On the Road Again Until recently,performance tires were fitted mostly on sportyor luxury

Chapter 13, Problem 31

(choose chapter or problem)

On the Road Again Until recently,performance tires were fitted mostly on sportyor luxury vehicles. Now they come standard on manyeveryday sedans. Increased levels of handling and griphave come at the expense of tread wear. The data thatfollows is abstracted from a report on all-season tiresby Consumer Reports8 in which several aspects ofperformance were evaluated for n = 26 different tireswherey overall score x1 dry brakingx2 wet braking x3 handlingx4 roll resistance x5 tread lifeBrand and Model Price ($) y x1 x2 x3 x4 x5Michelin HydroEdge 116 84 4 5 4 3 5Continental ProContactECOPLUS 90 82 4 4 3 5 3Michelin Energy Saver A/S 120 82 4 4 3 5 3 Brand and Model Price ($) y x1 x2 x3 x4 x5Hankook Optimo H727 96 82 4 4 3 3 3Pirelli P4 Four Seasons 98 80 4 5 3 2 2Goodyear Assurance TripleTred 121 80 4 4 3 3 3Pirelli Cinturato P5 98 78 3 5 3 2 3Kumho Solus KR21 77 78 4 5 3 3 4Maxxis Escapade MA-T1 77 76 3 4 4 3 4Toyo Extensa A/S 99 76 3 4 3 3 3Cooper GFE 83 76 3 4 3 4 2Toyo Versado LX 91 76 4 4 3 3 5BFGoodrich Traction T/A T 90 74 4 4 4 2 3General Altimax RT 77 74 3 5 3 3 3Yokohama Avid TRZ 81 74 4 5 3 2 3Dayton Quadra LE 74 74 3 4 3 3 3Cooper CS4 Touring 86 72 3 5 3 2 3Uniroyal Tiger Paw Tour SR 77 72 4 4 2 5 2Yokohama Avid Touring-S 70 70 4 4 3 4 4Cooper Lifeliner GLS 78 68 3 4 3 4 2Yokohama Avid T4 85 66 3 4 3 3 2Bridgestone Turanze EL400 97 66 3 4 2 3 2Falken Sincera SN828 82 64 3 5 3 3 1Dunlop SP 60 79 64 3 3 2 2 4Sumitomo HTR T4 67 64 3 4 3 4 2Firestone FR710 80 60 3 5 3 3 4The variables x1 through x5 are coded using the scale5 excellent, 4 very good, 3 good, 2 fair, and1 poor.a. Use a program of your choice to find the correlationmatrix for the variables under study includingprice. Is price significantly correlated with any ofthe study variables? Which variables appear to behighly correlated with y, the overall score?b. Write a model to describe y, overall score, as afunction of the variables x1 dry braking,x2 wet braking, x3 handling, x4 rollresistance, and x5 tread life.c. Use a regression program of your choice to fit thefull model using all of the predictors. What proportionof the variation in y is explained by regression?Does this convey the impression that the model adequatelyexplains the inherent variability in y?d. Which variable or variables appear to be goodpredictors of y? How might you refine the modelin light of these results? Use these variables inrefitting the model. What proportion of the variationis explained by this refitted model? Commenton the adequacy of this reduced model in comparisonto the full model