1. Say we have two quantitive explanatory variables, X1 and X2, and a quantitative continuous response Y. Say we have two population models. MdEl 1 l3: K = ,Bn +le + ngg +513. Model 2 is: Y; = n +31X1i+ ng-i +3X11'X21' + 71. a. Is Model 1 nested under Model 2'? Yes or no. h. In Model 1, what would a null hypothesis of .31 = II} irnply with how X1 affects the response? c. [11 Model 2, if' ,33 is not equal to I], what does that imply with how X1 is affecting Y. Explain in a sentence or two. d. In Model 2, given that X1 is in the model already, say you want to test if' X2 affects the response directly, and also that effect depends on the level of X1. What should he the null and alternative be? e. In Model 2, if you want to test if' X1 and K; have any association with Y, what would the null and alternative he? f. In Model 2, now say X2 is a categorical yes ,fno covariate {D for no and 1 for yes}. Interpret the effect of' X1 on the response variable Y