Comprehensive Calculator Guide
This calculator gives Pearson’s correlation coefficient r and r² between two variables, with the strength and direction of the linear link. Study hours and marks for six students give r = 0.99; temperature and hot coffee sales give r = −0.997.
Reading r
r runs from −1 to 1; the sign is the direction, the size the strength. r² is the share of variation explained. Correlation isn’t causation, and r misses curved links and is swayed by outliers.
How to Use
- Enter the first variable.
- Enter the second in the same order.
- Press “Calculate” to see r, r² and the strength.
Formula Used
r = Σ(x − x̄)(y − ȳ) ÷ √(Σ(x − x̄)² Σ(y − ȳ)²)
Practical Examples
- Example 1
- Study and marks: 0.988.
- Example 2
- Heat and hot coffee: −0.997.
Important Tips
- Keep pairs aligned.
- Plot first.
- Use 10+ pairs.
Common Mistakes to Avoid
- Inferring causation.
- Misaligned lists.
- Reading r = 0 as no relation.
Frequently Asked Questions
- Strong r?
- About 0.7+.
- r vs r²?
- Direction and strength vs share explained.
- Spearman instead?
- For ranks or non-linear links.