申論題

4. (Total 40%) Consider a multiple linear regression model as

whereβo is the intercept, βjis the slope parameter associated withXj (j = 1,2, ..., k).

Given n observationson Y, ) : i = 1.2.... ,n}.Let

=0,1,... . , k, be the ordinary least squares (OLS) estimates for the parameters

of this model, denote the residual associated with the i-th observation, and t_jde-

note the t-ratio for B_j j = 0,1

(2) (10%) Under the classical linear model assumptions, please show how to con- struct the F test statistic for the joint test H₀ : β₁ = β₂.  β₃ = 0, and write down the decision rule given the significance level a.