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Read the following description of a data set. $\newline$ A movie theater manager is studying the snack buying habits of her customers. She expects that when longer movies are shown, people buy more snacks. Each week she calculates the average duration of all movies being shown and the percentage of customers who buy snacks.The manager calculates the average movie duration (in minutes), $x$ , and the percentage of the customers who bought snacks, $y$ .The least squares regression line of this data set is: $y = 0.262x - 15.968$ $\newline$ Complete the following sentence: $\newline$ If the average movie duration increased by one minute, the least squares regression line predicts that the percentage of customers who buy snacks would increase by ___.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

A movie theater manager is studying the snack buying habits of her customers. She expects that when longer movies are shown, people buy more snacks. Each week she calculates the average duration of all movies being shown and the percentage of customers who buy snacks.The manager calculates the average movie duration (in minutes),

x

, and the percentage of the customers who bought snacks,

y

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

y = 0.262x - 15.968

\newline

Complete the following sentence:

\newline

If the average movie duration increased by one minute, the least squares regression line predicts that the percentage of customers who buy snacks would increase by ___.

Analyze regression equation: Analyze the given regression equation $y = 0.262x - 15.968$ . Here, the slope is $0.262$ , which represents the change in the percentage of customers buying snacks for each additional minute of movie duration.
Calculate percentage increase: To find out how much the percentage of customers who buy snacks increases when the average movie duration increases by one minute, we use the slope of the regression line. Since the slope is $0.262$ , this means that for every one minute increase in movie duration, the percentage of customers buying snacks increases by $0.262\%$ .

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