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 a 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 fundamental change of x and y. And this will help us to have the correlation coefficient in the process.

## Key Takeaways

- Covariance measures the degree to which two variables are linearly related.
- Correlation measures the degree and direction of the linear relationship between two variables.
- Covariance can be positive, negative, or zero, while correlation ranges from -1 to +1.

**Covariance vs Correlation**

Correlation is more commonly used as it is a standardized measure that is easier to interpret. Covariance values can be difficult to interpret because they depend on the scale of the variables being measured. Correlation is a standardized measure that is not affected by differences in scale.

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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**

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

Definition | Covariance indicates the extent to which two random variables will depend 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. | Considering a standard scale, the correlation will provide a covariance measure. 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 the 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 concerning each other, which is also an extension of the variance concept, it 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 indicates that higher-than-average values of one variable pair with those of the other.

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, the covariance’s number depends on the data. Comparing covariance will become difficult among data sets with different ranges of scales.

There can be a value sometimes that can symbolise a strong and limited relationship in one set of data. At the same time, it will show the opposite result in another set of data.

The correlation coefficient deals with the issue by adjusting the covariance values in this case. They also create a dimensionless quantity which will assist in comparing different data sets.

**What is the Correlation?**

Correlation is the statistical measurement that signifies the extent of two or more variables that fluctuate.

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

We use correlation in statistics to test the relationship between quantitative or categorical variables.

Simply put, 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 computed as the correlation coefficient, which contains a value between -1 and +1. Knowing what the future holds is vital in social sciences, such as government and healthcare.

For that, correlations are helpful as they can help to find out what relationship variables have and also let us know if we can predict the upcoming pattern of behaviour.

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.
- In statistics, covariance tends to vary from negative 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 challenging for calculated correlation values to be compared across any two variables, irrespective of their units and dimensions.
- Covariance is known to be scale-dependent, while correlation is known to be the opposite. This means the difference in scale can deliver a different covariance.

**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

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.