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I am reading a paper and come across the following information:

 Predictor    Dependent Variable    R Square    Beta    P
     A                D                .12      .35   <0.05
     B                D                .16      .40   <0.05
     C                D                .13      .36   <0.05

Authors are using linear regression to compute the correlation between A and D, B and D and C and D, and they claim there is significant positive correlations between each and every one of them. I am confused and do not understand how can the authors draw such a conclusion with the presented data?

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The significance of the correlation between y and x is related to the significance of the coefficient in the regression of y on x.

Specifically, for the usual t-test on correlation under normality, they have the same p-value (they're said to be equivalent tests).

The conclusion that the correlation positive is based on the sign of the regression coefficient - in simple regression they have the same sign.

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  • $\begingroup$ You mean the p-value is less than 0.05 so it's a strong correlation? $\endgroup$ – user1935724 Nov 16 '14 at 2:53
  • $\begingroup$ No; statistical significance does not imply the correlation is strong, just that it's not consistent with a population correlation of zero. $\endgroup$ – Glen_b -Reinstate Monica Nov 16 '14 at 2:55
  • $\begingroup$ I guess I still not get what you mean. In this case how does the author conclude their claim? Because normally we look at R square, right? $\endgroup$ – user1935724 Nov 16 '14 at 2:57
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    $\begingroup$ My answer already explains how the correlations were concluded to be significantly different from 0 (that they're positive comes from the sign of the estimate of $\beta$). That covers the claim. That has nothing to do with concluding the correlation is strong, which was not mentioned in your statement of what they claimed. It's not clear to me where the difficulty lies. $\endgroup$ – Glen_b -Reinstate Monica Nov 16 '14 at 3:02
  • $\begingroup$ You mean any positive value of beta will make the correlation significant? $\endgroup$ – user1935724 Nov 16 '14 at 3:06

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