Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l }
\text { Source } & \text { SS } & \text { df } \
\mathrm { X } _ { 1 } & 535.9569 & 1 \
\mathrm { X } _ { 2 } & 1,167.5634 & 1 \
\mathrm { X } _ { 3 } & 18.9886 & 1 \
\text { Error } & 3,459.6803 & 8
\end{array}$$
-What is the proportion of the variation explained by the multiple regression model?
A).53
B).12
C).18
D).19
E).33

Question

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\mathrm { X } _ { 1 } & 535.9569 & 1 \
\mathrm { X } _ { 2 } & 1,167.5634 & 1 \
\mathrm { X } _ { 3 } & 18.9886 & 1 \
\text { Error } & 3,459.6803 & 8
\end{array}$$
-What is the proportion of the variation explained by the multiple regression model?
A).53
B).12
C).18
D).19
E).33

Quizplus · Accepted Answer

The proportion of the variation explained by the multiple regression model is calculated using the formula $R^2 = \frac{SS_{\text{Regression}}}{SS_{\text{Total}}}$, where $SS_{\text{Regression}}$ is the sum of squares due to regression (sum of the SS for $X_1$, $X_2$, and $X_3$) and $SS_{\text{Total}}$ is the total sum of squares (sum of $SS_{\text{Regression}}$ and $SS_{\text{Error}}$). Here, $SS_{\text{Regression}} = 535.9569 + 1,167.5634 + 18.9886 = 1,722.5089$ and $SS_{\text{Total}} = 1,722.5089 + 3,459.6803 = 5,182.1892$. Thus, $R^2 = \frac{1,722.5089}{5,182.1892} \approx 0.33$ or 33%.

Below Is a Partial Multiple Regression ANOVA Table -What Is the Proportion of the Variation Explained by the l