5. (40 Points) Analysis of a Pastry Sweetness Experiment: An experiment was done to assess how moisture content (4 levels) and sweetness of a pastry product (2 levels) affect a taster's rating of the product. Data-set: pastry.csv In a designed experiment, the eight possible combinations of four moisture levels and two sweetness levels are studied. Two pastries are prepared and rated for each of the eight combinations, so the total sample size is n = 16. The y-variable is the rating of the pastry. The two x-variables are moisture (x1) and sweetness (x2). The values (and sample sizes) of the x-variables were designed so that the x-variables were not correlated. a) Fit two simple linear regressions: y versus x1 and y versus x2. Write the fitted regression equations and perform hypothesis for the slopes of each model. Write your conclusions. b) Fit a Multiple linear additive regression of y versus x1 and x2. Write the fitted equation and a 95% confidence interval for the slopes. c) The estimated coefficient for Moisture is 4.425 in both the simple and the multiple regression. The estimated coefficient for Sweetness is 4.375 in both the simple and the multiple regression. This result does not generally occur. Why is it the case here? d) Calculate and interpret a 98% confidence interval for the mean response when x1=7 and x2=2. e) The researcher wants to predict the rating of a product when x1=12 and x2=6. What is your conclusion? 2A B C 1 Rating Moisture Sweetness 2 64 4 N 3 73 4 61 4 76 72 80 71 00 00 00 01 01 01 01 4 83 10 83 A NA NA NA NANA NANA 11 89 12 86 13 93 8 14 88 10 15 95 10 16 94 10 17 100 10 18 19