Answer: The following data resulted from an experiment to

Chapter 13, Problem 13.34

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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 0 1x 2x2 using the unstandardized variable x? d. What is the estimated standard deviation of 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? 35.

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