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Read the following description of a data set. $\newline$ A reporter for a college magazine is writing a feature about student participation in on-campus organizations. He wants to see if there is a relationship between student population and the number of on-campus organizations.To begin, he recorded the number of students, $x$ , and the number of officially recognized student organizations, $y$ , for several colleges.The least squares regression line of this data set is: $y = 0.017x + 176.089$ $\newline$ Complete the following sentence: $\newline$ For each additional student, the least squares regression line predicts there would be ___ more student organizations.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

A reporter for a college magazine is writing a feature about student participation in on-campus organizations. He wants to see if there is a relationship between student population and the number of on-campus organizations.To begin, he recorded the number of students,

x

, and the number of officially recognized student organizations,

y

, for several colleges.The least squares regression line of this data set is:

y = 0.017x + 176.089

\newline

Complete the following sentence:

\newline

For each additional student, the least squares regression line predicts there would be ___ more student organizations.

Identify slope: Identify the slope of the least squares regression line. The equation given is $y = 0.017x + 176.089$ . The slope of the least squares regression line is the coefficient of $x$ , which is $0.017$ . This slope represents the change in the number of student organizations for each additional student.
Interpret slope: Interpret the slope. $\newline$ In the equation $y = 0.017x + 176.089$ , $x$ represents the number of students and $y$ represents the number of officially recognized student organizations. The slope of $0.017$ indicates that for each additional student, the number of student organizations is predicted to increase by $0.017$ .

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