Testing multiple exclusion restrictions with the F test and R-squared figures Suppose your friend Jacques needs your assistance testing five exclusion restrictions in a multiple linear regression model at the 95% level. Specifically, his null hypothesis is that β6 ,..., β10 are all equal to 0, after controlling for the independent variables x1 ,..., x5. The original, unrestricted model consisted of 10 population slope parameters, β1 ,..., β10, plus an intercept parameter β0 and was estimated using a random using a random sample of 440 observations. You ask Darnell for the residual sum of squares from the restricted and restricted models. He says he lost those figures, but he did save the R- squared values. The R-squared for the unrestricted model is 0.237, while the R-squared for the restricted model is 0.234.
Since the unrestricted model hasdegrees of freedom, while the restricted model hasthe number of exclusion restrictions must be q =.
Note: The critical value for the F-distribution, at the 95% level, is 2.6.
After computing the F-statistic, you advise Darnell that because the F-statistic is he shouldthe null hypothesis that β6 ,..., β10 are jointly significant.