Pearson Correlation & Covariance Calculator
Paste matched X and Y observations to measure linear association and inspect covariance on the original measurement scales.
Correlation standardizes association; covariance keeps the original scale
Pearson r divides the paired cross-deviation by both variables’ spread, producing a unitless measure from −1 to 1. Covariance uses the same paired deviations without that standardization, so its magnitude depends on the units of X and Y.
Lynara reports both sample covariance and population covariance because the denominator depends on whether the entered pairs are treated as a sample or the complete population of interest. Neither statistic establishes a causal relationship.
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Formula
r = cross-deviation sum ÷ √(SSx × SSy); covariance = cross-deviation sum ÷ n or (n − 1)
Example
For X = 1, 2, 3 and Y = 2, 4, 6, r = 1, population covariance = 4/3 and sample covariance = 2.
Useful for
- Statistics homework
- Paired-data correlation
- Sample and population covariance
- Checking linear association
Questions
What is the difference between correlation and covariance?
Covariance keeps the variables’ units and scale, while Pearson r standardizes the relationship to a unitless value from −1 to 1.
Does r = 1 prove one variable causes the other?
No. Perfect linear association does not establish causation.