# Answer true or false to each of the following statements and explain your answers.a. A polynomial regression equation of degree k in the centered predictor variable gives different predicted values than the polynomial regression equation of degree k in the uncentered predictor variable.b. The utility of a power of x in a polynomial regression equation depends on what other powers of x are in the regression equation.c. High correlations among the predictor variables have little effect on the t-tests for the individual utility of a predictor variable.

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a. A polynomial regression equation of degree k in the centered predictor variable gives different predicted values than the polynomial regression equation of degree k in the uncentered predictor variable.
b. The utility of a power of x in a polynomial regression equation depends on what other powers of x are in the regression equation.
c. High correlations among the predictor variables have little effect on the t-tests for the individual utility of a predictor variable.

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Step 1

(a)

Whether a polynomial regression equation is centered or uncentered does not affect the predicted values of the response variable.

Thus, the statement “A polynomial regression equation of degree k in the centered predictor variable gives different predicted values than the polynomial regression equation of degree k in the uncentered predictor variable.” is False.

Step 2

(b)

In polynomial regression, the predictors are all various powers of x. As a result, the predictors are very much correlated among themselves, most of the time. This correlation among the predictors defines how useful a particular power of x in the polynomial regression equation would be,...

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