Studentized residuals

Studentized residuals allow comparison of differences between observed and predicted target values in a regression model across different predictor values. They can also be compared against known distributions to assess the residual size.

Residuals for regression models are obtained by subtracting the target value predicted by the model from observed target value for each data record. Studentized residual is computed as the regression residual divided by its adjusted standard error.

Standard error of the residual is given by the square root of the mean square for the error source. The adjustment of the standard error consists in multiplying it by the square root of leverage value subtracted from one. Leverage value is computed based on the design matrix and design matrix row for the given data row. It adjusts the standard deviation by taking into account predictor values. As a result, all studentized residuals have the same standard deviation.