Correlation Calculator
Compute the Pearson correlation coefficient (r) between two sets of data (X and Y).
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Understanding Correlation
Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together. A positive correlation indicates the extent to which those variables increase or decrease in parallel; a negative correlation indicates the extent to which one variable increases as the other decreases.
Pearson Correlation Coefficient (r) Formula:
Where:
- xi, yi = Individual data points
- &bar;x, &bar;y = Mean of data set X and Y respectively
- Σ = Summation
Correlation Examples
| Data X | Data Y | Correlation (r) | Interpretation |
|---|---|---|---|
| 1,2,3,4,5 | 2,4,6,8,10 | 1.00 | Perfect Positive |
| 1,2,3,4,5 | 10,8,6,4,2 | -1.00 | Perfect Negative |
| 1,2,3,4,5 | 5,3,8,1,6 | ~0.00 | No Linear Correlation |
Frequently Asked Questions
What is correlation?
Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect.
What is the correlation coefficient (Pearson r)?
The Pearson product-moment correlation coefficient (r) is a measure of the linear correlation between two sets of data. It ranges from -1 to +1. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
What do positive, negative, and zero correlation mean?
Positive correlation (r > 0): As one variable increases, the other tends to increase. Negative correlation (r < 0): As one variable increases, the other tends to decrease. Zero correlation (r ≈ 0): There is no linear relationship between the variables.