regression coefficient are negative r is negative) ` r = – . Example . In a laboratory experiment on correlation research study the equation of the two regression lines were found to be 2X– Y + = and X – Y + = . Find the means of X and Y .
Also work out the values of the regression coefficient and correlation between the two variables X and Y . Solving the two regression equations we get mean values of X and Y. 2X–Y = – ... ( ) 3X–2Y = – ...
( ) Solving equation ( ) and equation ( ) We get X = and Y = . Therefore the regression line passing through the means X = and Y = . The regression equation of Y on X is X – Y =– Y = X + Y = ( X + ) Y = X + ` b yx = (> ) The regression equation of X on Y is X – Y = – X = Y – X = Y X = Y ` b xy = The regression coefficients are positive r = ± xy yx = ± = . ` r = .
Example . For the given lines of regression X – Y =5and X– Y = . Find (i) Regression coefficients (ii) Coefficient of correlation - - (i) First convert the given equations Y on X and X on Y in standard form and find their regression coefficients respectively. Given regression lines are 3X–2Y = ...
( ) X– Y = ... ( ) Let the line of regression of X on Y is 3X– Y = X = Y + X = (2Y+ ) X = (2Y+ ) X = Y+ ` Regression coefficient of X on Y is b xy = (< ) Let the line of regression of Y on X is X – Y = – Y = – X + Y =