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Read the following description of a data set. Emilia wants to figure out how long it usually takes to get through a supermarket checkout line. For several weeks, she observed the checkout lines she waited in. Emilia counted how many people were ahead of her in each line she joined, $x$ , and how many minutes it took her to get to the front of that line, $y$ . The least squares regression line of this data set is: $y = 0.518x + 4.194$ $\newline$ Complete the following sentence: $\newline$ For each additional person ahead of Emilia, the least squares regression line predicts that she would have to wait an extra $\_\_$ minutes.

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Interpret regression lines

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Q. Read the following description of a data set. Emilia wants to figure out how long it usually takes to get through a supermarket checkout line. For several weeks, she observed the checkout lines she waited in. Emilia counted how many people were ahead of her in each line she joined,

x

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

y

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

y = 0.518x + 4.194

\newline

Complete the following sentence:

\newline

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

\_\_

minutes.

Regression Line Explanation: The least squares regression line provided is $y = 0.518x + 4.194$ . In this equation, $y$ represents the total time Emilia waits, and $x$ represents the number of people ahead of her in line. The coefficient of $x$ ( $0.518$ ) indicates the change in the total wait time for each additional person in line.
Calculation of Extra Time: To find out how much extra time Emilia has to wait for each additional person ahead of her, we look at the coefficient of $x$ in the regression equation, which is $0.518$ . This means that for each additional person, the wait time increases by $0.518$ minutes.
Conclusion: There is no need for further calculations as the coefficient directly answers the question prompt.

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