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Read the following description of a data set. $\newline$ A sporting goods chain is planning to open a new store in Putnam County. In order to decide on an optimal location, their market researchers gathered data on sports facilities in towns across the county.The researchers considered the population (in thousands), $x$ , and the number of sports facilities, $y$ , in each town.The least squares regression line of this data set is: $y = 0.524x - 38.329$ $\newline$ Complete the following sentence: $\newline$ If a town had one thousand more people, the least squares regression line predicts that it would have $\_\_$ more sports facilities.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

A sporting goods chain is planning to open a new store in Putnam County. In order to decide on an optimal location, their market researchers gathered data on sports facilities in towns across the county.The researchers considered the population (in thousands),

x

, and the number of sports facilities,

y

, in each town.The least squares regression line of this data set is:

y = 0.524x - 38.329

\newline

Complete the following sentence:

\newline

If a town had one thousand more people, the least squares regression line predicts that it would have

\_\_

more sports facilities.

Calculate Slope: The equation given is $y = 0.524x - 38.329$ . The slope of the least squares regression line is the coefficient of $x$ , which is $0.524$ .
Interpret Slope: In the equation $y = 0.524x - 38.329$ , $x$ represents the population of the town in thousands, and $y$ represents the number of sports facilities in that town. The slope of $0.524$ indicates that for each increase of one thousand people in the town's population, the number of sports facilities is predicted to increase by $0.524$ .

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