Correlation vs. Regression: A Key Difference That Many Analysts Miss
Correlation analysis (specifically, Pearson’s pairwise correlation) and regression analysis (specifically, bivariate ordinary least squares (OLS) regression) have many features in common:
Indeed, the popular R-squared that is obtained in bivariate OLS regression is literally just the Pearson’s correlation coefficient (r) squared.
It’s therefore not surprising that many analysts often use correlation and bivariate regression interchangeably. So what’s the difference?
Analysts know the big difference is how we interpret the key quantities that each analysis produces. The correlation coefficient (r) that we obtain from correlation analysis is a standardized number, falling somewhere on a -1 to +1 scale (where -1 indicates a perfectly negative linear correlation, while +1 indicates a perfectly positive linear correlation) regardless of the variables we’re analyzing.
Regression, on the other hand, produces a beta coefficient (b), which can be any number, and which tells us the average change in Y given a one-unit increase in X. In other words, b is in units of the specific Y variable we are studying. As such, to make any substantive sense of b, we really need to know the details about what X and Y are and how they’re being measured.
