Regression and Correlation

Regression and correlation are two fundamental statistical concepts that are commonly used to analyze and predict data. They both involve relationships between variables, but they are used for slightly different purposes.

Correlation

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It’s a common tool for describing simple relationships without making a statement about cause and effect.

The correlation coefficient (r) is a value between -1 and 1. When r is closer to 1, it indicates a strong positive correlation (i.e., when one variable increases, the other tends to increase). When r is closer to -1, it indicates a strong negative correlation (i.e., when one variable increases, the other tends to decrease). An r close to 0 indicates that there's no linear relationship between the variables.

Regression

Regression analysis is a set of statistical processes for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables.

The simplest form of regression is linear regression, where we find the best fitting straight line through the data points. The best fitting line is called a regression line. The black diagonal line in Figure 2 is the regression line and consists of the predicted score on Y for each possible value of X.

In a regression model, the dependent variable is predicted or explained by one or more independent variables. The dependent variable is also called the outcome, target, or criterion variable, and the independent variables are also called predictor, explanatory, or regressor variables.

Difference between Correlation and Regression

Correlation and regression are related but are not the same.

  • Correlation is used to represent the linear relationship between two variables. On the other hand, regression is used to fit the best line and estimate one variable on the basis of another variable.

  • Correlation does not imply causation. It can only tell you what the relationship is, but it can't tell you why the relationship exists. On the other hand, regression can tell you how an independent variable affects a dependent variable.

  • Correlation coefficients only range from -1 to +1, but regression coefficients can be any real number.

Both correlation and regression are important tools in statistics for understanding and predicting data.