Pearson Correlation Coefficient Interpretation
Let X=(1,2,3,...,20). Suppose that with and with . Pearson correlation coefficient is defined by formula
If , we can say that X and Y have a linear correlation. If then X and Y has a strong linear correlation, if then X and Y has a modest linear correlation, and if then X and Y has a weak linear correlation. Using this formula, we get (X,Y)=0.9 and (X,Z)=0.5. However, the relationship between X and Y is actually quadratic but they have the high correlation coefficient that indicate linear correlation.
So, my question is what is "linear correlation" actually between X and Y ? Since (X,Z)=0.5 indicate the modest correlation coefficient, what is another intepretation of this value? What is the difference between (X,Y) and (X,Z), noting that Y and Z is not a linear function of X.