Distinguish between correlation and regression.

Question

Accepted Answer

Correlation and regression are both concerned with the relationship between two variables, but they serve different purposes:

| Basis | Correlation | Regression |
|---|---|---|
| Purpose | Measures the **degree and direction** of the linear relationship between two variables | Establishes a **functional equation** to estimate/predict one variable from the other |
| Output | A single number, $r$, between $-1$ and $+1$ | Two full regression equations (lines), each with an intercept and a slope |
| Symmetry | Symmetric — $r_{xy} = r_{yx}$, no distinction between dependent/independent variable | Asymmetric — a distinct dependent and independent variable, and two different lines depending on which is which |
| Cause-effect | Does not imply causation, only association | Also does not by itself imply causation, but is used specifically to predict a dependent variable's value |
| Use | Answers 'how strongly are $X$ and $Y$ related, and in which direction?' | Answers 'given a value of $X$ (or $Y$), what value should we expect for $Y$ (or $X$)?' | …

Q.Distinguish between correlation and regression.

Concept understanding — Regression and Its Meaning

Basis	Correlation	Regression
Purpose	Measures the degree and direction of the linear relationship between two variables	Establishes a functional equation to estimate/predict one variable from the other
Output	A single number, $r$ , between $-1$ and $+1$	Two full regression equations (lines), each with an intercept and a slope
Symmetry	Symmetric — $r_{xy} = r_{yx}$ , no distinction between dependent/independent variable	Asymmetric — a distinct dependent and independent variable, and two different lines depending on which is which
Cause-effect	Does not imply causation, only association	Also does not by itself imply causation, but is used specifically to predict a dependent variable's value
Use	Answers 'how strongly are $X$ and $Y$ related, and in which direction?'	Answers 'given a value of $X$ (or $Y$ ), what value should we expect for $Y$ (or $X$ )?'

Q.Distinguish between correlation and regression.

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