Covariance

What is the definition of covariance?

• Covariance is a measure of central tendency

• Covariance is a measure of dispersion

• Covariance is a measure of correlation

• Covariance is a statistical measure that shows the extent to which two variables change together.

How is covariance calculated?

• Cov(X, Y) = Σ[(Xᵢ + X̄)(Yᵢ - Ȳ)] / n

• Cov(X, Y) = Σ[(Xᵢ - X̄)(Yᵢ - Ȳ)] / (n - 1)

• Cov(X, Y) = Σ[(Xᵢ - X̄)(Yᵢ + Ȳ)] / (n - 1)

• Cov(X, Y) = Σ[(Xᵢ + X̄)(Yᵢ + Ȳ)] / n

What are some properties of covariance?

• Covariance is always positive

• Covariance is not affected by outliers

• Covariance can be positive, negative, or zero depending on the relationship between the variables.

• Covariance is a measure of central tendency

What are some applications of covariance?

• Social media analysis

• Portfolio management, image processing, genetics

• Agricultural irrigation

• Weather forecasting

Explain the relationship between covariance and correlation.

• Covariance and correlation are the same thing

• Covariance and correlation are not related

• Covariance is a measure of how two variables change together, while correlation is a standardized measure that ranges from -1 to 1.

• Covariance is always positive, while correlation can be negative

What are the limitations of using covariance?

• Covariance lacks a standardized scale and is sensitive to the units of measurement.

• Covariance is not suitable for comparing variables with different units

• Covariance does not provide information on the strength of the relationship between variables

• Covariance assumes a linear relationship between variables

In a dataset, if the covariance between two variables is positive, what does it indicate?

• The variables have a negative linear relationship.

• The variables have a positive linear relationship.

• The variables are not related.

• The variables have a curvilinear relationship.

If the covariance between two variables is zero, what does it suggest about their relationship?

• There is no linear relationship between the two variables.

• The variables have a non-linear relationship.

• The variables are perfectly negatively correlated.

• The variables are perfectly positively correlated.

How does the scale of the variables affect the covariance value?

• The scale of the variables affects the covariance value by giving more weight to variables with larger scales.

• Covariance value is solely determined by the mean of the variables

• Variables with smaller scales have more influence on the covariance value

• The scale of the variables has no impact on the covariance value

Can covariance be used to determine the strength of the relationship between variables?

• Sometimes

• Yes

• Always

• No