1. The Relationship between VariablesFirst, correlation measures the degree of relationship between two variables. Regression analysis is about how one variable affects another or what changes it triggers in the other.
2. CausalitySecond, correlation doesn’t capture causality but the degree of interrelation between the two variables. Regression is based on causality. It shows no degree of connection, but cause and effect.
3. Are X and Y Interchangeable?Third, a property of correlation is that the correlation between x and y is the same as between y and x. You can easily spot that from the formula, which is symmetrical. Regressions of y on x and x on y yield different results. Think about income and education. Predicting income, based on education makes sense, but the opposite does not.
4. Graphical Representation of Correlation and Regression AnalysisFinally, the two methods have a very different graphical representation. Linear regression analysis is known for the best fitting line that goes through the data points and minimizes the distance between them. Whereas, correlation is a single point.
Key Differences Between Correlation and RegressionTo sum up, there are four key aspects in which these terms differ.
- When it comes to correlation, there is a relationship between the variables. Regression, on the other hand, puts emphasis on how one variable affects the other.
- Correlation does not capture causality, while regression is founded upon it.
- Correlation between x and y is the same as the one between y and x. Contrary, a regression of x and y, and y and x, yields completely different results.
- Lastly, the graphical representation of a correlation is a single point. Whereas, a linear regression is visualized by a line.