After having an understanding about the concept and application of simple correlation and simple regression, we can draw the difference between them. They are:
1) Correlation coefficient ‘r’ between two variables (X and Y) is a measure of the direction and degree of the linear relationship between them, which is mutual. It is symmetric (i.e., rxy = ryx ) and it is inconsiderable which, of X and Y, is dependent variable and which is independent variable. Whereas regression analysis aims at establishing the functional relationship between the two variables under study, and then using this relationship to predict the value of the dependent variable for any given value of the independent variable. It also reflects upon the nature of the variables (i.e., which is the dependent variable and which is independent variable). Regression coefficients, therefore, are not symmetric in X and Y (i.e., rxy≠ ryx ).
2) Correlation need not imply cause and effect relationship between the variables under study. But regression analysis clearly indicates the cause and effect relationship between the variables. The variable corresponding to cause is taken as independent variable and the variable corresponding to effect is taken as dependent variable.
3) Correlation coefficient ‘r’ is a relative measure of the linear relationship between X and Y variables and is independent of the units of measurement. It is a number lying between ±1. Whereas the regression coefficient byx (or bxy) is an absolute measure representing the change in the value of the variable Y (or X) for a unit change in the value of the variable X (or Y). Once the functional form of the regression curve is known, by susbstituting the value of the dependent variable we can obtain the value of the independent variable which will be in the unit of measurement of the variable.
4) There may be spurious (non-sense) correlation between two variables which is due to pure chance and has no practical relevance. For example, the correlation between the size of shoe and the income of a group of individuals. There is no such thing as spurious regression.
5) Correlation analysis is confined only to study of linear relationship between the variables and, therefore, has limited applications. Whereas regression analysis has much wider applications as it studies linear as well as non-linear relationships between the variables.
