Interpretation of Pearson correlation results I have a question about interpreting the Pearson Correlation Coefficient results. As you can see in the figure below, the r-value is close to 0 (no correlation) but the p-value is 0.98 (no confidence/no significance). So, it is correct to say "no correlation with high significance" means "either positive or negative correlation"?

 A: If you did what I think you did, that is estimated a (Pearson) correlation coefficient and performed a null hypothesis test, then the results are telling you that the correlation coefficient is equal to $0.01$ and that the p-value is equal to $0.98$.
The p-value is referring to the null hypothesis (which you are trying to reject), which is that the correlation coefficient is equal to $0$, the alternative being that the correlation coefficient is not equal to $0$ (for a two-sided test). Since you did not reject your null hypothesis (assuming an $\alpha<0.98$, usually $0.05$), because your p-value is equal to $0.98$, then you keep your null hypothesis of no correlation (the coefficient being equal to $0$), despite the estimated coefficient of $0.01$.
Note: your data does not really appear to be linear in the first place, so a Pearson correlation coefficient is probably not appropriate.
A: I'm going to advise you to dispense with the specifics of the math for a moment.  Look at your plot.  Do those data look linear?  At all?
If your answer to that question is "no," then you can stop trying to interpret the results of your linear regression.  The results you've gotten are consistent with the regression being uninterpretable - but you don't need the mathematical results to see that this is an inappropriate model that you should abandon.  All you need is to glance at the graph.
