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: 266–270):

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 ˆ

0 ˆ

1x

ˆ

2x2 ˆ

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 SSE’s 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?