Question

Calculate the coefficient of correlation, if:
(i) Covariance between X and Y = 9.2
(ii) Variance of X = 11.5
(iii) Variance of Y = 14.2

Answer 1

Given, Cov(x,y) = 9.2

$$\begin{gathered} {\mathrm{\sigma }}_x^2=11.5\Rightarrow {\mathrm{\sigma }}_x^{}=3.39 \\ {\mathrm{\sigma }}_y^2=14.2\Rightarrow {\mathrm{\sigma }}_y^{}=3.76 \\ \mathrm{Now}, \\ r=\frac{\mathrm{Cov}\left(x,y\right)}{{\mathrm{\sigma }}_x^{}{\mathrm{\sigma }}_{\mathrm{y}}^{}} \\ \mathrm{Substituting}\mathrm{the}\mathrm{given}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{formula}\mathrm{we}get, \\ \mathrm{or},r=\frac{9.2}{3.39\times 3.76} \\ \Rightarrow r=0.721 \end{gathered}$$

Hence, coefficient of correlation is 0.721.