Question

Calculate the coefficient of correlation between $X$ and $Y$ series from the following data:
$n=15,\overline{x}=25,\overline{y}=18,{\sigma }_X=3.01,{\sigma }_Y=3.03,\sum (x_i-\overline{x})(y_i-\overline{y})=122$.

Answer 1

Correlation $=\rho =\frac{Cov(X,Y)}{{\sigma }_x{\sigma }_y}$

$Cov(x,y)=\sum _{i=1}^n\frac{(X_i-\overline{X})(Y_i-\overline{Y})}{n-1}$

$Cov(X,Y)=\frac{122}{14}=\frac{61}{7}$

$\rho =\frac{61}{7\left(3.01\right)\left(3.01\right)}=0.955$