Find the Least-Squares Regression Line and Use the Line to Make

question 145

Multiple Choice

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.

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