The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are x
acid extractable cations and y
exchangeable 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 x

(x  x)/sx and fitting the regression function y
*0

*1x *2(x )2 yielded the accompanying computer output.

Parameter Estimate Estimated SD

*0 .8733 .0421

*1 .3255 .0316

*2 .0448 .0319

a. Estimate Y50.

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

c. What is the estimated regression function ˆ

0 ˆ

1x

ˆ

2x2 using the unstandardized variable x?

d. What is the estimated standard deviation of ˆ

2 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?