Chapter 13.3, Problem 34E

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 5 acid extractable cations and y 5 exchangeable acidity/total cation exchange capacity (“Exchangeable Acidity in Unburnt Colliery Spoil,” Nature, 1969: 161):

x		-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 $x\text{'}=(x-\bar{x})/s_x$ and fitting the regression function $y={\beta }_0^{*}+{\beta }_1^{*}x\text{'}+{\beta }_2^{*}{(x\text{'})}^2$ yielded the accompanying computer output.

a. Estimate ${\mu }_{Y\cdot 50}$

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

c. What is the estimated regression function ${\hat{\beta }}_0+{\hat{\beta }}_{1}x+{\hat{\beta }}_2{x}^2$ using the unstandardized variable x?

d. What is the estimated standard deviation of ${\hat{\beta }}_2$ 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?