variance, Standard deviation, Covariance, Correlation Coefficient

• variance

- σ2 is variance

- X is the variable

- μ is mean

- N is the total number of variables.

 

• Standard deviation

A square root of variance.

 

For instance,

 

• Covariance

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

COVARIANCE.P(x,y); 데이터가 모집단일 경우, n 으로 나눠줌
COVARIANCE.S(x,y); 데이터가 표본일 경우, n-1 로 나눠줌

For instance,

 

• The feature of covariance 

If cov(X, Y) is greater than zero, then we can say that the covariance for any two variables is positive and both the variables move in the same direction.

 

If cov(X, Y) is less than zero, then we can say that the covariance for any two variables is negative and both the variables move in the opposite direction.

 

If cov(X, Y) is zero, then we can say that there is no relation between two variables.

 

• Correlation Coefficient

 

For instance,

r={covariance / x Standard deviation * y Standard deviation} 

r= 375 / (15.8 * 24.1) = 0.985

 

Based on the value of correlation coefficient, we can estimate the type of correlation between the given two variables.