( ) be the regression equation of Y on X. - - Correlation and Regression analysis Y = X + Y = X + therefore b yx = Clearly equation ( ) would be treated as regression equation of X on Y Y – X – = X = Y – X = Y – therefore b xy = The Correlation coefficient r = ± xy yx r = = . NOTE It may be noted that in the above problem one of the regression coefficient is greater than and the other is less than . Therefore our assumption on given equations are correct.
Example . Find the means of X and Y variables and the coefficient of correlation between them from the following two regression equations: X – Y + = 20X–9Y– = We are given X – Y + = ... ( ) X – Y – = ... ( ) Solving equation ( ) and ( ) We get Y = Putting the value of Y in equation ( ) We get X = Hence X = and Y = Calculating correlation coefficient Let us assume equation ( ) be the regression equation of X on Y 4X = Y – X = ( Y – ) X = Y – b xy = = .
Let us assume equation ( ) be the regression equation of Y on X Y = X – Y = ( X – ) Y = X – b yx = = . But this is not possible because both the regression coefficient are greater than . So our above assumption is wrong. Therefore treating equation ( ) has regression equation of Y on X and equation ( ) has regression equation of X on Y .
So we get b yx = = . and b xy = = . The Correlation coefficient r = ± xy