Pearson Correlation Calculator
Calculate Pearson's r to measure linear relationship strength and direction between two variables
Data Input
Enter your (X, Y) coordinate pairs
Pearson Correlation Results
Enter at least 3 complete (X, Y) coordinate pairs to calculate Pearson correlation
Example: Height and Weight Correlation
Sample Data Points
Data: (1,1), (3,2), (3,3), (5,4)
X values: 1, 3, 3, 5
Y values: 1, 2, 3, 4
Sample size: n = 4
Step-by-Step Calculation
Step 1: Calculate means: x̄ = 12/4 = 3, ȳ = 10/4 = 2.5
Step 2: Calculate sums: Σx² = 44, Σy² = 30, Σxy = 36
Step 3: Apply formula: r = (36 - 4×3×2.5) / √[(44-4×9)(30-4×6.25)]
Step 4: Simplify: r = 6 / √(8×5) = 6/6.32 ≈ 0.95
Results Interpretation
Pearson r: 0.95 (Very Strong Positive correlation)
R-squared: 0.90 (90% of variance explained)
Meaning: Strong positive linear relationship between variables
Evans' Correlation Scale
Correlation Tips
r = +1: Perfect positive correlation
r = -1: Perfect negative correlation
r = 0: No linear relationship
Correlation ≠ Causation
Only detects LINEAR relationships
R² shows explained variance
Understanding Pearson Correlation
What is Pearson Correlation?
The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables. It quantifies how well the relationship between variables can be described by a straight line.
Key Properties
- •Range: -1 to +1
- •Symmetric: r(X,Y) = r(Y,X)
- •Unitless (scale-invariant)
- •Only measures linear relationships
Correlation vs. Causation
Strong correlation does not imply causation! Variables may be correlated due to: coincidence, confounding variables, or indirect relationships.
Pearson Correlation Formula
Standard Formula:
r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)²Σ(yi - ȳ)²]
Computational Formula:
r = [Σ(xiyi) - nx̄ȳ] / √[(Σxi² - nx̄²)(Σyi² - nȳ²)]
Relationship to R-squared
R² = r² represents the coefficient of determination - the proportion of variance in one variable explained by the other variable.
Applications:
- Psychology: IQ vs. academic performance
- Economics: Income vs. spending patterns
- Medicine: Blood pressure vs. age
- Marketing: Advertising spend vs. sales
- Science: Temperature vs. chemical reaction rates
Remember: Pearson correlation only detects linear relationships. Non-linear relationships may show low correlation despite strong associations.