For pairs of observations the following results are obtained ∑ X = , ∑ Y = , ∑ X = , ∑ Y = , ∑ XY = Find the equation of the lines of regression and estimate the value of X on the first line when Y = and value of Y on the second line if X = . Here N = , X = N = = , Y = N Y = = and the regression coefficient b xy = N Y Y N XY X Y R R = g = . The regression line of X on Y is X – X = b xy ( Y – Y ) X – = . ( Y – ) X = .
Y – When Y = , the value of X is estimated as X = . ( )– = . The regression coefficient b yx = N X N XY X Y R R g = . Thus b yx = .
then the regression line Y on X is Y – Y = b yx ( X – X ) Y – = . ( X – ) Y = .8X+ . - - Correlation and Regression analysis When X = the value of Y is estimated as Y = . ( )+ .
Y = Example . The two regression lines are X + Y = and X + Y = . Find the correlation coefficient. Let the regression equation of Y on X be X + Y = Y = – X + Y = (– X + ) Y = – .
X + v v = – . Implies by x = r v v =– . Let the regression equation of X on Y be X + Y = X = (– Y + )=– . Y + .
v v = – . Implies b xy = r v v =– . r = ± xy yx = – g (Since both the