a. Transform the variables by means of the correlation transformation (7.44) and fit the standardized regression model (7.45). b. Calculate the coefficients of determination between all pairs of predictor variables. Do these indicate that it is meaningful here to consider the standardized regression coefficients as indicating the effect of one predictor variable when the others are held constant? c. Transform the estimated standardized regression coefficients by means of (7.53) back to the ones for the fitted regression model in the original variables. Verify that they are the same as the ones obtained in Problem 6.15c. 7.19. Refer to Commercial properties Problem 6.18. a. Transform the variables by means of the correlation transformation (7.44) and fit the stan- dardized regression model (7.45). b. Interpret the standardized regression coefficient b;. c. Transform the estimated standardized regression coefficients by means of (7.53) back to the ones for the fitted regression model in the original variables. Verify that they are the same as the ones obtained in Problem 6.18c. 7.20. A speaker stated in a workshop on applied regression analysis: "In business and the social sciences, some degree of multicollinearity in survey data is practically inevitable." Does this statement apply equally to experimental data? 7.21. Refer to the example of perfectly correlated predictor variables in Table 7.8. a. Develop another response function, like response functions (7.58) and (7.59), that fits the data perfectly. b. What is the intersection of the infinitely many response surfaces that fit the data perfectly? 7.22. The progress report of a research analyst to the supervisor stated: "All the estimated regression coefficients in our model with three predictor variables to predict sales are statistically sig- nificant. Our new preliminary model with seven predictor variables, which includes the three variables of our smaller model, is less satisfactory because only two of the seven regression coefficients are statistically significant. Yet in some initial trials the expanded model is giving more precise sales predictions than the smaller model. The reasons for this anomaly are now being investigated." Comment. 7.23. Two authors wrote as follows: "Our research utilized a multiple regression model. Two of the predictor variables important in our theory turned out to be highly correlated in our data set. This made it difficult to assess the individual effects of each of these variables separately. We retained both variables in our model, however, because the high coefficient of multiple determination makes this difficulty unimportant." Comment. 7.24. Refer to Brand preference Problem 6.5. a. Fit first-order simple linear regression model (2.1) for relating brand liking (Y) to moisture content (X,). State the fitted regression function. b. Compare the estimated regression coefficient for moisture content obtained in part (a) with the corresponding coefficient obtained in Problem 6.5b. What do you find? C. Does SSR(X,) equal SSR(X, |X2) here? If not, is the difference substantial? d. Refer to the correlation matrix obtained in Problem 6.5a. What bearing does this have on your findings in parts (b) and (c)? . *7.25. Refer to Grocery retailer Problem 6.9. a. Fit first-order simple linear regression model (2.1) for relating total hours required to handle
