Even though you have selected a best model using appropriate covariate selection techniques, it is still necessary to check that the model fits well. Diagnostics provide us with a set of tools to do this.
Diagnostics check that key assumptions made when fitting the linear regression model are in fact satisfied.
QQ and PP plots can be used to check that the estimated residuals are approximately normally distributed.
Plots of estimated residuals vs. fitted values, and estimated residuals vs. explanatory variables, should also be made, to check that these are independent.
The hat matrix
can be used to prove independence of estimated residuals and fitted values, and of estimated residuals and explanatory variables.
In addition the data should be checked for outliers and points of strong influence.
Outlier: a data point which is unusual compared to the rest of the sample. It usually has a very large studentised residual.
Influential observation: makes a larger than expected contribution to the estimate of . It will have a large value of Cook’s distance.