Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated. However, it is also often used informally as a general measure of how monotonically related two variables are.
https://stats.stackexchange.com/questions/29713/what-is-covariance-in-plain-language
• Both correlation and covariance are measures of relation between two random variables. Correlation is the measure of strength of the linearity of the two variables and covariance is a measure of the strength of the correlation. • Correlation coefficient values are a value between -1 and +1, whereas the range of covariance is not constant, but can either be positive or negative.
http://www.differencebetween.com/difference-between-correlation-and-vs-covariance/
Covariance measures the linear relationship between two variables. 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.
http://support.minitab.com/en-us/minitab-express/1/help-and-how-to/modeling-statistics/regression/supporting-topics/basics/what-is-covariance/
Difference Between Variance and Covariance. Variance and covariance are two measures used in statistics. Variance is a measure of the scatter of the data, and covariance indicates the degree of change of two random variables together. Variance is rather an intuitive concept, but covariance is defined mathematically in not that intuitive at first.
http://www.differencebetween.com/difference-between-variance-and-vs-covariance/
Covariance measures the linear relationship between two variables. Correlation coefficients are standardized. Thus, a perfect linear relationship results in a coefficient of 1. The correlation measures both the strength and direction of the linear relationship between two variables.
http://support.minitab.com/en-us/minitab-express/1/help-and-how-to/modeling-statistics/regression/supporting-topics/basics/what-is-covariance/
In other words, covariance is a measure of the strength of the correlation between two random variables. In another perspective, it can be seen that correlation is just the normalized version of covariance, where the covariance is divided by the product of the standard deviations of the two random variables.
http://www.differencebetween.com/difference-between-correlation-and-vs-covariance/
If X and Y are two random variables, with means (expected values) μX and μY and standard deviations σX and σY, respectively, then their covariance and correlation are as follows: so that. where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables.
https://en.wikipedia.org/wiki/Covariance_and_correlation
This scaling makes correlation invariant to changes in scale of the original variables, (which Akavall points out and gives an example of, +1). The scaling constant is the product of the standard deviations of the two variables. (2) If two variables are independent, their covariance is $0$. But, having a covariance of $0$ does not imply the variables are independent. This figure (from Wikipedia)
https://stats.stackexchange.com/questions/29713/what-is-covariance-in-plain-language
If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. σ X X {\displaystyle \sigma _{XX}} ), which is called the variance and is more commonly denoted as σ X 2 , {\displaystyle \sigma _{X}^{2},} the square of the standard deviation.
https://en.wikipedia.org/wiki/Covariance_and_correlation
Covariance values are not standardized. Therefore, the covariance can range from negative infinity to positive infinity. Thus, the value for a perfect linear relationship depends on the data. Because the data are not standardized, it is difficult to determine the strength of the relationship between the variables.
http://support.minitab.com/en-us/minitab-express/1/help-and-how-to/modeling-statistics/regression/supporting-topics/basics/what-is-covariance/
what is standardized covariance
Covariance measures the linear relationship between two variables. Correlation coefficients are standardized. Covariance measures the linear relationship between two variables.