Question

$\sum(x - \bar{x})(y - \bar{y}) = 54$
$\sum(y - \bar{y})^2 = 112$
$\sum(x - \bar{x})^2 = 30$
$r=\frac{\sum((x - \bar{x})(y - \bar{y}))}{sqrt{\sum(x - \bar{x})^2\times\sum(y - \bar{y})^2}}$
use the values and formula above to calculate pearsons $r$.
$\bigcirc 0.95$
$\bigcirc 0.93$
$\bigcirc 0.85$
$\bigcirc 0.97$
$\bigcirc 0.91$

Explanation:

Step1: Substitute given values

Given $\sum(x - \bar{x})(y - \bar{y})=54$, $\sum(x - \bar{x})^2 = 30$, $\sum(y - \bar{y})^2=112$. Substitute into the formula $r=\frac{\sum((x - \bar{x})(y - \bar{y}))}{\sqrt{\sum(x - \bar{x})^2\times\sum(y - \bar{y})^2}}$.
So $r=\frac{54}{\sqrt{30\times112}}$.

Step2: Calculate denominator

First calculate $30\times112 = 3360$. Then $\sqrt{3360}\approx57.96$.

Step3: Calculate $r$

$r=\frac{54}{57.96}\approx0.93$.

Answer:

0.93