In many polynomial regression problems, rather than fitting a “centered” regression function using , computational accuracy can be improved by using a function of the standardized independent variable

, where sx is the standard deviation of the xi

’s. Consider fitting the cubic regression function to the following data resulting from a study of the relation between thrust efficiency y of supersonic propelling rockets and the halfdivergence angle x of the rocket nozzle (“More on Correlating Data,” CHEMTECH, 1976: 266–270):

y 5 b0

* 1 b1

*

xr 1 b2

*

(xr)2 1 b3

*

(xr)3 xr 5 (x 2 x)/sx xr 5 x 2 x b1x 1 b2x 2 1 b3x 3 y 5 b0 1 b*3 b*2 b*1 b*0 y 5 b0

* 1 b1

*

xr 1 b2

*

(xr)2 1 b3

*

(xr) 3 xr 5 x 2 x x 5 4.3456

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?