answer all questions with explanation

(25 points) The following results were obtained from a preliminary study examining whether one of three types of diet combined with aerobic exer cise or a control would reduce cholesterol levels. Subjects who participated in the study had elevated cholesterol levels. The cholesterol levels of 16 subjects at completion of the pretrial are given in the table below. Sup- pose an effects model will be used to analyze the data where the model w111be ygjk = [J + 063? + ,63' -I- "fgj + Eijka where Z = 1,2, j = 1, 2, 3, a; and ,6,- are the main effects of Physical Activity and Diet, respectively, 7,,- is an interaction effect, and 61-3-1, is a random error term. The following table displays the data from the experiment: Diet Physical Activity Control Diet 1 Diet 2 Control 243 236 219 229 248 228 252 213 Aerobic 221 212 206 237 227 199 209 211 (a) (10 Points) The solution vector using sum to zero restrictions is A = (asblgnimh) = (225.6,8.8,9.6,3.4, 4.14.2). Use this solution vector to obtain estimates of the parameters which were in the full design matrix but not included in the reparameterized design matrix. (b) (8 Points) Calculate the means and adjusted means (least squares means) for the three levels of Diet. (0) (7 Points) Show that the difference in sample means for Physical Activity, p'l. p5,, is biased for on :12, which is why adjusted means should be used in the presence of unequal sample sizes. Note: p]; is the sample mean calculated from all observations at the ith level of Physical Activity or 1'75