Shift outliers in linear inference

Shifts in responses typically are obscured from users, so that regression proceeds as if unshifted. At issue is the infusion of such shifts into classical analysis. On projecting outliers into the “Regressor” and “Error” spaces of a model, findings here are that shifts in responses may account for shifts in the OLS solutions, or for inflated residuals, or both. These in turn impact estimation, prediction, and hypothesis tests, all of vital interest to users, and all considered here. Tools for identifying shifts are given. Case studies illustrate effects of shifts on regression, to include a reexamination of studies from the literature.