Empirical Exercises 171 A detailed description is given in Earnings_and_Height_Description, also available on the website. In this exercise, you will investigate the relationship between earnings and height. a. What is the median value of height in the sample? b. i. Estimate average earnings for workers whose height is at most 67 inches. ii. Estimate average earnings for workers whose height is greater than 67 inches. iii. On average, do taller workers earn more than shorter workers? How much more? What is a 95% confidence interval for the difference in average earnings? c. Construct a scatterplot of annual earnings (Earnings) on height (Height). ang Notice that the points on the plot fall along horizontal lines. (There are only 23 distinct values of Earnings). Why? (Hint: Carefully read the detailed data description.) d. Run a regression of Earnings on Height. i. What is the estimated slope? ii. Use the estimated regression to predict earnings for a worker who is 67 inches tall, for a worker who is 70 inches tall, and for a worker who is 65 inches tall. e. Suppose height were measured in centimeters instead of inches. Answer the following questions about the Earnings on Height (in cm) regression. i. What is the estimated slope of the regression? ii. What is the estimated intercept? iii. What is the R? iv. What is the standard error of the regression?