Question

3. Examples - Miscellaneous, problem 6 Aа Aa Assume you have conducted two regressions using the same data. The first regression on the full model had 11 independent variables and a sample size of 220. You then run a reduced model after eliminating 6 of the independent 101,421 variables that appeared insignificant on the basis of the individual t-tests. Data for the full model: SSR and MSE 901. Data for the reduced model: SSR = 10,005. What The partial F statistic for this test is The p-value for the above partial F-test is 10.1370 is your conclusion? 16.9101 Fail to reject the null hypothe Reject the null hypothesis an Reject the null hypothesis an Fail to reject the null hypothesis and proceed using the full model ed using the reduced model 9.2237 g the reduced model 112.5649 101.4606 g the full model Now conduct the same test, this time assuming the SSR from your reduced model is 92,948 The partial F-stat and the corresponding p-value are and respectively. What is your conclusion? Fail to reject the null hypothesis and proceed using the reduced model Reject the null hypothesis and proceed using the reduced model. Fail to reject the null hypothesis and proceed using the full model. Reject the null hypothesis and proceed using the full model.

Answer 1

SSR_f = 101421

MSE_f = 901

SSR_r = 10005

n = 220

k = 11

Eliminated variables, K_d = 6

Partial F = ((SSR_f - SSR_r )/K_d ) /MSE_f

= ((101421 - 10005)/6) / 901 = 16.9101

p-value for partial f test = F.DIST.RT(16.9101, k_d, n-k-1) = F.DIST.RT(16.9101, 6 , 208) = 0.0000

Reject the null hypothesis and proceed using the full model.

----

SSR_r = 92948

Eliminated variables, K_d = 6

Partial F = ((SSR_f - SSR_r )/K_d ) /MSE_f

= ((101421 - 92948)/6) / 901 = 1.5673

p-value for partial f test = F.DIST.RT(1.5673, k_d, n-k-1) = F.DIST.RT(1.5673, 6 , 208) = 0.1582

Fail to Reject the null hypothesis and proceed using the reduced model.