This problem is meant to demonstrate again the relationship between an F-test (in this case the partial F-test) and a t-test on slope. We learned under simple regression, that the overall F-test was equivalent to the t-test on slope as far as p-values go and that the F-test statistic equalled the t-test statistic on slope squared. Here we will find the same kind of result because the partial F-test when dropping a single variable has the exact same hypothesis as the individual t-test on that dropped variable.

You worked as an intern at We Always Win Car Insurance Company last summer and noticed that individual car insurance premiums depended very much on the age of the individual, the number of traffic tickets received by the individual, whether the car was a convertible and the population density of the city in which the individual lived.

To see if your conjecture is correct, you got the following EXCEL output.

The p-value for the partial F-test when the "group" of variables you are testing is made up of the variable DENSITY is (density is the variable you remove for your partial F-test): ?

The p-value for the t-test of the individual slope coefficient for DENSITY is?