Tire wear and pressure. Suppose you want to use the coding system for observational data to fit a second-order model to the tire pressure–automobile mileage data in Exercise 5.10 (p. 272), which are...

Tire wear and pressure. Suppose you want to use the coding system for observational data to fit a second-order model to the tire pressure–automobile mileage data in Exercise 5.10 (p. 272), which are repeated in the table.

(a) Give the equation relating the coded variable u to pressure, x, using the coding system for observational data.

(b) Calculate the coded values, u.

(c) Calculate the coefficient of correlation r between the variables x and x².

(d) Calculate the coefficient of correlation r between the variables u and u². Compare this value to the value computed in part c.

(e) Fit the model

using available statistical software. Interpret the results.