1. Say we have two quantitive explanatory variables, X, and X2, and a quantitative continuous response Y. Say we have two population models. Model 1 is: Yi = Bo + BIXli + B2X2+ er Model 2 is: Yi = Bo + BIXni + B2X2 + BaXliXai + ci. a. Is Model 1 nested under Model 2? Yes or no. b. In Model 1, what would a null hypothesis of , =0 imply with how X, affects the response? c. In Model 2, if B3 is not equal to 0, what does that imply with how X] is affecting Y. Explain in a sentence or two. d. In Model 2, given that X] 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 be the null and alternative be? c. In Model 2, if you want to test if X] and X2 have any association with Y, what would the null and alternative be? f. In Model 2, now say X2 is a categorical yeso covariate (0 for no and 1 for yes). Interpret the effect of Xi on the response variable Y