Question

the table shows the gpa of several students and the number of hours they spend exercising each week. what best describes the correlation coefficient for the data? what best describes the strength of the linear association between a students gpa and the number of hours the student exercises?

weak negative correlation
weak positive correlation
strong negative correlation
strong positive correlation

hours, x
10
5
3
12

grade point average, y
3.0
3.4
3.5
2.7

Explanation:

As the number of hours spent watching television ($x$) increases, the grade - point average ($y$) decreases. This is a negative relationship.
Looking at the data:

• When $x = 10$, $y=3.0$
• When $x = 5$, $y = 3.4$ (as $x$ decreases, $y$ increases)
• When $x=3$, $y = 3.5$ (as $x$ further decreases, $y$ further increases)
• When $x = 12$, $y=2.7$ (as $x$ increases, $y$ decreases)

The change in $y$ with respect to $x$ is not extremely large. For example, the difference in $x$ from $3$ to $12$ (an increase of $9$) leads to a decrease in $y$ from $3.5$ to $2.7$ (a decrease of $0.8$). So it is not a very strong relationship.

Answer:

Weak negative correlation