Suppose you want to use the coding system for observational data to fit a second-order model to the tire pressure–automobile mileage data given in the next table below.

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

    E(y) = β₀ + β₁u₁ + β₂u² 

using available statistical software. Interpret the results.

Transcribed Image Text:

TIRES Pressure x, pounds per square inch Mileage y, thousands Pressure x, pounds per square inch Mileage y, thousands 30 29.5 33 37.6 30 30.2 34 37.7 31 32.1 34 36.1 31 34.5 35 33.6 32 36.3 35 34.2 32 35.0 36 26.8 33 38.2 36 27.4