I'm fairly new to statistics and came up with a problem.
I have a sample with a variation coefficient CV = 0.517 for variable x, and I want to prove this variable is not correlated with a second variable y.
In my college textbook it is said that with CV within 0 and 0.1 the mean of the sample is representative, so that would make the mean of my x variable potentially unrepresentative. Therefore, Pearson coefficients of correlation are not to be fully trusted. Linear regressions aren't suitable either. When plotted in a scatter plot (as shown below), the variables seem to not be correlated.
I want to prove they aren't correlated. I can not use the Pearson coefficient (which is r = -0.196) because of the reason explained before. What can I use to show their lack of correlation?
I'm fairly new to statistics, as you may notice. Thank you in advance.