Studies show that in

covariance sign is the only important thing. If there is a positive value, it

means that both variables will change in the same direction and in the case of negative

value, it means that they vary in the opposite direction.

Covariance only shows the direction which may not be enough to get the relationship totally. This is the reason why we prefer to separate covariance with the basic change of x and y. And this will help us to have the correlation coefficient in the process.

**Covariance vs Correlation**

**The main difference between covariance and correlation is that covariance measures the strength or weakness of the correlation between two or more sets of random variables. On the other hand, correlation means to serve as an extended form of covariance.**

The term covariance means it will try to look for the measurement of how many variables can change together. To simply put it when both variables are capable of changing in the same way without creating or making any relationship then it is called covariance.

**Comparison Table Between Covariance and Correlation**

Parameter of Comparison | Covariance | Correlation |
---|---|---|

Definition | Covariance is known as an indicator of the extent to which two random variables will be dependent on each other. And higher number tends to denote higher dependency. | Correlation is also known as an indicator that shows how strongly two variables are related two to each other, provided other conditions are there. Its maximum value is +1 |

Values | Covariance is limited to values between -∞ and +∞. | Correlation lies in the range between -1 and +1. |

What is their relationship? | Correlation is capable of getting deduced from covariance. | If we consider a standard scale, the correlation will provide a measure of covariance. In this case, correlation can be deduced with standard deviation by dividing the calculated covariance. |

How scale range affects? | Covariance gets affected by any change in scales. | On the other hand, correlation does not get affected by the change in scales. |

Units | Covariance has units when it is deduced by the multiplication of two numbers and units they have. | A correlation has no unit, as it is a number between -1 and +1. |

**What is Covariance?**

When two variables are

measured by something to see how they move with respect to each other and which

is also an extension of the variance concept is called covariance.

**If one says that two items vary together then it means that there is a covariance between the two items which can be either positive or negative covariance.**

Positive covariance tends to indicate that higher than average values of one variable pair with higher than average values of the other variable.

On the other hand, negative covariance tends to say that higher than average values of one variable pair with lower than average values of the other variable.

In this case,

covariance’s number is depending on the data. To compare covariance will become

difficult among data sets with different ranges of scales.

There can be a value

sometimes that is capable of symbolizing a relationship that is strong and

limited in one set of data. At the same time, it will show the opposite result

in another set of data.

In this case, the

correlation coefficient deals with the issue by adjusting the values of the

covariance. They also create a dimensionless quantity which will assist the comparison

of different data sets.

**What is the Correlation?**

Correlation is known as the statistic measurement which signifies the extent of two or more variables that fluctuates together.

A positive correlation is the indicator of the extent to which those variables parallelly increase or decrease, whereas a negative correlation is the indicator of the extent to which one variable increases and the other one decreases at the same time.

**In statistics, to test the relationship between quantitative variables or categorical variables we use correlation.** To put it simply, it is a measurement of how things are related to each other. According to a study, we know how variables are correlated and it is called correlation analysis.

In advanced portfolio management, correlations are used and also computed as the correlation coefficient, which contains a value in between -1 and +1. To know what the future holds is a vital thing in social sciences such as- government and healthcare.

For that correlations are useful as it can help to find out what relationship variables have, and also let us know if we can make predictions about the upcoming pattern of behavior.

These statistics are being used for budgets and business plans by businesses.

**Main Differences Between Covariance and Correlation**

- The expected value of variation between two random variables from their expected values is known as covariance. On the other hand, a correlation does not have variation like covariance, even when the definition of correlation is almost as same as covariance.
- Covariance measures two random variables that vary together. At the same time, correlation measures how far or close two variables are from being independent of each other.
- In statistics, covariance tends to vary from negative infinity to positive infinity while correlation does it from -1 to 1.
- Covariance is not a unit-free measure. On the other hand, correlation is a unit-free measure of the inter-dependency of two variables. Also, this makes it less hard for calculated correlation values to be compared across any 2 variables that are irrespective of their units and dimensions.
- Covariance is known to be scale-dependent while correlation is known to be the opposite. Meaning, the difference in scale can deliver a different covariance.

**Conclusion**

The fact is covariance and correlation are very closely related to each other and also at the same time they have so many differences.

**Covariance tends to define the type of interaction between variables, and correlation does the same too but it also defines the strength of the relationship.**

For this, plenty of time correlation is called as the special case of covariance. Though if anyone has to pick between the two, so many analysts prefer to choose correlation as it does not get affected by the changes in dimensions, locations, and scale.

**References**

- https://www.researchgate.net/profile/Karl_Joereskog/publication/24062332_Structural_Analysis_of_Covariance_and_Correlation_Matrices/links/0046352b8b078d34d6000000.pdf
- https://projecteuclid.org/download/pdf_1/euclid.aos/1176349937
- https://academic.oup.com/biomet/article-abstract/87/3/603/293706