Answer to Question #104684 in Economics for Pulkit

Question

Find coefficient of correlation, if variance of X series=2.25, standard deviation of Y series=4and regression equation of X on Y is X+0.3Y=1.8

Answer 1

Formula for coefficient of correlation is the following:

$r=\frac{cov(x,y)}{\sigma_{x}\times \sigma_{x}\times\sigma_{y}\times\sigma_{y}}$

In the regression equation, which is the equation of the type 

$y=a+bx$  , coefficient $b$  has the following meaning:

$b=\frac{cov(x,y)}{\sigma_{x}\times\sigma_{x}}$

Therefore, coefficient of correlation can be written:

$r=\frac{b}{\sigma_{y}\times\sigma_{y}}$

Coefficient b of our regression equation is 

$\frac{1}{0.3}=3.33$

$r=\frac{3.33}{16}=0.208$