I have a population $x$ with $\sigma/\mu=a$, and a second population $y$ with $\sigma/\mu=b$. The linear regression is $y=cx$. How would I find the correlation between $y$ and $x$, given that the populations are homoscedastic and normal?
If they were independent, I know the correlation would be zero, but I tried putting some sample data in Excel and got a numerical answer. What would be the general way to solve this?