Difference between Correlation and Regression

This is the question I have faced many times while appearing for interviews. The answer is very simple, but I was not able to present properly.

Here is the proper answer to this question:

Here correlation means Karl Pearson's correlation coefficient

To put it simply, the correlation coefficient is the square root of the R-sq of regression.

• Correlation shows the linear relationship between two variables, But regression is used to fit a line and predict one variable based on another variable.

• Correlation is used in quantification of the association between two variables, But regression is used to identify the effect of one unit change in an independent variable (x) on dependent variable (y).

• In correlation, there is no difference between dependent and independent variable. Correlation between x and y will be as same as the correlation between y and x. But Regression of y on x will be different from the regression of x on y. (Different regression lines for two regressions).

•       Even regression itself cannot answer causality. We have to use Granger causality test to answer the causality from x to y or vice-versa.

Summary:

Correlation	Regression
Shows the linear relationship	Is used to fit a line and predict one variable
No difference of dependent and independent variable	It makes a great difference. Different best fit lines for different specifications

You can also watch this video to know difference between correlation and regression. In this video, I have explained the differences using MS Excel and live data. So it would be easy to build an intuition for near future.