- 2074 Chaitra · 4 marks
Differentiate correlation and regression
Short answer
Correlation measures the strength and direction of linear association between variables without distinguishing dependent and independent variables. Regression finds an equation to predict one variable from another. Correlation coefficient r is symmetric and unitless, while regression coefficients are asymmetric and depend on scale; r squared equals their product.
Differentiate between Correlation and regression analysis.
| Basis | Correlation | Regression |
|---|---|---|
| Meaning | Measures the degree and direction of linear association between two variables | Finds the average functional relationship so that one variable can be estimated from the other |
| Variables | No distinction between dependent and independent variables | One variable is dependent, the other independent |
| Measure | Correlation coefficient r, a pure number in [−1, +1] | Regression coefficients b_yx, b_xy with units |
| Symmetry | r_xy = r_yx | b_yx ≠ b_xy in general; two regression lines |
| Cause and effect | Does not imply causation; may be a chance or spurious relation | Presumes a cause-and-effect (explanatory) relationship |
| Objective | To know how closely variables move together | To predict or estimate values of the dependent variable |
| Effect of scale/origin | Independent of change of origin and scale | Independent of origin but not of scale |
| Representation | Single number (or scatter diagram) | Equation of line, e.g. Y = a + bX |
Relation between them: r² = b_yx · b_xy, and r = b_yx·(σx/σy).
✓ Answer checked by Claude Sonnet 5.5
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