Matematika

Kalkulačka kovariácie

Covariance Calculator

X Values (space/comma separated)

Y Values

✓Výsledky

Covariance

4.4286

Correlation (r)

0.9764

8

Correlation: Strong positive

What is Covariance Calculator?

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Covariance measures how two variables change together. Positive covariance means they tend to increase together; negative means one increases as the other decreases. It is the foundation of correlation and portfolio theory.

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Vzorec

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f(x)Cov(X,Y) = E[(X − μₓ)(Y − μᵧ)] = (Σ(xᵢ − x̄)(yᵢ − ȳ)) / (n−1)

Variable Legend

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Symbol	Meno	Jednotka	Popis
X, Y	two variables/datasets	—	—
μₓ, μᵧ	means of X and Y	—	—
Cov(X,Y)	covariance	—	measure of joint variability
n	number of data points	—	—

How to Covariance Calculator

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1Sample covariance: Cov(X,Y) = Σ(xᵢ−x̄)(yᵢ−ȳ) / (n−1)
2Positive: variables move together
3Negative: variables move oppositely
4Zero: no linear relationship

Worked Examples

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Example 1

Given:X=[2,4,4,4,5], Y=[1,3,3,4,4]

Výsledok:Cov ≈ 0.95 (positive relationship)

Real-World Applications

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Portfolio analysis and risk management

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Finance and stock correlation

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Machine learning (feature relationships)

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Statistical analysis and regression

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Quality control and process monitoring

Covariance Interpretation

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Sign	Meaning	Example
Positive	Variables increase together	Height & weight
Negative	Inverse relationship	Price & demand
Zero	No linear relationship	Shoe size & IQ
Normalised = r	Correlation coefficient	−1 to +1 range

Frequently Asked Questions

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What does positive covariance mean?

Positive covariance: when X increases, Y tends to increase. They vary together.

What does zero covariance mean?

Zero covariance suggests no linear relationship, but nonlinear relationships may exist.

How is covariance related to correlation?

Correlation = Cov(X,Y) / (σₓ × σᵧ). Correlation is covariance normalized to [−1, 1].

References

›Covariance — Khan Academy

Deep Dive

Read the full guide on how to use this calculator effectively

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Accuracy-checked

Reviewed October 2026

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