A manager wishes to determine the relationship between the number of years her sales representatives havebeen employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation ofthe regression line for the given data. What would be the predicted sales if the sales representative wasemployed by the firm for 30 years Is this reasonable? Why or why not? Round the regression line values to thenearest hundredth. $\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Years employed, } \mathrm{x} & 2 & 3 & 10 & 7 & 8 & 15 & 3 & 1 & 11 \
\hline \text { Sales, } \mathrm{y} & 31 & 33 & 78 & 62 & 65 & 61 & 48 & 55 & 120
\end{array}$
A) $\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 143,820$; No; it is not reasonable. 30 years of employment is well outside the scope of the model.
B) $\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 143,820 ;$ Yes, it is reasonable.
C) $\hat { y } = 3.53 \mathrm { x } - 37.92 ; \$ 67,980 ; \mathrm { No }$; it is not reasonable. 30 years of employment is well outside the scope of the model.
D) $\hat { y } = 3.53 \mathrm { x } - 37.92 ; \$ 67,980$; Yes; it is reasonable.

Question

A manager wishes to determine the relationship between the number of years her sales representatives havebeen employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation ofthe regression line for the given data. What would be the predicted sales if the sales representative wasemployed by the firm for 30 years Is this reasonable? Why or why not? Round the regression line values to thenearest hundredth. $\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Years employed, } \mathrm{x} & 2 & 3 & 10 & 7 & 8 & 15 & 3 & 1 & 11 \
\hline \text { Sales, } \mathrm{y} & 31 & 33 & 78 & 62 & 65 & 61 & 48 & 55 & 120
\end{array}$
A) $\hat  { y } = 3.53 \mathrm { x } + 37.92 ; \$ 143,820$; No; it is not reasonable. 30 years of employment is well outside the scope of the model.
B) $\hat  { y } = 3.53 \mathrm { x } + 37.92 ; \$ 143,820 ;$ Yes, it is reasonable.
C) $\hat  { y } = 3.53 \mathrm { x } - 37.92 ; \$ 67,980 ; \mathrm { No }$; it is not reasonable. 30 years of employment is well outside the scope of the model.
D) $\hat { y } = 3.53 \mathrm { x } - 37.92 ; \$ 67,980$; Yes; it is reasonable.

Quizplus · Accepted Answer

The correct regression equation is $\hat  { y } = 3.53 \mathrm { x } + 37.92$, and the predicted sales for 30 years of employment would be \$143,820. However, predicting for 30 years is not reasonable because it extrapolates far beyond the range of the data provided, which could lead to inaccurate predictions.

A Manager Wishes to Determine the Relationship Between the Number