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Explain the relation/difference between covariance and correlation.

Covariance

Correlation

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The **covariance** is a measure for how two variables are related to each other, i.e., how two variables vary with each other.

The values of **correlation **are standardized but covariance values are not. The **correlation **coefficient can be obtained by dividing the covariance of the variables by the product of their standard deviation values. Standard deviation measures the variability of datasets absolutely. When it is divided by the standard deviation it falls in the range of -1 to +1, which is the range of correlation values. The normalized form of covariance is correlation.

**Covariance**

- Covariance is a measure to indicate the extent to which two random variables change in tandem.
- Covariance is nothing but a measure of correlation.
- Covariance indicates the direction of the linear relationship between variables.
- Covariance can vary between -∞ and +∞
- Covariance is affected by the change in scale. If all the values of one variable are multiplied by a constant and all the values of another variable are multiplied, by a similar or different constant, then the covariance is changed.
- Covariance assumes the units from the product of the units of the two variables.
- Covariance of two dependent variables measures how much in real quantity (i.e. cm, kg, liters) on average they co-vary.
- Covariance is zero in case of independent variables (if one variable moves and the other doesn’t) because then the variables do not necessarily move together.

**Correlation**

- Correlation is a measure used to represent how strongly two random variables are related to each other.
- Correlation refers to the scaled form of covariance.
- Correlation on the other hand measures both the strength and direction of the linear relationship between two variables.
- Correlation ranges between -1 and +1
- Correlation is not influenced by the change in scale.
- Correlation is dimensionless, i.e. It’s a unit-free measure of the relationship between variables.
- Correlation of two dependent variables measures the proportion of how much on average these variables vary w.r.t one another.
- Independent movements do not contribute to the total correlation. Therefore, completely independent variables have a zero correlation.

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