1. What is Covariance?

Covariance measures how much two random variables vary together. It's a measure of the relationship between two variables, indicating whether they tend to increase or decrease together.

2. How Does the Calculator Work?

The calculator uses the covariance formula:

Where:

• \( x_i \) — Individual x values
• \( \bar{x} \) — Mean of x values
• \( y_i \) — Individual y values
• \( \bar{y} \) — Mean of y values
• \( n \) — Number of data points

Explanation: The formula calculates the average of the product of deviations from their respective means.

3. Interpretation of Covariance

Details: Positive covariance indicates variables tend to move together, negative means they move inversely, and zero means no linear relationship.

4. Using the Calculator

Tips: Enter comma-separated values for both X and Y variables. Both lists must have the same number of values (minimum 2 values each).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between covariance and correlation?
A: Covariance measures direction of relationship, while correlation measures both direction and strength (standardized between -1 and 1).

Q2: What are the units of covariance?
A: The units are the product of the units of X and Y, making interpretation difficult. This is why correlation is often preferred.

Q3: When is covariance used?
A: Primarily in portfolio theory to understand how different assets move together, and as a building block for other statistical measures.

Q4: What does a covariance of zero mean?
A: It means there is no linear relationship between the variables, but there could still be a non-linear relationship.

Q5: How does sample size affect covariance?
A: With larger samples, covariance becomes more reliable. Small samples may give misleading covariance values.