Q.Calculate the correlation co-efficient from the following data : $N = 9$, $\sum X = 45$, $\sum Y = 108$, $\sum X^2 = 285$, $\sum Y^2 = 1356$, $\sum XY = 597$.

$r=\dfrac{N\sum XY-\sum X\sum Y}{\sqrt{[N\sum X^2-(\sum X)^2][N\sum Y^2-(\sum Y)^2]}}=\dfrac{513}{\sqrt{540\times540}}=\dfrac{513}{540}=0.95$.

A Karl Pearson correlation computation from the Correlation and Regression unit of the Tamil Nadu HSC Class-11 Business Statistics syllabus.

Step 1 — Formula.

$r=\frac{N\sum XY-\sum X\sum Y}{\sqrt{\big[N\sum X^2-(\sum X)^2\big]\big[N\sum Y^2-(\sum Y)^2\big]}}.$

Step 2 — Numerator. $N\sum XY-\sum X\sum Y=9(597)-45(108)=5373-4860=513.$

Step 3 — Denominator terms. …