Difference Between Correlation and Regression Analysis

Correlation and regression analysis are constructed under different assumptions, they furnish different types of information and it is not always clear as to which measure should be used in a given problem situation. The following are the points of difference between the two:

1.    Whereas correlation coefficient is a measure of degree of co variability between X and Y, the objective of regression analysis is to study the ‘nature of relationship’ between the variables so that we may be able to predict the value of one on the basis of another.

2.    Correlation is merely a tool of ascertaining the degree of relationship between two variables and, therefore, we cannot say that one variable is the cause and other the effect. However, in regression analysis one variable is taken as dependent while the other as independent – thus making it possible to study the cause and effect relationship. It should be noted that the presence of association does not imply caution, but the existence of causation always implies association. Statistical evidence can only establish the presence or absence of association between variables, whether causation exists or not depends purely on reasoning.

3.    In correlation analysis r_xy is a measure of direction and degree of linear relationship between two variables X and Y. rxy  and r_yx are systematic (r_xy = r_yx ) i.e., it is immaterial which of X and Y is dependent variable and which is dependent variable. In regression analysis the regression coefficient b_xy and b_yx are not symmetric, i.e., b_xy ≠ b_yx and hence it definitely makes a difference as to which variable is dependent and which is independent.

4.    There may be nonsense correlation between two variables which is purely due to change and has no practical relevance such as increase in income and increase in weight of a group of people. However, there is nothing like nonsense regression.

5.    Correlation coefficient is independent of change of scale and origin while regression coefficients are independent of change of origin but not of scale.
 
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