Question

You have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations. Suppose you are interested in testing that X2, X3, and X4 are jointly significant at 5% significance level. The appropriate F test has _____________ numerator degrees of freedom.

Answer 1

You could think the structural model of the form:

Now there are 46 observations. You want to test the following null hypothesis:

Against the alternative that any one of the equality doesn't hold.

For doing this you need to calculate the residual sum of squares (RSS) for the model before putting this restriction and after putting this restriction.

Accordingly we will derive the values (value of RSS for the restricted model) and (value of RSS for the unrestricted model).

The required F statistic will be calculated as:

Where q is the number of restrictions =3

n is the sample size =46

k is number of explanatory variables=6

Thus, F has 3 numerator degrees of freedom.