Joint hypothesis test

PrepNuggets

LEVEL II

A joint hypothesis test is an F-test to evaluate nested models, which consist of a full or unrestricted model, and a restricted model. The F-statistic is calculated using the formula shown. The null hypothesis would be that all coefficients of the excluded variables are equal to zero, and the null that at least one of the excluded coefficients is not equal to zero. Likewise, we reject the null hypothesis if the F-statistic is greater than the critical value. In essence, this is a combined test for coefficients of all excluded variables.

The F-test is actually a special case of the joint hypothesis test where all independent variables are excluded. Mathematically, the F-statistic can be simplified to MSR over MSE for this special case.