Statistics

Correlation Coefficient Formula - Statistics

Learn the correlation coefficient formula with examples, step-by-step guide, and calculator tools. Measure the strength and direction of linear relationship between two variables

The correlation coefficient formula is a fundamental concept in statistics. Measure the strength and direction of linear relationship between two variables. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}\]

Variables

r
Correlation coefficient (-1 to 1)
xᵢ, yᵢ
Paired values
x̄, ȳ
Means of x and y

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [1,2,3,4,5] → Perfect positive correlation: r = 1.0

Example 2

Example 2: 1

Frequently Asked Questions

What is the correlation coefficient formula?

Measure the strength and direction of linear relationship between two variables

How do I calculate correlation coefficient formula?

Use the formula: r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}. Follow the steps provided above.

What tools can help with correlation coefficient formula?

We provide online calculators: correlation-calculator

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