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 sample correlation coefficient equals
A) .8045.
B) -.8045.
C) .3528.
D) -.3528.

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 sample correlation coefficient equals
A) .8045.
B) -.8045.
C) .3528.
D) -.3528.

Quizplus · Accepted Answer

The sample correlation coefficient is calculated as:$$r = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sqrt{\sum (x - \bar{x})^2 \sum (y - \bar{y})^2}}$$Plugging in the given values, we get:$$r = \frac{466}{\sqrt{234 * 1434}} = 0.8045$$Therefore, the correct answer is A.

A Regression and Correlation Analysis Resulted in the Following Information