#### Question

The regression equation of Y on X is y = `2/9` xand the regression equation of X on Y is `x=y/2+7/6`

Find : (i) Correlation coefficient between X and Y.

(ii) `σ_y^2 if σ _x^2=4`

#### Solution

The repression eqn. of y on x is y =`2/9x`

Comparing with y − `barY = b_yx (x − barx)`

Here ` b_yx=2/9`

Now the regression eqn. of x on y is x =`y/2+7/6`

Comparing with` x-barx=bxy=1/2`

(a) we have, correlation coefficient between x and y is

`r=sqrt(b_(yx) b_(xy))`

=`sqrt2/9xx1/2=sqrt1/9+-1/3`

∴ `r=1/3 (∵b_(yx) and b_(xy) "are positive")`

(b) `σ_x^2=4⇒ σ_x=2`

We have `b_yx= r.σ_y/σ_x`

∴ `2/9=1/3 σ_y/2`

⇒ `σ_y=12/9`

⇒ `σ_y=4/3`

Is there an error in this question or solution?

#### APPEARS IN

Solution The Regression Equation of Y on X is Y = 2 9 Xand the Regression Equation of X on Y is X = Y 2 + 7 6 Find : (I) Correlation Coefficient Between X and Y. (Ii) σ 2 Y If σ 2 X = 4 Concept: Statistics - Bivariate Frequency Distribution.