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Can a simple correlation coefficient measure any type of relationship? - Economics

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Question

Can a simple correlation coefficient measure any type of relationship? 

Short Note

Solution

No, the simple correlation coefficient cannot measure any type of relationship. The simple correlation coefficient can measure only the direction and magnitude of the linear relationship between the two variables. It cannot measure non-linear relationships like quadratic, trigonometric, cubic, etc. Therefore, in such cases, the purview of the simple correlation coefficient falls short. For example, the simple correlation coefficient may depict that X and Y are not correlated in the equation X = Y2, hence it may be concluded that both the variables are independent, but such a conclusion may be wrong.

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Types of Correlation
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Chapter 7: Correlation - Exercise [Page 105]

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NCERT Statistics for Economics [English]
Chapter 7 Correlation
Exercise | Q 12. | Page 105
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