I analyze a set of multivariate measurements. It is known that several pairs of independent variables show high linear correlation. The graph below shows a scatterplot of one such pair (X and Y, upper pane), as well the residuals as a function of Y (lower left pane) and the histogram of these residuals (lower right pane)
As one can see, there is a strange peak in the residual histogram. Many of the remaining linearly-dependent variable pairs from the same data set have a similar peak. I have double checked, and I'm sure there are no duplicate records in the data set. What might be the reason for such a behaviour?
PS Please don't ask me to elaborate on the problem domain, I'm not allowed to.