Pet Foods, Revisited This exercise uses base 10 logs instead of natural logs. (a) Using the pet food data of the text example, transform the price and volume data using natural logs and then using...

Pet Foods, Revisited This exercise uses base 10 logs instead of natural logs.

(a) Using the pet food data of the text example, transform the price and volume data using natural logs and then using base 10 logs. Then plot the natural log of volume on the natural log of price, and the base 10 log of volume on the base 10 log of price. What’s the difference in your plots?

(b) Fit the linear equation of the log of volume on the log of price in both scales. What differences do you find between the fitted slopes and intercepts?

(c) Do the summary statistics
 and
 differ between the two fitted equations?

(d) Create a scatterplot for the loge of volume on the log₁₀
of volume, and then fit the least squares line. Describe how this relationship explains the similarities and differences.

(e) Which log should be used to estimate an elasticity, or does it not matter?