Question 2. (12 marks) A car manufacturer conducts an experiment to determine the effects of shape of the body and tire pressure on the mileage of a new model of car that they are producing. They have 5 cars for each combination of shape (A, B, or C) and tire pressure (low, medium, high, or very high). They record the mileage (in km/100 L) based on one test drive of each car. However, the mileages of two of the cars were measured improperly and thus discarded. They then fit a two-way ANOVA model with interaction effect to the data. They confirm that the assumptions underlying this model are reasonable. Some output is below. > anova (fit) Analysis of Variance Table Response: Mileage of Sum Sq Mean Sq F value Pr (>F) shape 2 18721.0 9360.5 31. 1277 2. 825e-09 Pressure 3 13915 . 3 4638.4 15. 4248 4.423e-07 Shape : Pressure 6 1650.4 275 .1 0.9147 0. 493 Residuals 46 13832.8 300. 7 > summary (fit) Call: 1m(formula = Mileage ~ Shape * Pressure) Residuals: Min 1Q Median 3Q Max -29.834 -11.595 -0. 551 9 . 068 41. 419 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 525 . 352 8. 671 60.590