2. Consider the following regression model as = $30 +31$n +2l'z'2 + 331% +51: 3': 1: ' " an Assume 51, - -- ,5\" are Lid and 51: ~ N(0, :72). a) For obtaining a testing statistic we can employ the Ftest for H0 : A = c. Find A and c for following hypothesis test. (i) Testing whether the third independent variable gives a signicant contribution to the model (i.e. H0 : ,63 = 0). (1i) Hf] :l = ? and g = O. b) Denote (X'X)_1 = C = (ca-j). Give the Fstatistic for the hypothesis H0 : g : 0 and 33 = U. 3. Suppose that we have two independent data sets from the same process. One was collected in the past and another was collected recently. The observations are; {(1% yi), 3' = 1: _ . _ and} and {($13 3110' 2' Z \"1 'l' 1: ' \" anl -l- n2}. Two models are postulated yt' = a0+01$i+51i=11m1n11 yi : 0+61$+h t=n1+15... a\": where n = T11 + H2. Suppose that it is of interest to test equality of the slope of the two regression lines, i.e., Hg : 0:1 2 51. We express these separate models as a single model 331 1 0 $1 U m 1 0 1'2 0 n n n n 1 al) ym : 1 0 3m 0 3 +32 X-le. yn1+1 0 1 0 $111 +1 (61