Chapter B, Problem 26RP

Paper Strength. Refer to Problem 6, where we considered the regression analysis of tensile strength of Kraft paper on concentration of hardwood. Use the technology of your choice to obtain output similar to that in Outputs B.89 and B.90 on pages B-167–B-168.

1. a. Obtain a scatterplot of tensile strength versus hardwood concentration. Would the method of transformations be useful in straightening this scatterplot? Explain your answer.
2. b. Based on the scatterplot in part (a), what polynomial would you use to fit the data?
3. c. Determine the centered predictor variable and then use it and the forward selection method to decide on the degree of the polynomial regression equation relating tensile strength to hardwood concentration.
4. d. Use the centered predictor variable and the backward elimination method to decide on the degree of the polynomial regression equation relating tensile strength to hardwood concentration.
5. e. Do the forward selection and backward elimination methods yield the same results? If so, is that always the case?
6. f. Obtain plots of residuals versus fitted values and a normal probability plot of the residuals for the polynomial regression equation obtained by the forward selection method. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
7. g. Does your analysis in part (f) reveal any violations of the assumptions for regression inferences? Explain your answer.