Re: Maths n Stats

Posted by Manvendra on Apr 28, 2012; 9:01am
URL: http://discussion-forum.276.s1.nabble.com/Maths-n-Stats-tp7508328p7508390.html

Q5 :

In an analysis of bivariate data (X and Y) the following results were obtained.
Variance of X (s x2) = 9 , product of the regression coefficient of Y on X and X on Y is 0.36, and the regression coefficient from the regression of Y on X (b yx ) is 0.8.

A : 16

var ( X ) = 9

product of regression coefficient of Y on X and X on Y = 0.36

  {mean(XY) - mean(X) mean(Y)} / var(X) = regression coefficient of Y on X = 0.8
  {mean(XY) - mean(X) mean(Y)} / var(Y) = regression coefficient of X on Y.

Now,

0.36 = {mean(XY) - mean(X) mean(Y)} / var(X)  *  {mean(XY) - mean(X) mean(Y)} / var(Y)
0.36 = 0.8 * 0.8 * 9 / var(Y)

var(Y) = .8 * .8 * 9 / .36 = 16