Statistics & Data

Correlation Coefficient

Calculate Pearson's r, covariance, and visual regression.

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Pearson's r
0.000
Coefficient of Determination (R²)
0.000
Interpretation
N/A
Covariance
0.000
Scatter Plot & Regression Line y = mx + b

Calculation Breakdown

Follow the math step-by-step to see how Pearson's r is derived from your data.

Enter data and click "Process" to generate the step-by-step table.
📐 The Pearson Formula

The Pearson correlation coefficient (r) measures the linear relationship between two datasets. It ranges from -1 to 1.

r = n(Σxy) - (Σx)(Σy)
√[nΣx² - (Σx)²][nΣy² - (Σy)²]

Where n is the number of pairs, Σxy is the sum of the products of paired scores, and Σx, Σy are the sums of the x and y scores respectively.

📊 Interpreting the Value
  • 1.0: Perfect positive correlation. As X increases, Y increases proportionally.
  • 0.8 to 0.99: Very strong positive correlation.
  • 0.6 to 0.79: Strong positive correlation.
  • 0.4 to 0.59: Moderate positive correlation.
  • 0.2 to 0.39: Weak positive correlation.
  • -0.19 to 0.19: Very weak or no correlation.
  • (Negative values follow the same strength scale, but indicate an inverse relationship: as X goes up, Y goes down).

Note: Correlation does not imply causation. A strong correlation only means the variables move together, not that one causes the other.

🎯 Coefficient of Determination (R²)

R² is literally the square of the correlation coefficient (r). It is expressed as a percentage or a decimal from 0 to 1.


Meaning: It represents the proportion of the variance in the dependent variable (Y) that is predictable from the independent variable (X).


Example: If r = 0.8, then R² = 0.64. This means 64% of the variation in Y can be explained by the variation in X.