The article Vital Dimensions in Volume Perception: Can the

Chapter 0, Problem 13.28

(choose chapter or problem)

The article Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach? (Journal of Marketing Research [1999]: 313326) gave the accompanying data on the dimensions of 27 representative food products (Gerber baby food, Cheez Whiz, Skippy Peanut Butter, and Ahmeds tandoori paste, to name a few). Maximum Minimum Product Width Width 1 2.50 1.80 2 2.90 2.70 3 2.15 2.00 4 2.90 2.60 5 3.20 3.15 6 2.00 1.80 7 1.60 1.50 8 4.80 3.80 9 5.90 5.00 10 5.80 4.75Product Width Width 11 2.90 2.80 12 2.45 2.10 13 2.60 2.20 14 2.60 2.60 15 2.70 2.60 16 3.10 2.90 17 5.10 5.10 18 10.20 10.20 19 3.50 3.50 20 2.70 1.20 21 3.00 1.70 22 2.70 1.75 23 2.50 1.70 24 2.40 1.20 25 4.40 1.20 26 7.50 7.50 27 4.25 4.25 a. Fit the simple linear regression model that would allow prediction of the maximum width (in cm) of a food container based on its minimum width (in cm). b. Calculate the standardized residuals (or just the residuals if you dont have access to a computer program that gives standardized residuals), and plot them to determine whether there are any outliers. Would eliminating these outliers increase the accuracy of predictions using this regression? If so, eliminate the outlying data point (a 1-liter Coke bottle) and refit the regression. c. Interpret the estimated slope and, if appropriate, the intercept. d. Do you think that the assumptions of the simple linear regression model are reasonable? Give statistical evidence for your answer.