Forward search added-variable t-tests and the effect of masked outliers on model selection

Monitoring the t-tests for individual regression coefficients in ‘forward’ search fails to identify the importance of observations to the significance of the individual regressors. This failure is due to the ordering of the data by the search. We introduce an added-variable test which has the desired properties since the projection leading to residuals destroys the effect of the ordering.An example illustrates the effect of several masked outliers on model selection. Comments are given on the related test for response transformations.