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Why does correlation not imply independence?
Correlation measures linear association between two given variables and it has no obligation to detect any other form of association else. So those two variables might be associated in several other non-linear ways and correlation could not distinguish from independent case.
The words uncorrelated and independent may be used interchangeably in English, but they are not synonyms in mathematics. Independent random variables are uncorrelated, but uncorrelated random variables are not always independent.
Why do we say that if two variables are independent then the correlation between them need not be 0?
The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables. If the variables are independent, Pearson’s correlation coefficient is 0, but the converse is not true because the correlation coefficient detects only linear dependencies between two variables.
Why is covariance 0 for independent?
If X and Y are independent variables, then their covariance is 0: Cov(X, Y ) = E(XY ) − µXµY = E(X)E(Y ) − µXµY = 0 The converse, however, is not always true. Cov(X, Y ) can be 0 for variables that are not inde- pendent.
What is an independent correlation?
The two variables compared to each other in a correlation are called the independent variable and the dependent variable. As the names suggest, an independent variable is one whose change tends to be beyond human control. Time is often used as an independent variable because it goes on whether we like it or not.
How do you explain correlation?
Correlation is a term that refers to the strength of a relationship between two variables where a strong, or high, correlation means that two or more variables have a strong relationship with each other while a weak or low correlation means that the variables are hardly related.
What is the correlation between two variables?
By Karl Wallulis. The correlation between two variables describes the likelihood that a change in one variable will cause a proportional change in the other variable. A high correlation between two variables suggests they share a common cause or a change in one of the variables is directly responsible for a change in the other variable.