A study was performed on a type of bearing to find the relationship of amount of wear y to x1 = oil viscosity and x2 = load. The following data were obtained. (From Response Surface Methodology, Myers, Montgomery, and Anderson-Cook, 2009.) Attach file is table. Note: Solve Part (a), (d), (e) using Matrix form. (a) Fit a regression model of y on x1 and x2 by the matrix form showing Y, X, A and beta_hat. (b) Estimate σ2 using multiple regression of y on x1 and x2 (M1). (c) Construct ANOVA table for model in part (a). (d) Compute 95% confidence intervals for all coefficients of the linear model. (e) Compute predicted values, a 90% confidence interval for mean wear, and a 90% prediction interval for observed wear if x1 = 20 and x2 = 1000. Test the following at the 0.05 level using F-test. (f) H0: β1 = 0 versus H1: β1 ≠ 0; (g) H0: β2 =0 versus H1: β2 ≠ 0. (h) Do you have any reason to believe that the model M1 should be changed? Why or why not? (i) Consider two other models: one is the model with interaction (M2) and the other is including the interaction term and the quadratic terms of x1 and x2, ie. y~x1+x2+x1^2+ x2^2+x1x2. Compare M1, M2, M3 using both R2 and adjust_R2.