THE ANSWERS CHOSEN MAY NOT BE CORRECT

You have fit a regression model with two regressors to a data set that has $20$ observations. The total sum of squares is $1200$ and the model sum of squares is $1050.$ Suppose that you add a third regressor to the model and as a result, the model sum of squares is now $1100.$ Which of the following statements is true when testing for the improvement the new factor to the model at $=0\mathrm{.}01.$

A$.$ We need more information to tell.

B$.$ Since $F_0=8$ which is more than $F_{0\mathrm{.}01,2\mathrm{.}17}=6\mathrm{.}11$ we reject the null hypothesis and conclude the third regressor contribute significantly to the model.

C$.$ Since $F_0=58\mathrm{.}67$ which is more than $F_{0\mathrm{.}01,3\mathrm{.}16}=5\mathrm{.}29,$ we reject the null hypothesis and conclude the third regressor contribute significantly to the model.

D$.$ Since $F_0=59\mathrm{.}5$ which is more than $F_{0\mathrm{.}01,2\mathrm{.}17}=6\mathrm{.}11,$ we reject the null hypothesis and conclude the third regressor contribute significantly to the model.

E$.$ Since $F_0=8$ which is less than $F_{0\mathrm{.}01,1\mathrm{.}16}=8\mathrm{.}53,$ we fail to reject the null hypothesis and conclude the third regressor does not contribute significantly to the model.