CEO Performance (Refer to in Section 4.1) The following data represent the total

Chapter 14, Problem 19

(choose chapter or problem)

(Refer to in Section 4.1) The following data represent the total compensation for 10 randomly selected chief executive officers (CEOs) and the company's stock performance in 2009.

\(\begin{array}{lcc} \text { Company } & \begin{array}{l} \text { Compensation } \\ \text { (millions of dollars) } \end{array} & \begin{array}{l} \text { Stock } \\ \text { Return (%) } \end{array} \\ \hline \text { Kraft Foods } & 26.35 & 5.91 \\ \hline \text { Sara Lee } & 12.48 & 30.39 \\ \hline \text { Boeing } & 19.44 & 31.72 \\ \hline \text { Middleby } & 13.37 & 79.76 \\ \hline \text { Exelon } & 12.21 & -8.40 \\ \hline \text { Northern Trust } & 11.89 & 2.69 \\ \hline \text { Abbott Laboratories } & 26.21 & 4.53 \\ \hline \text { Archer Daniels Midland } & 14.95 & 10.80 \\ \hline \text { McDonald's } & 17.57 & 4.01 \\ \hline \text { Baxter International } & 14.36 & 11.76 \\ \hline \text { Source Chicago Tribune, May 23, 2010 } & \end{array}\)

(a) Treating compensation as the explanatory variable, x, determine the estimates of \(\beta_{0}\) and \(\beta_{1}\).

(b) Assuming the residuals are normally distributed, test whether a linear relation exists between compensation and stock return at the \(\alpha=0.05\) level of significance.

(c) Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.

(d) Based on your results to parts (b) and (c), would you recommend using the least-squares regression line to predict the stock return of a company based on the CEO's compensation? Why? What would be a good estimate of the stock return based on the data in the table?