What is the main difference between correlation analysis and regression analysis?

(1) The correlation answers the STRENGTH of linear association between paired variables, say X and Y. On the other hand, the regression tells us the FORM of linear association that best predicts Y from the values of X. 

(2a) Correlation is calculated whenever: 

* both X and Y is measured in each subject and quantify how much they are linearly associated. 

* in particular the Pearson's product moment correlation coefficient is used when the assumption of both X and Y are sampled from normally-distributed populations are satisfied 

* or the Spearman's moment order correlation coefficient is used if the assumption of normality is not satisfied. 

* correlation is not used when the variables are manipulated, for example, in experiments.

(2b) Linear regression is used whenever: 

* at least one of the independent variables (Xi's) is to predict the dependent variable Y. Note: Some of the Xi's are dummy variables, i.e. Xi = 0 or 1, which are used to code some nominal variables. 

* if one manipulates the X variable, e.g. in an experiment. 

(3) Linear regression are not symmetric in terms of X and Y. That is interchanging X and Y will give a different regression model (i.e. X in terms of Y) against the original Y in terms of X. On the other hand, if you interchange variables X and Y in the calculation of correlation coefficient you will get the same value of this correlation coefficient. 

(4) The "best" linear regression model is obtained by selecting the variables (X's) with at least strong correlation to Y, i.e. >= 0.80 or <= -0.80 

(5) The same underlying distribution is assumed for all variables in linear regression. Thus, linear regression will underestimate the correlation of the independent and dependent when they (X's and Y) come from different underlying distributions.