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Bootstrapping regression

Now let's see how bootstrapping works with regression. Bootstrapping helps estimate the uncertainty of non-standard estimators. Consider the \(R^{2}\) statistic associated with a regression. When you run a simple least squares regression, you get a value for \(R^{2}\). But let's see how can we get a 95% CI for \(R^2\).

Examine the DataFrame df with a dependent variable \(y\) and two independent variables \(X1\) and \(X2\) using df.head(). We've already fit this regression with statsmodels (sm) using:

reg_fit = sm.OLS(df['y'], df.iloc[:,1:]).fit()

Examine the result using reg_fit.summary() to find that \(R^{2}=0.3504\). Use bootstrapping to calculate the 95% CI.

Diese Übung ist Teil des Kurses

Statistical Simulation in Python

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Anleitung zur Übung

  • Draw a bootstrap sample from the original dataset using the sample() method of a pandas DataFrame. The number of rows should be the same as that of the original DataFrame.
  • Fit a regression similar to reg_fit() using sm.OLS() and extract the \(R^{2}\) statistic using the parameter rsquared.
  • Append the \(R^{2}\) to the list rsquared_boot.
  • Calculate 95% CI for rsquared_boot as r_sq_95_ci using np.percentile().

Interaktive Übung

Vervollständige den Beispielcode, um diese Übung erfolgreich abzuschließen.

rsquared_boot, coefs_boot, sims = [], [], 1000
reg_fit = sm.OLS(df['y'], df.iloc[:,1:]).fit()

# Run 1K iterations
for i in range(sims):
    # First create a bootstrap sample with replacement with n=df.shape[0]
    bootstrap = ____
    # Fit the regression and append the r square to rsquared_boot
    rsquared_boot.append(____(bootstrap['y'],bootstrap.iloc[:,1:]).fit().rsquared)

# Calculate 95% CI on rsquared_boot
r_sq_95_ci = ____
print("R Squared 95% CI = {}".format(r_sq_95_ci))
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