According to the World Health Organization, obesity has reached epidemic proportions globally. While obesity has generally been linked with chronic disease and disability, researchers argue that it may also affect wages. Body Mass Index (BMI) is a widely used weight measure that also adjusts for height. A person is considered normal weight if BMI is between 18.5 to 25, overweight if BMI is between 25 to 30, and obese if BMI is over 30. The accompanying table shows a portion of data on the salary of 30 college-educated men with their respective BMI; the complete data, labeled BMI, are available on the text website.
a. Estimate a linear model with salary as the response variable and BMI as the explanatory variable. What is the estimated salary of a college-educated man with a BMI of 25? With a BMI of 30?
b. Estimate an exponential model using log of salary as the response variable and BMI as the explanatory variable. What is the estimated salary of a college-educated man with a BMI of 25? With a BMI of 30?
c. Which of the above two models is more appropriate for this application? Use R2 for comparison.