In many polynomial regression problems, rather than fitting a "centered" regression function using x' = x - x̅, computational accuracy can be improved by using a function of the standardized independent variable x' = (x - x̅)/sx, where sx is the standard deviation of the xi's. Consider fitting the cubic regression function y = β0* + β1* x' + β2*(x')2 + β3 *(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):

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 β̂0 + β̂1x + β̂2x2 + β̂3x3 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?

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x5 105 20 25 30 35 y .985 .996 .988 .962 .940 .915 878 Parameter Estimate 9671 -0502 一,0176 .0062 Estimated SD 0026 0051 .0023 .0031 a ;