Use a = [4] The heat generated in calories per gram for a particular type of cement as a function of the quantities of three additives (X1 , X2 and X3 ) is shown in the following table Y X1 X2 X3 24.8 10 31 22.8 12 35 15.2 5 15 38.6 17 42 ONaUAWNE 17.4 8 16.3 6 29.5 12 28.8 10 43.2 18 10 36.2 23 11 11.6 16 12 42.5 20 40 Given that: 326.9 .714284 0.027295 -.0178310 -.0652843 1.587 4778.6 0338028 -.0064318 -.0411836 -2.698 X' Y = , (X'X) 1 = b = B= 11505.9 .0024052 .0039297 0.570 2407.4 .0745995 6.664 a- Write down the estimated regression function. How b2 interpreted here? b- Set up the ANOVA table. Conduct an F test to determine whether or not there is a linear association between the heat generated and the three additives; use a = 0.01. State the alternatives, decision rule, and conclusion. c- Obtain a 95% prediction interval for the heat generated with the additives X1 = 12, X2 = 20 and X3 = 8