X+ . Y = – . X+ . - - When X is , Y will be Y = – .
( )+ . = – + . = . (when the price is ` , the likely demand is .
) Example . Obtain regression equation of Y on X and estimate Y when X = from the following: Y Y dx = ( X– ) dx dy = ( Y– ) dy dxdy – – – – - - - - ∑ X = ∑ Y = ∑ dx = ∑ dx = ∑ dy = ∑ dy = ∑ dxxy = Table . X = N = = . Y = N Y = = .
(i) Regression coefficients of Y on X: b yx = N N dx dy dy - ] ^ g = = = . b yx = . (ii) Regression equation of Y on X : Y Y = b yx Y – . = .
X+ . ` The regression equation of Y on X is Y = . X + . Estimation of Y when X = Y = .
( )+ . = . Example . Find the means of X and Y variables and the coefficient of correlation between them from the following two regression equations: Y –X– = 3Y–2X– = .
We are given Y – X – = ... ( ) 3Y–2X– = ... ( ) 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