Regression is the measure of the average relationship between two or more variable in terms of the original units of the data. It is a statistical tool with the help of which the unknown values of one variable can be estimated from known values of another variable.
Kinds of Regression
Kinds of Regression may be studied on the basis of:
1. Change in proportions
2. Number of variation
1. Basis of Change in Proportion: There are two important regressions on the basis of change in proportion. They are:
(a) Linear regression
(b) Non-linear regression
(a) Linear Regression: Regression is said to be linear when one variable move with the other variable in fixed proportion
(b) Non-Linear Regression: Regression is said to be non-linear when one variable move with the other variable in changing proportion.
2. Basis of Number of Variables: On the basis of number of variables, regression may be:
(a) Simple
(b) Partial
(c) Multiple
(a) Simple Regression: When only two variables are studied it is a simple regression.
(b) Partial Regression: When more than two variables are studied keeping other variables constant, it is called partial regression.
(c) Multiple Regressions: When at least three variables are studied and their relationships are simultaneously worked out, it is a case of multiple regressions.
Uses of Regression:
(1) Helpful to statisticians: The study of regression helps the statisticians to estimate the most probable value of one variable of a series for the given values of the other related variables of the series.
(2) Nature of relationship: Regression is useful in describing the nature of the relationship between two variables.
(3) Estimation of relationship: Regression analysis is widely used for the measurement and estimation of relationship among economic variables.
(4) Predictions: Regression analysis is helpful in making quantitative predictions on the basis of estimated relationship among variables.
(5) Policy formulation: The predictions made on the basis of estimated relationship are used in policy making.
Limitations of Regression:
(1) No change in relationship: Regression analysis is based on the assumption that while computing regression equation; the relationship between variables will not change.
(2) Conditions: The application of regression analysis is based on certain conditions like, for existence of linear relationship between the variables; exact values are needed for the independent variable.
(3) Spurious relationships: There may be nonsense and spurious regression relationships. In such case, the regression analysis is of no use.
Difference between Correlation and Regression:
(1) Nature of relationship: Correlation explains the degree of relationship, whereas regression explains the nature of the relationship.
(2) Causal relationship: Correlation does not explain the cause behind the relationship whereas regression studies the cause and effect relationship.
(3) Prediction: Correlation does not help in making prediction whereas regression enable us to make prediction.
(4) Origin and scale: Correlation coefficient is independent of the change of origin and scale, whereas regression coefficient is independent of change of origin but not of scale.