14.28 ● This exercise requires the use of a computer package.

The article “Vital Dimensions in Volume Perception:

Product Material Height Maximum Width Minimum Width Elongation Volume 1 glass 7.7 2.50 1.80 1.50 125 2 glass 6.2 2.90 2.70 1.07 135 3 glass 8.5 2.15 2.00 1.98 175 4 glass 10.4 2.90 2.60 1.79 285 5 plastic 8.0 3.20 3.15 1.25 330 6 glass 8.7 2.00 1.80 2.17 90 7 glass 10.2 1.60 1.50 3.19 120 8 plastic 10.5 4.80 3.80 1.09 520 9 plastic 3.4 5.90 5.00 0.29 330 10 plastic 6.9 5.80 4.75 0.59 570 11 tin 10.9 2.90 2.80 1.88 340 12 plastic 9.7 2.45 2.10 1.98 175 13 glass 10.1 2.60 2.20 1.94 240 14 glass 13.0 2.60 2.60 2.50 240 15 glass 13.0 2.70 2.60 2.41 360 16 glass 11.0 3.10 2.90 1.77 310 17 cardboard 8.7 5.10 5.10 0.85 635 18 cardboard 17.1 10.20 10.20 0.84 1250 19 glass 16.5 3.50 3.50 2.36 650 20 glass 16.5 2.70 1.20 3.06 305 21 glass 9.7 3.00 1.70 1.62 315 22 glass 17.8 2.70 1.75 3.30 305 23 glass 14.0 2.50 1.70 2.80 245 24 glass 13.6 2.40 1.20 2.83 200 25 plastic 27.9 4.40 1.20 3.17 1205 26 tin 19.5 7.50 7.50 1.30 2330 27 tin 13.8 4.25 4.25 1.62 730 Can the Eye Fool the Stomach?” (Journal of Marketing Research [1999]: 313–326) gave the data, shown in the table on page 728, on dimensions of 27 representative food products.

a. Fit a multiple regression model for predicting the volume (in ml) of a package based on its minimum width, maximum width, and elongation score.

b. Why should we consider adjusted R2 instead of R2 when attempting to determine the quality of fit of the data to our model?

c. Perform a model utility test.