Question

read the following description of a data set.
the counselor at sparrowtown high school suspects that students are signed up for too many extracurricular activities and thinks this negatively affects their academic performance. he decided to compile information about several students to find out.
for each of the students, the counselor recorded the number of extracurricular activities, x, and the gpa (out of 4.0), y.
the least squares regression line of this data set is: y = -0.787x + 4.873
complete the following sentence:
if a student signs up for one more extracurricular activity, the least squares regression line predicts that the students gpa would decrease by

Explanation:

Step1: Analyze the regression - line equation

The general form of a linear regression line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the given equation $y=-0.787x + 4.873$, the slope $m=-0.787$.

Step2: Interpret the slope

The slope of the regression line represents the change in the dependent variable ($y$, GPA in this case) for a one - unit change in the independent variable ($x$, number of extracurricular activities). A negative slope means that as $x$ increases by 1, $y$ decreases.

Answer:

$0.787$