In a study comparing four groups with six observations in each group,the MSE = 487 and the MSG = 3456.What is the value of the coefficient of determination?
A)0.484
B)0.516
C)0.587
D)0.939

Question

Quizplus · Accepted Answer

The coefficient of determination, $R^2$, is calculated as $R^2 = \frac{SSG}{SST}$, where $SSG$ is the sum of squares between groups and $SST$ is the total sum of squares. $SST = SSG + SSE$, where $SSE$ is the sum of squares within groups (error). Given $MSE = 487$ and $MSG = 3456$, with 4 groups of 6 observations each, we have $n = 24$ total observations and $k = 4$ groups. $SSE = MSE \times (n - k) = 487 \times (24 - 4) = 487 \times 20$. $SSG = MSG \times (k - 1) = 3456 \times 3$. Thus, $R^2 = \frac{SSG}{SSG + SSE} = \frac{3456 \times 3}{3456 \times 3 + 487 \times 20}$. Calculating this gives $R^2 \approx 0.516$, indicating that approximately 51.6% of the variability is explained by the group differences.

In a Study Comparing Four Groups with Six Observations in Each