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Read the following description of a data set. $\newline$ Emmett wants to figure out how long it usually takes to get through a supermarket checkout line. For several weeks, he observed the checkout lines he waited in. Emmett counted how many people were ahead of him in each line he joined, $x$ , and how many minutes it took him to get to the front of that line, $y$ . The least squares regression line of this data set is: $y = 0.982x + 13.674$ $\newline$ Complete the following sentence: $\newline$ For each additional person ahead of Emmett, the least squares regression line predicts that he would have to wait an extra $\_\_$ minutes.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

Emmett wants to figure out how long it usually takes to get through a supermarket checkout line. For several weeks, he observed the checkout lines he waited in. Emmett counted how many people were ahead of him in each line he joined,

x

, and how many minutes it took him to get to the front of that line,

y

. The least squares regression line of this data set is:

y = 0.982x + 13.674

\newline

Complete the following sentence:

\newline

For each additional person ahead of Emmett, the least squares regression line predicts that he would have to wait an extra

\_\_

minutes.

Regression Line Explanation: The least squares regression line provided is $y = 0.982x + 13.674$ . In this equation, $y$ represents the total time Emmett waits to get to the front of the line, and $x$ represents the number of people ahead of him. The coefficient of $x$ ( $0.982$ ) indicates the change in the total wait time for each additional person in line.
Coefficient Interpretation: To find out how much extra time Emmett would have to wait for each additional person ahead of him, we look at the coefficient of $x$ in the regression equation. This coefficient, $0.982$ , represents the additional minutes he would have to wait per person.

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