Why should we consider adjusted r2 instead of r2 when

Question

This exercise requires the use of a computer package. The article "Vital Dimensions in Volume Perception:

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.