Do higher-paid chief executive officers (CEOs) control bigger companies? Let us study x = annual CEO salary ($ millions) and y = annual company revenue ($ billions). The following data are based on information from Forbes magazine and represent a sample of top U.S. executives. Use this information for Questions 1-7.
x (salary, millions) 0.8 1.0 1.1 1.7 2.3
y (revenue, billions) 14 11 19 20 25
1. Draw a scatter diagram. Using the scatter diagram (no calculations), would you estimate the linear correlation coefficient to be positive, close to 0, or negative? Explain your answer.
2. For the given data compute each of the following.
(c) The slope b and y intercept a of the least-squares line; write out the equation for the least-squares line.
(d) Graph the least-squares line on your scatterplot of
Problem 1
3. Compute the sample correlation coefficient r. Compute the coefficient of determination. Give a brief explanation of the meaning of the coefficient of determination in the context of this problem.
4. Compute the standard error of estimate Se. 4.
5. If a CEO has an annual salary of $1.5 million, what is his or her annual company revenue as predicted by the least-squares line?
6. Find a 90% confidence interval for your prediction of
Problem 5.
7. Using the sample correlation coefficient r computed in Problem 3, test whether or not the population correlation coefficient is different from 0. Use = 0.01. Is r significant in this problem? Explain