Question 6 [3+2=5 points]: In a study on weight gain in rabbits, researchers randomly assigned rabbits to 1,2, or 3mg of one of dietary supplements A or B (one rabbit to each level of each supplement, which is not enough, of course). Consider the linear model Y : n + lm] + ,8ng + e, Where 1:1 is the dosage level of the supplement, and 3:2 is a dmnmy variable indicating the type of supplement used. (a) Compute the variance ination factor for variable 31. You should be able to do this completely without the use of statistical software. Explain, using the word 7'orthogonal\" Why the variance ination factor is the value computed. (b) Now suppose that the researcher used levels 1,2, and 3 for supplement A, and levels 2, 3 , and 4 for supplement B. Use software if desired. What is the variance inflation factor for variance as; in this case? Is it larger or smaller than in part (a) above? Why? (Hint: To get started with part (a), you might go ahead and use R and the vif() function. You'll have to invent a response vector 3;; try y