intuition behind covariance

Covariance is a measure of how much two variables change together. Compare this to Variance, which is just the range over which one measure (or variable) varies.

1. What does covariance tell us?
2. What is the rule of covariance?
3. How do you prove covariance?
4. What is the relation between covariance and correlation?
5. Should I use correlation or covariance?
6. Can the covariance be greater than 1?
7. What is difference between covariance and variance?
8. What does a covariance of 0 mean?
9. Can covariance be greater than variance?
10. How do you show covariance is zero?
11. What is the covariance of two independent variables?
12. Is covariance an additive?

What does covariance tell us?

Covariance measures the directional relationship between the returns on two assets. A positive covariance means that asset returns move together while a negative covariance means they move inversely.

What is the rule of covariance?

From Wikipedia, the free encyclopedia. In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are random variables on the same probability space, and the covariance of X and Y is finite, then.

How do you prove covariance?

The covariance between X and Y is defined as Cov(X,Y)=E[(X−EX)(Y−EY)]=E[XY]−(EX)(EY).
...
The covariance has the following properties:

1. Cov(X,X)=Var(X);
2. if X and Y are independent then Cov(X,Y)=0;
3. Cov(X,Y)=Cov(Y,X);
4. Cov(aX,Y)=aCov(X,Y);
5. Cov(X+c,Y)=Cov(X,Y);
6. Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z);
7. more generally,

What is the relation between covariance and correlation?

Correlation refers to the scaled form of covariance. Covariance indicates the direction of the linear relationship between variables. Correlation on the other hand measures both the strength and direction of the linear relationship between two variables. Covariance is affected by the change in scale.

Should I use correlation or covariance?

In simple words, both the terms measure the relationship and the dependency between two variables. “Covariance” indicates the direction of the linear relationship between variables. “Correlation” on the other hand measures both the strength and direction of the linear relationship between two variables.

Can the covariance be greater than 1?

The covariance is similar to the correlation between two variables, however, they differ in the following ways: Correlation coefficients are standardized. Thus, a perfect linear relationship results in a coefficient of 1. ... Therefore, the covariance can range from negative infinity to positive infinity.

What is difference between covariance and variance?

In statistics, a variance is the spread of a data set around its mean value, while a covariance is the measure of the directional relationship between two random variables.

What does a covariance of 0 mean?

A Correlation of 0 means that there is no linear relationship between the two variables. We already know that if two random variables are independent, the Covariance is 0. We can see that if we plug in 0 for the Covariance to the equation for Correlation, we will get a 0 for the Correlation.

Can covariance be greater than variance?

Theoretically, this is perfectly feasible, the bi-variate normal case being the easiest example.

How do you show covariance is zero?

If X and Y are independent variables, then their covariance is 0: Cov(X, Y ) = E(XY ) − µXµY = E(X)E(Y ) − µXµY = 0 The converse, however, is not always true. Cov(X, Y ) can be 0 for variables that are not inde- pendent.

What is the covariance of two independent variables?

Property 2 says that if two variables are independent, then their covariance is zero. This does not always work both ways, that is it does not mean that if the covariance is zero then the variables must be independent.

Is covariance an additive?

The additive law of covariance holds that the covariance of a random variable with a sum of random variables is just the sum of the covariances with each of the random variables.