A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). $$\begin{array} { l l }
\Sigma x = 90 & \sum \left( y - \frac { y } { x } \right) \left( x - { } ^ { x } \right) = 466 \
\Sigma y = 170 & \sum ( x - ) ^ { 2 } = 234 \
n = 10 & \Sigma \left( y - y ^ { 2 } \right) ^ { 2 } = 1434 \
\mathrm { SSE } = 505.98 &
\end{array}$$ The coefficient of determination equals
A) .6472.
B) .3528.
C) .8045.
D) .5490.

Question

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). $$\begin{array} { l l } 
\Sigma x = 90 & \sum \left( y - \frac { y } { x } \right) \left( x - { } ^ { x } \right) = 466 \
\Sigma y = 170 & \sum ( x - ) ^ { 2 } = 234 \
n = 10 & \Sigma \left( y - y ^ { 2 } \right) ^ { 2 } = 1434 \
\mathrm { SSE } = 505.98 &
\end{array}$$  The coefficient of determination equals
A) .6472.
B) .3528.
C) .8045.
D) .5490.

Quizplus · Accepted Answer

The coefficient of determination is equal to the square of the correlation coefficient. The correlation coefficient is calculated as follows:$$r = \frac{\sum (x - \overline{x})(y - \overline{y})}{\sqrt{\sum (x - \overline{x})^2 \sum (y - \overline{y})^2}}$$Plugging in the given values, we get:$$r = \frac{466}{\sqrt{234 * 1434}} = 0.8045$$Therefore, the coefficient of determination is:$$r^2 = 0.8045^2 = 0.6472$$

A Regression and Correlation Analysis Resulted in the Following Information