gledanju0

2022-06-26

Q:/ You examine the correlation between two continuous variables X and Y, and find that this correlation is close to zero. A hypothesis test on this correlation would have you retain the null hypothesis and conclude there is no correlation between X and Y. This means that there is no relationship between X that can be used in a predictive model. Is this True/False?
A:/ Is this true or false and why?

### Answer & Explanation

Xzavier Shelton

I believe the correct test would have the null hypothesis as being that r is 0, and the alternative would be that r is simply non-zero (using two-sided test), not that r=1 or r=-1. The variables X and Y do not necessarily have to be perfectly correlated to be used in a predictive model.
Second, with a statistical test, you can only state that your data does not support the conclusion that X and Y are correlated at your given significance level, but not definitively that they are not correlated.

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