Question

Calculate the pearson correlation coefficient for the following data

X 7 2 8 4 5

Y 4 4 7 6 7

Answer 1

The Pearson correlation coefficient formula is given below,

$r=\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n\Sigma X^2-(\Sigma X)^2][n\Sigma Y^2-(\Sigma Y)^2]}}$, where $n=$ sample size

To find Pearson correlation coefficient of the given data, we first calculate the following table

Here $n=5$ .

$\therefore$ $r=\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n\Sigma X^2-(\Sigma X)^2][n\Sigma Y^2-(\Sigma Y)^2]}}$ $=\frac{(5×151)-(26×28)}{\sqrt{[(5×158)-(26)^2].[(5×166)-(28)^2]}}$ $=\frac {27}{\sqrt {5244}}=0.37$ (approximately)