A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | }
\hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \
\hline \text { Irtercept } & 624.5369 & 78.49712 & 7.956176 & 6.88 E - 06 \
\hline \boldsymbol { x } _ { 1 } & 8.569122 & 1.652255 & 5.186319 & \mathbf { 0 . 0 0 0 3 0 1 } \
\hline \mathbf { x } _ { 2 } & 4.736515 & 0.699194 & 6.774248 & \mathbf { 3 . 0 6 E - 0 5 } \
\hline
\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \
\hline \text { Repression } & 2 & 1660914 & \mathbf { 8 3 0 4 5 7 . 1 } & 58.31956 & 1.4 \mathrm { E } - 06 \
\hline \text { Residual } & 11 & 156637.5 & 14239.77 & & \
\hline \text { Total } & 13 & 1817552 & & & \
\hline
\end{array}$$ The coefficient of multiple determination is ____________.
A)0.0592
B)0.9138
C)0.1149
D)0.9559
E)1.0000

Question

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } 
\hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \
\hline \text { Irtercept } & 624.5369 & 78.49712 & 7.956176 & 6.88 E - 06 \
\hline \boldsymbol { x } _ { 1 } & 8.569122 & 1.652255 & 5.186319 & \mathbf { 0 . 0 0 0 3 0 1 } \
\hline \mathbf { x } _ { 2 } & 4.736515 & 0.699194 & 6.774248 & \mathbf { 3 . 0 6 E - 0 5 } \
\hline
\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \
\hline \text { Repression } & 2 & 1660914 & \mathbf { 8 3 0 4 5 7 . 1 } & 58.31956 & 1.4 \mathrm { E } - 06 \
\hline \text { Residual } & 11 & 156637.5 & 14239.77 & & \
\hline \text { Total } & 13 & 1817552 & & & \
\hline
\end{array}$$ The coefficient of multiple determination is ____________.
A)0.0592
B)0.9138
C)0.1149
D)0.9559
E)1.0000

Quizplus · Accepted Answer

The coefficient of multiple determination, $R^2$, is calculated as the ratio of the regression sum of squares (SS) to the total sum of squares (SS). From the tables, the regression SS is 1660914 and the total SS is 1817552. Thus, $R^2 = \frac{1660914}{1817552} = 0.9138$, indicating that approximately 91.38% of the variability in the dependent variable can be explained by the model.

A Multiple Regression Analysis Produced the Following Tables The Coefficient of Multiple Determination Is ____________