Shift outliers in linear inference

Shifts in responses typically are obscured to users, so that regression proceeds as if unshifted. At issue is the infusion of such shifts into the classical analysis. On projecting outliers into the “Regressor” and “Error” spaces of a model, our findings are that shifts in responses account for shifts in the OLS solutions and for inflated residuals. These in turn impact estimation, prediction, and hypothesis tests, all of vital interest to users, and all documented. Tools for identifying shifted responses are given. Case studies illustrate effects of such shifts, to include a reexamination of studies from the literature. AMS Subject Classification: 62J05 and 62J20