Regression literally means ―return‖or ―go back‖. In the 19th century, Francis Galton at first used regression in his paper ―Regression towards Mediocrity in Hereditary Stature‖ for the study of hereditary characteristics.
Use of regression in modern times is not limited to hereditary characteristics only but it is widely used for the study of expected dependence of one variable on the other.
Therefore, the method by which best probable values of unknown data of a variable are calculated for the known values of the other variable is called regression.
Regression helps in forecasting, decision making and in studying two or more variables in economic field. It also shows the direction, quality and degree of correlation.
Regression Lines :
Regression line is that line which gives the best estimate of dependent variable for any given value of independent variable. If we take the case of two variables X and Y, we shall have two regression lines as the regression of X on Y and the regression of Y on X.
Regression Line X and Y : In this formation, Y is independent and X is dependent variable, and best expected value of X is calculated corresponding to the given value of Y.
Regression Line Y on X : Here Y is dependent and X is independent variable, best expected value of Y is estimated equivalent to the given value of X.
An important reason of having two regression lines is that they are drawn on least square assumption which stipulates that the sum of squares of the deviations from different points to that line is minimum. The deviations from the points from the line of best fit can be measured in two ways – vertical, i.e. parallel to Y – axis, and horizontal i.e. parallel to X axis.
For minimizing the total of the squares separately, it is essential to have two regression lines.
Single line of Regression : When there is perfect positive or perfect negative correlation between the two variables (r = ±1) the regression lines will coincide or overlap and will form a single regression line in that case.
