.linewidth': 2\n",
"})\n",
"predictions = result.get_prediction()\n",
"conf_low, conf_upp = predictions.conf_int(alpha=0.05, obs=True).T\n",
"pred_low, pred_upp = predictions.conf_int(alpha=0.05, obs=False).T\n",
"\n",
"# Init plot and label axes\n",
"f, ax = plt.subplots()\n",
"ax.set_title('Simulated observations')\n",
"ax.set_xlabel('X values')\n",
"ax.set_ylabel('y values')\n",
"\n",
"# Plot the data\n",
"ax.plot(X, y, 'o', label='observations')\n",
"y_regress = m_coef * X + b_coef\n",
"ax.plot(X, y_regress, '-', label='regression')\n",
"\n",
"# Plot the intervals\n",
"ax.plot(X, conf_low, '--', color='red', label='95% conf lower')\n",
"ax.plot(X, conf_upp, '--', color='red')\n",
"ax.plot(X, pred_low, ':', color='green', label='prediction ')\n",
"ax.plot(X, pred_upp, ':', color='green')\n",
"ax.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Final thoughts\n",
"\n",
"This is everything you need to get linear regression going in Python. The hard part not shown here is wrangling the data into a format to drop into this framework. Often your data has null values to remove, or perhaps you need to transform it to be linear first before running the regression. For example, if you're fitting a power law (which is linear on log-log plots), you first need to take the logarithm of your x and y arrays, take the linear regression of those arrays, and finally convert the regression parameters back to linear space. In that case you also want to plot your data on log axes.\n",
"\n",
"As always, Google & StackOverflow are your friends! A lot of data scientists have been switching to Python recently, so there is a rich and active community - and many forums full of questions - dedicated to doing statistics in Python."
]
}
]
}
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