A major publishing company would like to develop an equation that will help it in determining the cost of books that it publishes. It has a sample of 207 books that have been published recently. Of the 207 books in the sample, 83 are hardcover and 124 are softcover. Hardcover books obviously are priced at a premium, so some adjustment for this will need to be made. Data on the following variables are available: . y = the cost of producing the book (COST) . 1 = the number of pages in the book (PAGES) . 12 = 1 if the book is softcover and 0 if it is hardcover (SOFTCOVER) Consider the interaction model: COST = Bo + BIPAGES + B2SOFTCOVER + BPSOFT where PSOFT = PAGES * SOFTCOVER is the interaction variable. Fit this model to data using SAS and obtain the output as follows: Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr>F Model 3 6594.91911 Error 203 4201.12386 Corrected Total 206 10796 Root MSE 4.54920 R-Square 0.6109 Dependent Mean 20.11599 Adj R-Sq 0.6051 Coeff Var 22.61483 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr> () Intercept 19.50043 0.91366 21.34 PAGES 0.01647 0.00273 6.02 SOFTCOVER -7.92117 1.38692 5.71 PSOFT -0.00954 0.00407 -2.34 Answer the following questions using the SAS output. Note that F(0.05,2,203) = 3.04, F(0.05,3,203) = 2.65, t(0.025,203) = 1.97 and t(0.05.203) = 1.65. (a). (4 points) Report the estimated regression equation.(b). (6 points) Write out the estimated regression equation between COST and PAGES for hard- cover and softcover books separately. (c). (10 points) Is there any difference between the regression lines for hardcover and softcover books? State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a = 0.05. The ANOVA table for the model COST = Bo + BIPAGES below: Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr>F Model 1 684.72537 684.72537 13.88 0.0003 Error 205 10111 49.32350 Corrected Total 206 10796 (d). (10 points) Is there a difference between the slopes of the regression lines representing the relationship between COST and PAGES for hardcover and softcover books? State the hy- potheses to be tested, the decision rule, the test statistic, and your decision. Use o = 0.05