For a two-sided F test conducted at the .05 significance level, wouldn’t the table with the right hand tail area equal to .025 be more appropriate?
For the two-sided t test, the statistic utilized is the one with .025 tail area.
Footnote 22 of the Multiple Linear Regression chapter states a one tailed test is utilized because MSR necessarily increases relative to MSE as the explanatory power of the regression increases
They’re telling you it’s a one-tailed test at 5%— put the entire 5% in the upper tail (by telling you it necessarily increases). I wouldn’t worry about the technical aspects of why, in this case, but understand how to conduct these tests properly.
F-distribution has reciprocals of right tail in the left tail and vice versa. The way the test is conducted is to have the value of the ratio always > 1 and hence we only have to look at the right tail (it would be redundant to check both tails). The critical values reported are indeed for 2.5% (in the right tail) but are reported as 5% (again because we are forcing the test as a one-tail test to avoid redundancy).