Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Analysis of Residuals

The analysis of residuals is important for any regression model. While numerical analysis is more profound, practice shows that numerical tests are unsatisfactory for small samples. However, it is possible to use graphical methods for analyzing residuals. This usually gives better results, since the human brain is trained to recognize patterns.

Besides the distribution of the residuals (they have to be normally distributed), any dependence on one or more of the descriptor variables has to be detected and addressed. Plots of the residuals against the independent variable(s) usually give hints as to  whether the assumptions of a least squares regression are fulfilled (i.e. the detection of outliers, misfits, and heteroscedasticity is much easier by means of residual plots).

The following slide show displays some examples of data sets which do not fulfill these assumptions.

Last Update: 2012-10-08