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The sample correlation coefficient can then be calculated by

The Pearson product-moment correlation coefficient will always be between -1 and 1. The closer the value is to either -1 or 1 the more highly correlated the two variables. A correlation coefficient equal to either -1 or 1 indicates a perfect linear relationship between the two variables. A correlation coefficient close to 0 simply indicates that the two variables are not linearly related, however they still may be highly correlated in a nonlinear sense.

For example, suppose that X takes on the integer values between -50 and 50 with equal probability. Furthermore, let Y be equal to the square of X. Then the Pearson product-moment correlation coefficient will be equal to 0. Oftentimes people take this to mean that X and Y are not correlated. This conclusion is clearly not true as we know that Y is completely determined by X. Thus we can only say that X and Y are not linearly correlated. This rather vague conclusion is one of the disadvantages of using the Pearson correlation coefficient.

-- ErinEsp - 01 Jan 2011

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Topic revision: r1 - 01 Jan 2011 - 18:21:45 - ErinEsp

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