xy r = = . Example . The following table shows the sales and advertisement expenditure of a form Title Sales Advertisement expenditure ( ` in Crores) Mean SD . - - Coefficient of correlation r = .
. Estimate the likely sales for a proposed advertisement expenditure of Rs. crores. Let the sales be X and advertisement expenditure be Y Given X = , Y = , σ x = , σ y = .
and r = . Equation of line of regression x on y is X – X = r v v (Y– Y ) X – = ( . ) . ( Y – ) X – = Y – X = Y + When advertisement expenditure is crores i.e., Y = then sales X = ( )+ = which implies sales is .
Example . There are two series of index numbers P for price index and S for stock of the commodity. The mean and standard deviation of P are and and of S are and respectively. The correlation coefficient between the two series is .
. With these data obtain the regression lines of P on S and S on P . Let us consider X for price P and Y for stock S . Then the mean and SD for P is considered as X = and σ x = .
respectively and the mean and SD of S is considered as Y = and σ y = . The correlation coefficient between the series is r ( X , Y ) = . Let the regression line X on Y be = r v v (Y– Y ) X – = ( . ) (Y– ) X – = .
(Y– ) X – .8Y– . = (or) X = . Y + . The regression line Y on X be Y – Y = r v v (X– X ) Y – = ( .