Correlation and Dependence

Introduction

In the field of statistics, dependence can be defined as any statistical relationship that exists between two random variables or two sets of data. On the other hand, correlation refers to any of a wide range of statistical relationships involving dependence. The correlation between the physical appearance of parents and their children and the correlation between the demand and price of a product are some common examples of dependent phenomena.

Correlation

Correlation is a statistical measure that specifies the extent to which two or more variables fluctuate together. A positive correlation shows the extent to which the variables increase or decrease in parallel. On the other hand, a negative correlation indicates the extent to which one variable increases as the other decreases. When the increase or decrease of one variable reliably predicts a similar fluctuation in another variable, there may be a tendency to think that the change in one variable is causing the change in the other. However, correlation does not imply causation. There may be some other unknown reason for this to happen. Correlations are handy because they can signify a predictive relationship that can be utilized in practice.

Correlation may, at times, relate to any exit of two or more random variables from independence; however, on technical terms it refers to any of a number of specific types of relationships between mean values. There are numerous correlation coefficients that measure the degree of correlation. One of the most popular one among these is the Pearson correlation coefficient. This coefficient is responsive only to a linear relationship between two variables. There are a number of other correlation coefficients have been designed in order to be stronger compared to the Pearson correlation. These coefficients are more sensitive to nonlinear relationships.

Dependence

Dependence may refer to any circumstances in which random variables do not satisfy a mathematical condition of probabilistic independence. The most common way to measure the dependence between two quantities is by using the Pearson correlation coefficient. It is derived by dividing the covariance of the two variables by the product of their standard variations. It may not always be possible to define the dependence between random variables using the information given by a correlation coefficient. In these cases, distance correlation or Brownian correlation may be used to get a measure of dependence between two variables.

Applications

Correlation and dependence are applicable to a number of fields. One of the most important applications of this concept is in the field of research. Correlation and dependence also have a number of applications in risk management related to finance and insurance.

Conclusion

Both correlation and dependence are interdependent as correlation coefficients are used in order to effectively measure the dependence of two or more variables.

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