: X – X = b xy (Y- Y ) X – = . ( Y – ) X – = . Y – . ` The regression equation X on Y is X = .
Y – . . - - Correlation and Regression analysis (ii) Regression coefficient of Y on X: b yx = N N XY Y - ] ]g = ` b yx = . (iii) Regression equation of Y on X: Y – Y = b yx (X– X ) Y– = .
` The regression equation of Y on X is Y = . X + . Example . Calculate the two regression equations of X on Y and Y on X from the data given below, taking deviations from a actual means of X and Y .
Price ( ` ) Amount demanded Estimate the likely demand when the price is ` . Calculation of Regression equation (i) Regression equation of X on Y: X– X = r v v ( Y–Y ) From the Table . , we get X = = , Y = = b xy = r v v xy = =– . X – = – .
(Y– ) X– = – .12Y+ . X = – .12Y+ . x = ( X – ) x – – – ∑ X = ∑ x = ∑ x = Y y = ( Y – ) y xy – – – – – ∑ Y = ∑ y = ∑ y = ∑ xy = – Table . (ii) Regression Equation of Y on X: Y– Y = r v v ( X – X ) b yx = r v v xy = – =– .