(10] Q 7. The Tri-City Office Equipment Corporation sells an imported copier on a franchise basis and performs preventive maintenance and repair service on this copter. The users of the copiers are either training institutions that use a small model, or business firms that use a large, commercial model. An analyst at Tri-City wishes to fit a regression model including both number of copier serviced (X,) and type of the copter (X,) ma predictor variables and estimate the effect of copier model on total number of minutes spent (i.e. the service time) (Y) by the service person, where Xy = I for small size copiers and X, = 0 for the large sized ones. Assuming that normal regression models were the appropriate class of models, the analyst fitted more than one models to select the beat model. In the outputs of parts (a) and (b) in the following, the variables X1, X, XX, appear as symbols X1, X2, X1X2 respectively. Thus, X1X2 stands for the product of X, and Ka and represents their interaction. (a) By fitting a linear regression of 1' on X, and X, using R codes, a part of the output obtained was as follows. summary (la(Y - X1 + X2)) Call : In(formula = Y - X1 + X2) Coefficients: Estimate Sed. Error (Intercept) -0.8225 3.0997 X1 15. 0461 0. 4900 X2 0.7507 2.7799 Residual standard error: 9.011 on 42 degrees of freedom anova (Im (formula = Y ~ X1 + 12)) Analysis of Variance Table Response: Y Df Son Sq Mean 8q XI 76950 76960 X2 Residuals 42 3410 81 Assuming that normal regression model E(Y) - A + AX, + AX, was appropriate, 7 i. (Marks= 4jestimate the effect of copier model on mean service time with a 95%% confidence interval. it. [Marks =1) Interpret your result. (b) After examining the residuals, the analyst included an interaction term XX, in the model (thereby fitting the linear regression model with three predictors X1, X2 and XIX2). The analyst found: residual sum of squares - 3154 on 41 degrees of freedom. 1. [Marks=2] Using the outputs in parts (a) and (b), calculate the extra sum of squares associated with X1X2 given X1 and X2. ii. [Marks 3) Is there any indication that including the interaction XX, term in the model for the above part (a) would be helpful? Use a = 0.05