Backward Stepwise Regression. Verify the claim that for the case of AIC selection, step (b)

of the algorithmcan be implemented by calculating the classical (homoskedastic) t-ratio for each active regressor and find the regressor with the smallest absolute t-ratio.

Hint: Use the relationship between likelihood ratio and F statistics and the equality between F and Wald statistics to show that for tests on one coefficient the smallest change in the AIC is identical to identifying the smallest squared t statistic.