I have an experiment with N=34 measured points. For each point I measure a variable $x$ and a variable $y$. In my paper I reported the average and the standard deviation of $x_i -y_i$ (where $i$ is the sample index). I've qualitatively plotted the scatter plot $x-y$ vs $x$ and I've stated that I do not see any specific trend for $x-y$ vs $x$. Now the reviewer wants me to perform "a statistical test" (without any other specification) to exclude that any such trend exists. How can I do that?
If I measure the correlation coefficient between $x-y$ and $x$ I do find $r \approx 0.45$ which is statistically significant at p<0.05 with N = 34 points. However I'm pretty sure it's due to 4 points that are a bit outside of the normal distribution tails. If I remove them then $r\approx0.1$! These 4 points are clearly outside the main cloud of points.
So, what kind of test can I use to exclude something? Should I measure the average $r$ of a bootstrapping experiment? Is there any other test?