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

X:Y:
X:Y:
X:Y:

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

0.8 ≤ |r| ≤ 1.0Very Strong
0.6 ≤ |r| < 0.8Strong
0.4 ≤ |r| < 0.6Moderate
0.2 ≤ |r| < 0.4Weak
0.0 ≤ |r| < 0.2Very Weak

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.