Regression means stepping back towards the average. In statistics regression analysis is applicable to all those fields where two or more related variables have the tendency to go back to mean.
According to Blair “Regression is the measure of average relationship between two or more variables in terms of original units of data.”
The chief objective of Regression analysis is to know the nature of relationship between two variables and to use it for predicting the most likely value of the dependent variable corresponding to a given known value of the independent variable. However it may be noted that the regression relation is not reversible, i.e.,
The regression equation used to predict the value of Y from a given value of X can not be used to predict the value of X from a given value of Y.
So, the regression relation is average, irreversible and functional relation.
Methods of Studying Regression Regression can be studied either;
Graphically
Algebraically
In graphical method a scatter plot for the series must be prepared and two regression lines are drawn for predicting the values of X and Y variables.
The regression lines that is used to predict the value of Y on the basis of X is known as Y on X and the line which is used to predict the value of X for known value of Y is known as X on Y.
In case of perfect correlation between X and Y (+1 or -1) there is only one regression line. In other words, the two lines are identical.
Methods of Studying Regression
Whenever a straight line is drawn to represent changes in dependent variable with respect to independent variable, the regression is known as Linear regression. If however the relationship between two variables can not be represented through straight line the regression is known as Non-Linear regression.
Regression lines can be drawn by one of the following methods:
Free hand curve method
Method of least squares
Free Hand Curve
Plot the pair values of X and Y through scatter diagram
Draw first regression line in such a way that positive deviations of all points from axis of Y gets cancelled by negative deviations of all points from axis of Y. This line is called Y on X.
Draw second regression line in such a way that positive deviations of all points from axis of X gets cancelled by negative deviations of all points from axis of X. This line is called X on Y.
The two regression lines cut each other at a point, that point is known as mean point of two series.
Method of Least Squares
In order to avoid difficulties related to free hand curve drawing method, a mathematical relationship is established between the movements of X and Y series and the algebraic equations are obtained to represent the relative movements of X and Y series.
The two normal equations that represented by:
Comments