  ### Home > GB8I > Chapter 6 Unit 7 > Lesson INT1: 6.1.1 > Problem6-9

6-9.

A researcher wanted to see if there was an association between the number of hours spent watching TV and students’ grade point averages. He found $r = –0.72$. Interpret the researcher’s results.

r represents the correlation coefficient.
Review the Math Notes box in section 4.2.4

Since $r$ is negative, there is a decreasing association (the slope is negative) between the hours spent watching TV and GPA.
The closer $r$ is to $1$ or $-1$, the closer to perfectly linear the association is.
$\mathbf{R}$-squared represents the percentage of variability that can be attributed to the dependent variable.

Therefore, there is a good, but not great association between these two variables, meaning as the number of TV watching hours increases, the GPA of the student tends to decrease.
Since $\mathbf{R}$-squared $= 0.5184$, so $51.84$% of the variability in GPA can be attributed to hours of TV watched.
Any other variability should be attributed to other factors.