Find the Least-Squares Regression Line and Use the Line to Make Predictions
-A manager wishes to determine the relationship between the number of miles traveled (in hundreds of miles) by her sales representatives and their amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. What would be the predicted sales if the sales representative traveled 0 miles? Is this reasonable? Why or why not?
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Miles traveled, } \mathrm{x} & 2 & 3 & 10 & 7 & 8 & 15 & 3 & 1 & 11 \
\hline \text { Sales, } \mathrm{y} & 31 & 33 & 78 & 62 & 65 & 61 & 48 & 55 & 120
\end{array}$

A) $\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 37,920$; No; it is not reasonable for a representative to travel 0 miles and have a positive amount of sales.

B) $\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 3792 ; \mathrm { No }$; it is not reasonable for a representative to travel 0 miles and have a positive amount of sales.
C) $\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 37,920$; Yes, it is reasonable.
D) $\hat { y } = 37.92 \mathrm { x } + 3.53$; $\$ 3792$; Yes, it is reasonable.

Question

Find the Least-Squares Regression Line and Use the Line to Make Predictions
-A manager wishes to determine the relationship between the number of miles traveled (in hundreds of miles) by her sales representatives and their amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. What would be the predicted sales if the sales representative traveled 0 miles? Is this reasonable? Why or why not?
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Miles traveled, } \mathrm{x} & 2 & 3 & 10 & 7 & 8 & 15 & 3 & 1 & 11 \
\hline \text { Sales, } \mathrm{y} & 31 & 33 & 78 & 62 & 65 & 61 & 48 & 55 & 120
\end{array}$

A) $\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 37,920$; No; it is not reasonable for a representative to travel 0 miles and have a positive amount of sales.

B) $\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 3792 ; \mathrm { No }$; it is not reasonable for a representative to travel 0 miles and have a positive amount of sales.
C) $\hat  { y } = 3.53 \mathrm { x } + 37.92 ; \$ 37,920$; Yes, it is reasonable.
D) $\hat   { y } = 37.92 \mathrm { x } + 3.53$; $\$ 3792$; Yes, it is reasonable.

Quizplus · Accepted Answer

The least-squares regression line equation is correctly given as $\hat { y } = 3.53x + 37.92$, which means that for every hundred miles traveled, sales increase by $3,530 on average, starting from a base of $37,920 when no miles are traveled. Predicting positive sales for 0 miles traveled might not be reasonable because it suggests sales can occur without any travel, which contradicts the premise of a relationship between travel and sales. However, the intercept represents the estimated sales when the miles traveled are zero, which could include other sales activities not requiring travel.