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 $r$.
o 0.95
o 0.91
o 0.85
o 0.97
o 0.93

Explanation:

Step1: Identify given values

$\sum(x - \bar{x})(y - \bar{y})=54$, $\sum(y - \bar{y})^2 = 112$, $\sum(x - \bar{x})^2=30$

Step2: Substitute into formula

$r=\frac{\sum((x - \bar{x})(y - \bar{y}))}{\sqrt{\sum(x - \bar{x})^2\times\sum(y - \bar{y})^2}}=\frac{54}{\sqrt{30\times112}}$

Step3: Calculate denominator

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

Step4: Calculate r

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

Answer:

0.93