Correlation and Regression

Core concepts

1. 01Correlation measures direction and strength of linear relation (−1 to +1).
2. 02Karl Pearson's coefficient is for quantitative data.
3. 03Spearman's rank correlation for qualitative / ranked data.
4. 04Regression: estimating one variable based on another using best-fit line.
5. 05Two regression lines: Y on X and X on Y; intersect at (x̄, ȳ).

Exam-critical pointers

• ⭐Both regression coefficients have the same sign as r.
• ⭐Product of regression coefficients ≤ 1 (since |r| ≤ 1).
• ⭐Probable Error = 0.6745 × (1 − r²)/√n (used for significance check).
• ⭐Distinguish regression from correlation — regression has cause-effect direction.