Question

1. a study of the effects of screen - time measured how many hours of screen time each of 125 high school students had per week during the school year and their gpa. the study found that students who have greater screen time tend to have a worse gpa than students who have less screen time. the study report says that \hours of screen time explained 9% of the observed variability in the gpa of the 125 students.\ what is the correlation between hours of screen time and gpa?

(a) r = - 0.30
(b) r = - 0.09
(c) r = 0
(d) r = 0.09
(e) r = 0.30

Explanation:

Step1: Recall the concept of correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. A negative \(r\) indicates an inverse relationship. Here, since students with greater screen - time tend to have a worse GPA, it is a negative correlation.

Step2: Analyze the strength of the relationship

The closer the absolute value of \(r\) is to 1, the stronger the linear relationship. Given that 9% of the variability in GPA is explained by screen - time, we know that \(r^{2}=0.09\) (because the coefficient of determination \(R^{2}\) gives the proportion of the variance in the dependent variable that is predictable from the independent variable). Then \(r = - 0.3\) (we take the negative value because of the inverse relationship).

Answer:

A. \(r=-0.30\)