Which statement best defines regression?

Which statement best defines regression?

• A. the correlation coefficient measuring strength
• B. the expected or average change in one variable (Y) per unit change in another variable (X) - measures cause and effect
• C. a measure of association
• D. a method for identifying outliers

Answer: (B)

Regression expresses how Y tends to change on average when X changes by a unit. In a simple linear model, Y ≈ β0 + β1X, and β1 is the slope—the expected change in Y for each one-unit increase in X. This makes regression a predictive tool: knowing X lets you estimate the typical Y and quantify the rate at which Y changes as X changes. It’s different from a simple correlation, which measures how strongly two variables move together but doesn’t specify how much Y changes per unit of X. While regression results can inform discussions about causality, they do not by themselves prove that changes in X cause changes in Y without proper study design and control of confounding factors. The other ideas—just measuring correlation strength, a broad notion of association, or identifying outliers—don’t capture the per-unit change in Y that defines regression.

Regression expresses how Y tends to change on average when X changes by a unit. In a simple linear model, Y ≈ β0 + β1X, and β1 is the slope—the expected change in Y for each one-unit increase in X. This makes regression a predictive tool: knowing X lets you estimate the typical Y and quantify the rate at which Y changes as X changes. It’s different from a simple correlation, which measures how strongly two variables move together but doesn’t specify how much Y changes per unit of X. While regression results can inform discussions about causality, they do not by themselves prove that changes in X cause changes in Y without proper study design and control of confounding factors. The other ideas—just measuring correlation strength, a broad notion of association, or identifying outliers—don’t capture the per-unit change in Y that defines regression.