What can be inferred from a 95% confidence interval on a correlation coefficient? If the only information you have for a pearson's correlation is the 95% confidence interval, what can you infer from that data?
For example, if you had a correlation coefficient of (0.24;0.78) what would be the best inference to make?
I don't have a strong background in stats so if someone could explain it without lots of equations that would be preferable, thanks!
 A: All you can say is the sample Pearson's correlation coefficient (r) in contained in the interval from 0.24 to 0.78. You are 95% confident that you will detect a significantly different correlation when testing values outside this interval. What this means is that variable X has some degree of positive linear relationship to variable Y in your sample. (I hesitate to use qualitative descriptors of this "strength" of the relationship because: 1) this is somewhat an outdated way to think of it, 2) what may be a strong correlation in one discipline may be weak in another, and 3) I have no idea of the sample size used to calculate the correlation coefficient.) If this experiment were conducted several independent times, with random sampling over the same population, then 95% (in the long run) will contain the population parameter, rho.
A: I make this comment from the perspective of someone who is analytical but who is not an expert in statistics.   One of the reasons for doing a linear regression is to get an answer to the question as to whether the values of two variables, x and y, are independent of each other.  Alternatively, the data set may contain evidence of some linkage between them.   If the confidence interval of "r" CONTAINS zero, that suggests that x and y are unrelated and that the calculated regression equation is of no value. If the confidence interval on "r" DOES NOT CONTAIN zero, there is a reason to believe there is reason to suspect that the value of x is somehow linked to the value of y.  In this case, if you are building a statistical or mathematical model that includes both x and y as variables, you might want to include something that represents this linkage...it might improve the predictiveness of the model.
As a caveat, because I am not a statistics expert, I could have this wrong.
