The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are extractable cations and acidity/total cation exchange capacity

(“Exchangeable Acidity in Unburnt Colliery Spoil,” Nature, 1969: 161):

x 23 5 16 26 30 38 52 y 1.50 1.46 1.32 1.17 .96 .78 .77 x 58 67 81 96 100 113 y .91 .78 .69 .52 .48 .55 Standardizing the independent variable x to obtain and fitting the regression function yielded the accompanying computer output.

Parameter Estimate Estimated SD

.8733 .0421

.3255 .0316

.0448 .0319

a. Estimate .

b. Compute the value of the coefficient of multiple determination. (See Exercise 28(c).)

c. What is the estimated regression function using the unstandardized variable x?

d. What is the estimated standard deviation of computed in part (c)?

e. Carry out a test using the standardized estimates to decide whether the quadratic term should be retained in the model. Repeat using the unstandardized estimates.

Do your conclusions differ?