Question

interpret the least squares regression line of this data set.
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 correct least squares regression line for the data set is:
y = 0.047x - 114.713
use it to complete the following sentence:
for each additional student, the least squares regression line predicts there would be more student organizations.

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Interpret the slope in the context of the problem

In the regression line \(y = 0.047x-114.713\), the coefficient of \(x\) (the slope \(m\)) represents the change in \(y\) (number of student organizations) for a unit change in \(x\) (number of students).

Answer:

\(0.047\)