Set up tests of whether a multiple regression's coefficients, taken two or more at a time, are jointly significant and explain what the outcome of such joint tests tells you

A single coefficient is tested with t = (estimate − hypothesised value) ÷ standard error, with n − k − 1 degrees of freedom, and the hypothesised value need not be zero. To test whether a group of q coefficients are all zero, compare an unrestricted model with a restricted one that drops them: F = [(SSE restricted − SSE unrestricted) ÷ q] ÷ [SSE unrestricted ÷ (n − k − 1)], where k counts the unrestricted model's variables. Reject when F exceeds the critical value with q and n − k − 1 degrees of freedom. Rejection means at least one of the coefficients is non-zero, not all of them. A common slip is to use the restricted model's SSE in the denominator.