To Determine Whether the Cash Bonus Paid by a Company

To determine whether the cash bonus paid by a company is related to annual pay, data were gathered for 10 loan officers at AMC Bank who received cash bonuses in 2012. The data, scatterplot, and summary statistics are shown below. $$\begin{array} { | l | l | l | } \hline & \text { ANNUAL PAY } & \text { CASH BONUS } \\\hline & \$ 70609 & \$ 11225 \\\hline & \$ 58487 & \$ 6238 \\\hline & \$ 104561 & \$ 14194 \\\hline & \$ 43922 & \$ 4188 \\\hline & \$ 82613 & \$ 11863 \\\hline & \$ 116250 & \$ 13671 \\\hline & \$ 76751 & \$ 7758 \\\hline & \$ 68513 & \$ 20760 \\\hline \text { Mean } & \$ 137000 & \$ 55000 \\\hline \text { Standard Deviation } & \$ 94469 & \$ 34368 \\\hline & & \$ 17927 \\\hline \text { Correlation } & \$ 85318 & \$ 15618 \\\hline\end{array}$$ Model a linear relationship with a least squares regression model.

-Using the estimated regression equation,
a. Estimate the cash bonus for an executive at Johnson Financial earning $82, 613 a year.
b. What is the residual for this estimate? What does it mean?