In many polynomial regression problems, rather than fitting a “centered” regression func...

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 s_x 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):

a. What value of y would you predict when the half-divergence angle is 20? When x = 25?

b. What is the estimated regression function 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 R^2’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?