Question

Find Karl Pearson's correlation coefficient if N = 50, $\sum X=75,\sum Y=80,\sum X^2=130,\sum Y^2=140$ and $\sum XY=128$.

Answer 1

Using Product moment method:

$r=\frac{N\sum XY-\sum X\sum Y}{\sqrt{N\times \sum X^2-(\sum X{)}^2}\sqrt{N\times \sum Y^2-(\sum Y{)}^2}}=\frac{50\times 128-\left(75\right)\left(80\right)}{\sqrt{50\times 130-(75{)}^2}\sqrt{50\times 140-(80{)}^2}}=\frac{6400-6000}{\sqrt{6500-5625}\sqrt{7000-6400}}=\frac{400}{\sqrt{875}\sqrt{600}}=\frac{400}{724.57}=0.55$