Answer: In many polynomial regression problems, rather

Chapter 13, Problem 13.33

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In many polynomial regression problems, rather than fitting a centered regression function using x x x, computational accuracy can be improved by using a function of the standardized independent variable x (x x)/sx, where sx is the standard deviation of the xis. Consider fitting the cubic regression function y *0 *1x *2(x ) 2 *3(x ) 3 to the following data resulting from a study of the relation between thrust efficiency y of supersonic propelling rockets and the half-divergence angle x of the rocket nozzle (More on Correlating Data, CHEMTECH, 1976: 266270): x | 5 10 15 20 25 30 35 y | .985 .996 .988 .962 .940 .915 .878 Parameter Estimate Estimated SD *0 .9671 .0026 *1 .0502 .0051 *2 .0176 .0023 *3 .0062 .0031 a. What value of y would you predict when the halfdivergence angle is 20? When x 25? b. What is the estimated regression function 0 1x 2x2 3x3 for the unstandardized model? c. Use a level .05 test to decide whether the cubic term should be deleted from the model. d. What can you say about the relationship between SSEs and R2 s for the standardized and unstandardized models? Explain. e. SSE for the cubic model is .00006300, whereas for a quadratic model SSE is .00014367. Compute R2 for each model. Does the difference between the two suggest that the cubic term can be deleted? 13.3 P