2. (i) Consider the linear regression model 292' = 50 +31% + 62' where E(,) = 0 and Var(i) = a2 and 61, . . . , an are uncorrelated. We would like to change the scale of our measurements for mvalues. For example, imagine 3:.- are in kilograms and we would like to write them in pounds. Therefore the regression model will be modied as follows 2% = [36 + Biw; + 61;- How do you estimate g, and B1 in terms of B0 and [31. What happens to T2. What if we change the scale of our measurements for y-values as well. Discuss and prove your claims. (ii) Generalization: Consider the regular multiple regression y = X ['3 + E where E() = 0 , 0011(6) = 021. Let A(n x n) be a known orthogonal matrix. Take Y* = Ay,X* = AX, 6* = A6. Prove a) E(*) = 0 and Cov(e*) = 02] b) Show that 5* = 6 and 23:1 63 = L1 6:2