Say we have two quantitive explanatory variables, X1 and X2, and a quantitative continuous

response Y. Say we have two population models.

Model 1 is: Yi = 0 + ₁X_1i + ₂X_2i +

Model 2 is: Yi = 0 + ₁X_1i + ₂X_2i + ₃X_1iX_2i+

a. Is Model 1 nested under Model 2? Yes or no.

b. In Model 1, what would a null hypothesis of 1 = 0 imply with how X1 affects the response?

c. In Model 2, if 3 is not equal to 0, 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 be the null and

alternative be?

e. In Model 2, if you want to test if X1 and X2 have any association with Y, what would the null

and alternative be?

f. In Model 2, now say X2 is a categorical yes/no covariate (0 for no and 1 for yes). Interpret the

effect of X1 on the response variable Y