Pg 144 Ch 7 - Stock and Watson - FRM Study Material

[Dr. Jayanthi Sankaran]

Hi David,

In the following:

Unrestricted regression:

TestScore = 649.6 - 0.29 x STR + 3.87 x Expn - 0.656 x PctEl (10.6)
R^2 unrestricted = 0.4366

Restricted regression, estimated by OLS is.

Test Score = 664.7 - 0.671 x PctEL, R^2 = 0.4149 (10.15)
(1.0) (.032

R^2 restricted = 0.4149

F = [(0.4366 - 0.4149)/2]/ [1 - 0.4366)/(420 - 3 - 1)] = 8.01
Because 8.01 exceeds the 1% critical value = 4.61, the hypothesis is rejected at the 1% level.

How do we calculated the 1% critical value = 4.61 with0ut information on degrees of freedom, in the exam?

Thanks!
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran

You would not be able to calculate the critical F value; rather you would need to use a (provided) lookup table. FWIW, the excel function here is =F.INV(99%, 2, 99999) = 4.605 or F.INV.RT(1%,2, 99999) where 99999 I am using as a proxy for infinite. The 2 degrees of freedom is due to the two restricted coefficients.

However, let me tell you, the testability of this is extremely low: I just don't see GARP ever quizzing candidates on the calculation/lookup of the F-statistic with (q) restrictions. I realized it is assigned but it's one of those blatantly "over-assigned" AIMs. It won't see the light of exam day, to be realistic. I hope that helps at least prevent getting bogged down in the calculations of matters that most practitioners would need to "lookup" anyways! Thanks,