# 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 - Mathematics and Statistics

Sum

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

Find:

1.  The correlation coefficient between X and Y.
2.  σ_y^2 if σ _x^2=4

#### Solution

The repression equation 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")

therefore r = 0.33

(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

therefore ""σ_y^2= 16/9

Is there an error in this question or solution?