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
a. Estimate
b. Compute the value of the coefficient of multiple determination. (See Exercise 28(c).)
c. What is the estimated regression function
d. What is the estimated standard deviation of
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?
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Probability and Statistics for Engineering and the Sciences
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