Difference between Correlation and Regression Analysis

1.**Degree and Nature of Relationship:** Coefficient of correlation measures the degree of covariance between two variables whereas the regression analysis tells about the nature of relationship between the variable so that one may be able to estimate or predict the value of one variable on the basis of another.

2**. Cause and Effect Relationship**: Correlation mearly acertains the degree of relationship between two variables and therefore one cannot say that one variable is the cause and other is the effect. In regression analysis one variable is taken as dependent variable while the other variable is taken as independent variable .Thus making it possible to study the cause and effect relationship.

3. The value of rx_{y } in the calculation of coefficient of correlation measured the direction and degree of relationship between two variable say x and y. The values of Ryx Symmetric , it shows that it is immaterial which of X and Y is dependent variable and which is independent variable. However in the case of regression analysis coefficients i.e. by xy are not symmetric i.e. b _{xy} * b_{yx} and therefore it certainly makes a difference as to which variable is dependent and which one is independent.

4. In case of correlation, there may be nonsense correlation between two variables X and Y which is due to merely chance and may not have any practical relevance, such as increase in income and increase of environmental temperature. However there cannot be a nonsense regression.

5. The value of coefficient of correlation is independent of changes of scale and point of origin. However regression coefficients are independent of changes of origin but not of scale.

6. While pointing out the difference between regression and correlation Werner z .Hirsch rightly stated that. While correlation analysis tests the closeness with which two phenomena co vary, regression analysis measured the nature and extent of the relation, that enabling us to make prediction.