Since Pearson correlation coefficient deal with linear correlation between two variables, I wonder if it is correct to show the variables on a log scale axis. For example, in the figure below, the R value is high and P value is low. So assuming alpha=0.05, we can say that there is a strong positive correlation between Y and X. However, the Y is shown on a log scale axis. Does that matter?
UPDATE:
If I don't use the log scale on the y-axis, the results is like below. As you can see, the R and P values are different.