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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Definitions:

Confidence Interval

A range of values, derived from the statistics of observed data, that is likely to contain the value of an unknown population parameter.

Confidence Interval

A range of values, derived from sample data, that is likely to contain the value of an unknown population parameter.

Population

In statistics, the entire set of individuals or items from which samples can be drawn for analysis.

Confidence Interval

An estimated range of values calculated from a given set of sample data, reflecting where the true population parameter is expected to lie with a certain level of confidence.