Correlation Calculator
Compute Pearson's correlation coefficient r between two paired datasets.
Inputs
Correlation Coefficient (r)
0.774597
R²
0.600000
Interpretation
Strong positive linear relationship
Step by step
Values used
X values (comma separated) = 1, 2, 3, 4, 5; Y values (comma separated) = 2, 4, 5, 4, 5
Formula applied
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √[Σ(xᵢ−x̄)² × Σ(yᵢ−ȳ)²]
Correlation Coefficient (r)
= 0.774597
R²
= 0.600000
Interpretation
= Strong positive linear relationship
How it works
Pearson's correlation coefficient r measures the strength and direction of the linear relationship between two variables. It ranges from −1 (perfect negative) to +1 (perfect positive). R² indicates the proportion of variance in Y explained by X.
Formula
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √[Σ(xᵢ−x̄)² × Σ(yᵢ−ȳ)²]
- xᵢ,yᵢ
- Paired data points
- x̄,ȳ
- Means of X and Y
Frequently Asked Questions
What does r = 0 mean?
An r of 0 indicates no linear relationship between the variables. However, a non-linear relationship may still exist.
What is the difference between correlation and causation?
Correlation measures association. Two variables can be highly correlated without one causing the other — both may be driven by a third factor.