For testing general linear hypotheses in multiple regression models. it is shown that non-stochastically shrunken ridge estimators yield the same centralF-ratios andt-statistics as does the least squares estimator. Thus although ridge regression does produce biased point estimates which deviate from the least squares solution, ridge techniques do not generally yield “new” normal theory statistical inferences: in particular, ridging does not necessarily produce “shifted” confidence regions. A concept, the ASSOCIATFD PROBABILITY of a ridge estimate, is defined using the usual, hyperellipsoidal confidence region centered at the least squares estimator, and it is argued that ridge estimates are of relatively little interest when they are so “extreme” that they lie outside of the least squares region of say 90 percent confidence.