# Question: This exercise uses base 10 logs instead of natural logs a

This exercise uses base 10 logs instead of natural logs.

(a) Using the pet food data of the text example, trans-form 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 r2 and se differ between the two fitted equations?

(d) Create a scatterplot for the loge of volume on the log10 of volume, and then ft 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?

(a) Using the pet food data of the text example, trans-form 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 r2 and se differ between the two fitted equations?

(d) Create a scatterplot for the loge of volume on the log10 of volume, and then ft 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?

**View Solution:**## Answer to relevant Questions

These data give the gross domestic product (a measure of the size of a national economy, in billions of dollars) and the amount of CO2 (carbon dioxide, in millions of tons) released into the atmosphere in 140 countries in ...1. An increase in the observed sample size from 100 customers to 400 customers in a study of promotion response using simple regression produces predictions that are twice as accurate. 2. Doubling the sample size used to ft ...In the regression of production time on number of units, how would the following statistics change had the response variable been expressed in hours rather than minutes? (a) b0 (b) b1 (c) se (d) t-statistic for b1 This dataset includes the annual prices of 223 commercial leases. All of these leases provide office space in a Midwestern city in the United States. For the response, use the cost of the lease per square foot. As the ...1. Average of y given x in the SRM 2. Standard deviation of errors 3. Standard deviation of residuals 4. Ratio of b1 to its standard error 5. Approximate standard error of b1 6. Approximate prediction interval (l) μ y∣x = ...Post your question