in different cases are described as follows. Case : When the actual values are taken When we deal with actual values of X and Y variables the two regression equations and their respective coefficients are written as follows: (i) Regression Equation of X on Y: = b xy Y Y where X is the mean of X series, Y is the mean of Y series, b xy = r v v = N Y Y N XY Y - ] ]g g is known as the regression coefficient of X on Y , and r is the correlation coefficient between X and Y , σ x and σ y are standard deviations of X and Y respectively. (ii) Regression Equation of Y on X ; Y Y = b yx where X is the mean of X series, Y is the mean of Y series, b yx = r x v v = )( N Y Y N XY Y is known as the regression coefficient of Y on X , and r is the correlation coefficient between X and Y, σ x and σ y are standard deviations of X and Y respectively. Case : Deviations taken from Arithmetic means of X and Y The calculation can very much be simplified instead of dealing with the actual values of X and Y , we take the deviations of X and Y series from their respective means.
In such a case the two regression equations and their respective coefficients are written as follows: (i) Regression Equation of X on Y: = b xy ( Y Y where X is the mean of X series, Y is the mean of Y series, b xy = r v v = xy is known as the regression coefficient of X on Y , x = ( X – X ) and y = ( Y – Y ) - - (ii) Regression Equation of Y on X ; Y–Y = b yx X where X is the mean of X series, Y is the mean of Y series, b yx