ADVERTISEMENTS:
The following points highlight the top three types of regression equations. The types are: 1. Regression Equation of Y on X 2. Regression Equation of Regression Line X on Y 3. Regression Equation of X on Y.
Type # 1. Regression Equation of Y on X:
Regression equation of Y on X= yx = a + b where X and Y are variables and ‘a’ and ‘b’ are unknown constants. Constant a is distance between the point of origin and the point where the regression line touches Y axis. Constant b is the steepness or slope of line and is also called coefficient of regression. It indicates that for every unit change in X, there will be two unit change in Y.
Constants ‘a’ and ‘b’ can be obtained by the following formulae:
Type # 2. Regression Equation of Regression Line X on Y:
Type # 3. Regression Equation of X on Y:
Since the magnitude of coefficient of correlation does not exceed 1, the value of regression coefficients bxy and byx will not be more than 1.
ADVERTISEMENTS:
The value of r may be both positive (+) and negative (-). The positive or negative value of coefficient of correlation r is expressed on the basis of positive or negative value of two regression coefficients. If both the regression coefficients are positive, the correlation coefficients will be positive and if the two regression coefficients are negative, the coefficient of correlation will be negative.
If the arithmetic means of deviations of two series is not considered and assumed mean is considered in place of that, the values of two regression coefficients will be expressed as follows:
where dx = deviation from the consumed mean (A) or dxy = (X-A)
and dy = deviation from assumed mean (B) or dy = (Y-B).
Regression Equation through Least Square Method:
Regression equation can be derived through least square method. Linear regression equations are the equations of those lines of best fit which are made on the basis of least square method. In this method ‘a’ and ‘b’ are determined of regression equation.
It is noteworthy here that in both the regression equations value of a and b are different. 
