ABSTRACT
One important inferential task in regression analysis is to assess where lies the true model x′β from which the observed data have been generated.
From Chapter 1, the unknown coefficients β can be estimated by βˆ given in (1.3). So the true regression model x′β is somewhere about x′βˆ. Furthermore, a 1−α confidence region for β is given in Theorem 1.2 by
{ β :
(β− βˆ)′(X′X)(β− βˆ) (p+1) ‖ Y −Xβˆ ‖2 /(n− p−1) ≤ f
} . (2.1)
This provides information on where the true model x′β can be: x′β is a plausible model if and only if β is contained in the confidence region (2.1). Equivalently one can test
H0 : β = β0 against Ha : β = β0; (2.2)
H0 is rejected if and only if (β0− βˆ)′(X′X)(β0− βˆ)
(p+1) ‖ Y −Xβˆ ‖2 /(n− p−1) > f α p+1,n−p−1.
