Correlation Coefficient Calculator
Calculate the correlation coefficient between two variables to measure their linear relationship.
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Table of Contents
What is Correlation?
Correlation is a statistical measure that describes the extent to which two variables change together. The correlation coefficient ranges from -1 to +1, where:
- +1 indicates a perfect positive correlation
- 0 indicates no correlation
- -1 indicates a perfect negative correlation
- Values between -1 and +1 indicate varying degrees of correlation
Interpreting Correlation
Strong Correlation
|r| > 0.7 indicates a strong relationship between variables.
Moderate Correlation
0.3 < |r| ≤ 0.7 indicates a moderate relationship.
Weak Correlation
0 < |r| ≤ 0.3 indicates a weak relationship.
No Correlation
r ≈ 0 indicates no linear relationship.
Correlation Formula
The Pearson correlation coefficient (r) is calculated using the following formula:
Where:
- r is the correlation coefficient
- x and y are the variables
- μx and μy are the means
- σx and σy are the standard deviations
- n is the number of data points
Examples
Example 1 Strong Positive Correlation
X: 1, 2, 3, 4, 5
Y: 2, 4, 6, 8, 10
Correlation ≈ 1.000
Perfect positive correlation
Example 2 Moderate Negative Correlation
X: 1, 2, 3, 4, 5
Y: 10, 8, 6, 4, 2
Correlation ≈ -0.800
Strong negative correlation
Example 3 No Correlation
X: 1, 2, 3, 4, 5
Y: 5, 2, 8, 1, 9
Correlation ≈ 0.000
No linear relationship