What is the difference between r and R²?

**r** (Correlation) measures strength and direction (-1 to 1). **R²** (Determination) measures how well data fits a regression model (0 to 1). R² is literally r squared!

What is considered a 'Strong' correlation?

Make sure to consider your field context. Generally: r > 0.7 is Strong, 0.3-0.7 is Moderate, and 0.9, while in social science, r > 0.4 might be significant.

Does correlation imply causation?

**No!** A strong correlation means the variables move together, but it does not measure if one *causes* the other. (e.g., Ice cream sales and sunburns are correlated, but ice cream doesn't cause sunburns—the sun does.)

This usually happens if one of your variables has zero variance (all numbers are identical), causing a division by zero in the formula. It also occurs if your X and Y lists have different lengths.

Correlation Calculator

Correlation Calculator Overview

Calculate Pearson's Correlation Coefficient (r)

The **Correlation Coefficient Calculator** computes **Pearson's r**, the gold standard for measuring the strength and direction of the linear relationship between two variables. Whether you are analyzing scientific data, business trends, or academic research, this tool quantifies how strongly X is related to Y. ### Understanding Your Results - **Pearson's r**: A value between -1 and 1. - **+1.0**: Perfect positive correlation (as X increases, Y increases precision). - **0.0**: No linear relationship. - **-1.0**: Perfect negative correlation (as X increases, Y decreases). - **R² (Coefficient of Determination)**: Tells you the percentage of the variance in the dependent variable that is predictable from the independent variable. ### Formula The calculator uses the standard Pearson Product-Moment Correlation formula: `r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)² * Σ(y - ȳ)²)`

How to Use Correlation Calculator

**Prepare Data**: Ensure you have paired data points (e.g., Height vs. Weight) with the same number of entries for both X and Y.
**Input Variable X**: Enter your first dataset, separated by commas, spaces, or newlines.
**Input Variable Y**: Enter your second dataset in the same order.
**Calculate**: Click to generate the Pearson 'r' value and the R-squared determination.
**Interpret**: Use the provided text guide to understand if your correlation is Weak, Moderate, or Strong.

Frequently Asked Questions

What is the difference between r and R²?: **r** (Correlation) measures strength and direction (-1 to 1). **R²** (Determination) measures how well data fits a regression model (0 to 1). R² is literally r squared!
What is considered a 'Strong' correlation?: Make sure to consider your field context. Generally: r > 0.7 is Strong, 0.3-0.7 is Moderate, and < 0.3 is Weak. In physics, you might demand r > 0.9, while in social science, r > 0.4 might be significant.
Does correlation imply causation?: **No!** A strong correlation means the variables move together, but it does not measure if one *causes* the other. (e.g., Ice cream sales and sunburns are correlated, but ice cream doesn't cause sunburns—the sun does.)
Why did I get 'NaN'?: This usually happens if one of your variables has zero variance (all numbers are identical), causing a division by zero in the formula. It also occurs if your X and Y lists have different lengths.

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