The following data is a subset of data obtained in an experiment to study the relationship between x = soil pH and y = A1 Concentration/EC ("Root Responses of Three Gramineae Species to Soil Acidity in an Oxisol and an Ultisol," Soil Science, 1973: 295-302):

A cubic model was proposed in the article, but the version of Minitab used by the author of the present text refused to include the x3 term in the model, stating that "x3 is highly correlated with other predictor variables." To remedy this, xÌ… = 4.3456 was subtracted from each x value to yield x' = x - xÌ…. A cubic regression was then requested to fit the model having regression function

The following computer output resulted:

a. What is the estimated regression function for the "centered" model?
b. What is the estimated value of the coefficient β3 in the "uncentered" model with regression function y = β0 + β1x + β2x2 + β3x3? What is the estimate of β2?
c. Using the cubic model, what value of y would you predict when soil pH is 4.5?
d. Carry out a test to decide whether the cubic term should be retained in the model.

x 4.0 4.07 4.08 4.10 4.18 65 x4.20 4.23 4.27 4.30 4.41 .30 y1.20 .78 83 98 45 x4.45 4.50 4.58 4.68 4.70 4.77 .10 y.76 40 39 20 24 13 07 04 Parameter Estimate Estimated SD 3463 1.2933 2.3964 -2.3968 0366 2535 3603 2.4590 BO