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I am trying to understand better the tests used to determine the existence of a linear relation between

two variables X,Y. AFAIK, one way of testing the strength of any linear relationship is by computing

##r^2##, where ##r## is the correlation coefficient; this measures the extend to which X determines Y, i.e., the extend to which the value of X contributes to the value of Y.

But then there is a second test, and I am confused as to how it relates to the one above. In this other tst, we do a hypothesis test for the slope of the regression line ## y=mx+b ## , with ## H_0: m=0, H_A: m \neq 0 ##. Are both these tests necessary, or is one used to corroborate the other? Are there situations where one test is preferable to the other?

Thanks.

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# Testing for Linear Relation:r^2 vs H_0: slope =0

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