EXAMPLE 16 Calculating and interpreting the coefficient of determination $r^2$

Calculate and interpret the value of the coefficient of determination $r^2$ for the memory score data.

Solution

From Example 14, we have $\text{SSE}=228$, and from Example 15 we have $\text{SSE}=216$. Thus,

Therefore, 94.74% of the variability in the memory test score $\left(y\right)$ is accounted for by the linear relationship between score $\left(y\right)$ and the time given for study $\left(x\right)$.