---
title: "Differentiate correlation and regression"
subject: "Probability and Statistics"
chapter: 5
key: "semester_5/probability_and_statistics:correlation-vs-regression-difference"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/correlation-vs-regression-difference
site: BCT Engineering
---

# Differentiate correlation and regression

Probability and Statistics · Chapter 5: Correlation and regression

- Asked in: 2074 Chaitra, 4 marks
- Video: [Correlation Vs Regression: Difference Between them with definition & Comparison Chart](https://www.youtube.com/watch?v=Ou2QGSJVd0U) — Key Differences
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/correlation-vs-regression-difference
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-5

## Question

Differentiate between Correlation and regression analysis.

## 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.

## Answer

| 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).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is true?
   A. Correlation designates a dependent variable; regression does not
   B. Regression treats one variable as dependent and the other as independent; correlation does not distinguish
   C. Both need a dependent variable
   D. Neither distinguishes
   Answer: B. Regression has dependent and independent variables; correlation treats both alike. (Key point: Variables treated)

2. Effect of change of origin and scale:
   A. Regression coefficient is independent of both
   B. Correlation depends on both
   C. Both depend on origin
   D. Correlation is independent of both; regression coefficient is independent of origin only
   Answer: D. r is unaffected by origin and scale, while slope changes with scale. (Key point: Origin and scale)

3. How are r and the regression coefficients related?
   A. r² = b_yx · b_xy
   B. r = b_yx + b_xy
   C. r = b_yx · b_xy
   D. r² = b_yx / b_xy
   Answer: A. The product of the two regression coefficients equals r². (Key point: Relation between them)

4. Regarding cause and effect:
   A. Correlation proves causation
   B. Correlation never exists without causation
   C. Regression has no assumption about variables
   D. Correlation does not imply causation (may be spurious); regression presumes an explanatory relationship
   Answer: D. Correlation may be chance or spurious; regression presumes an explanatory relationship. (Key point: Cause and effect)

## Related in Probability and Statistics

- [Correlation vs regression; marks correlation](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Acorrelation-vs-regression-statistics-maths) — Probability and Statistics, chapter 5
- [Correlation vs regression; stopping distance line](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Acorrelation-regression-plot-stopping-distance) — Probability and Statistics, chapter 5
- [Uses of correlation and regression in engineering](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Acorrelation-regression-uses-engineering) — Probability and Statistics, chapter 5

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