Consider the regression model 91:: 519m + 323%? +53m3 +51 i=1au-an with three covariates, no intercept and independent noise variables a; N N (0,02). The following data where collected on n = 8 observations: '5 1 2 3 4 5 6 7 8 mil 1 1 1 1 1 1 1 1 $12 1 1 1 1 0 0 0 0 {121-3 0 U 1 1 0 0 1 1 ya- 0.35 1.70 2.80 1.10 1.45 2.00 0.50 3.95 Let X = [$1,392,333] 6 1R8X3 and [9' = [51, g, 53F. For your convenience, l 0 0 10.65 8 (XTX)'1=[0 71; , XTy= [2.55], SSE=1.5289 0 l l 8.35 6 3 (a) At 5% level, test whether covariate m can be dropped from the model in the presence of the other two. (10 points) (b) Build a 95% condence interval for \"(33) = mT = $1131 +m2g+m353, for a case with $1 = :03 = 0 and 222 = 1. (10 points) (c) Perform a test at level 5%, for the null hypothesis 51 = 52 = 33, using the additional sum of squares principle. (10 points)