When fitting polynomial regression models, we often subtract from each x value to produce a “centered’’

regressor . This reduces the effects of dependencies among the model terms and often leads to more accurate estimates of the regression coefficients. Using the data from Exercise 12-72, fit the model

(a) Use the results to estimate the coefficients in the uncentered model . Predict y when

. Suppose that we use a standardized variable

, where sx is the standard deviation of x, in constructing a polynomial regression model. Fit the model

.

(b) What value of y do you predict when ?

(c) Estimate the regression coefficients in the unstandardized model .

(d) What can you say about the relationship between SSE and R2 for the standardized and unstandardized models?

(e) Suppose that is used in the model along with . Fit the model and comment on the relationship between SSE and R2 in the standardized model and the unstandardized model.