Until recently, performance tires were fitted mostly on sporty or luxury vehicles. Now they come standard on many everyday sedans. Increased levels of handling and grip have come at the expense of tread wear. The data that follows is abstracted from a report on all-season tires by Consumer Reports8 in which several aspects of performance were evaluated for n = 26 different tires where
y = overall score x1 = dry braking
x2 = wet braking x3 = handling
x4 = roll resistance x5 = tread life

The variables x1 through x5 are coded using the scale 5 = excellent, 4 = very good, 3 = good, 2 = fair, and 1 = poor.
a. Use a program of your choice to find the correlation matrix for the variables under study including price. Is price significantly correlated with any of the study variables? Which variables appear to be highly correlated with y, the overall score?
b. Write a model to describe y, overall score, as a function of the variables x1 = dry braking, x2 = wet braking, x3 = handling, x4 = roll resistance, and x5 = tread life.
c. Use a regression program of your choice to fit the full model using all of the predictors. What proportion of the variation in y is explained by regression? Does this convey the impression that the model adequately explains the inherent variability in y?
d. Which variable or variables appear to be good predictors of y? How might you refine the model in light of these results? Use these variables in refitting the model. What proportion of the variation is explained by this refitted model? Comment on the adequacy of this reduced model in comparison to the full model.

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