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I am having trouble isolating these two concepts.

If the sample correlation, using Pearson’s r, is 0 and statistically significant then we can conclude the data are not linearly related - there is no correlation.

If the sample correlation, whatever it may be, is statistically insignificant then we fail to reject the null hypothesis that the population correlation is 0. So essentially we are saying the population correlation is 0.

How are these two observation different?

user3138766
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  • You should always specify X in "statistically significantly different from X." Often X is zero, but that's not the only option. Thus statement #1 is hard to parse under the default interpretation. Your second statement is not how hypothesis testing works. Perhaps [this example](https://stats.stackexchange.com/questions/72579/explaining-p-value-to-a-sophisticated-layman/72583#72583) will give you some intuition and let you see the problem with statement #2 and perhaps #1. – dimitriy May 18 '21 at 00:57
  • My mistake on the last part. I ran a regression between two variables and got a correlation value. The p value associated with the regression coefficient is 0.54. Does this simply mean the correlation my regression spit out cannot be relied on? How would you describe it? – user3138766 May 18 '21 at 01:08
  • Regression doesn't directly estimate a correlation, it estimates coefficients. In the simplest one variable case, the slope coefficient [is related](https://byjus.com/maths/correlation-and-regression/) to the correlation. I would suggest that you edit your question to add the new info and the regression output. – dimitriy May 18 '21 at 01:22
  • I rewrote the question as a different question. I am not too good with this site. Would you please flag this question for deletion? – user3138766 May 18 '21 at 01:27

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