Regression equation is an equation that expresses the linear relationship between two variables. It is an algebraic expression of the regression line. Since there are two regression lines, there are two regression equations—the regression equation of X on Y is used to describe the variations in the values of X for given changes in Y and the regression equation of Y on X is used to describe the variations in the values of Y for given changes in X.
Regression equation of Y on X
The regression equation of Y on X is expressed as follows:
Y
= a
+ bX
= a + bXWhere Y is the dependent variable to be estimated and X is the independent variable. The parameter ‘a’ determines the level of the fitted line. The parameter ‘b’ determines the slope of the line, i.e., the change in Y for unit change in X.
is the dependent variable to be estimated and X is the independent variable. The parameter ‘a’ determines the level of the fitted line. The parameter ‘b’ determines the slope of the line, i.e., the change in Y for unit change in X. b = 
= a = 
- b
= - bRegression equation of X on Y
The regression equation of X on Y is expressed as follows:
X= a
+ bY
= a+ bY The parameter ‘a’ determines the level of the fitted line. The parameter ‘b’ determines the slope of the line, i.e., the change in X for unit change in Y.
b = 
= a = - b
= - bIllustration: Calculate the regression equation of Profit on Capital and Capital on Profit from the following data.
| Capital (X) | Profit (Y) |
| 5 | 2 |
| 10 | 3 |
| 15 | 5 |
| 20 | 8 |
| 25 | 12 |
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