residuals

LinearModel.residuals() → DataFrame

Compute the residuals \(\epsilon\) with respect to predicted values \(\hat{y}\).

Returns

pandas.DataFrame

Returns a copy of data with 3 more columns: intercept, predicted and residuals.

Raises

ValueError

• If data is None because the property data has not been set,

• if response_variable is not a column of data,

• If a posteriors is None because the sampling has not been done yet.

Notes

Predicted values are computed at data points \(X\) using the posteriors means for each regressor’s parameter:

\[\hat{y_i} = \beta_0 + \sum_{j = 1}^{m} \beta_j x_{i,j}\]

while residuals are the difference between the observed values and the predicted values of the response_variable:

\[\epsilon_i = y_i - \hat{y_i}\]