The following data is a subset of data obtained in an experiment to study the relationship between soil pH x 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):

x | 4.01 4.07 4.08 4.10 4.18 y | 1.20 .78 .83 .98 .65 x | 4.20 4.23 4.27 4.30 4.41 y | .76 .40 .45 .39 .30 x | 4.45 4.50 4.58 4.68 4.70 4.77 y | .20 .24 .10 .13 .07 .04 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, x
4.3456 was subtracted from each x value to yield x

x  x. A cubic regression was then requested to fit the model having regression function y
*0 *1x *2(x )2 *3(x )3 The following computer output resulted:

Parameter Estimate Estimated SD

*0 .3463 .0366

*1 1.2933 .2535

*2 2.3964 .5699

*3 2.3968 2.4590

a. What is the estimated regression function for the “centered” model?

b. What is the estimated value of the coefficient 3 in the

“uncentered” model with regression function y
0

1x 2x2 3x3

? What is the estimate of 2?

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.