I have observed the following pattern of behavior in my data-set and I'm wondering how I can explore whether I can predict Y using a value of X. This plot is a 2D histogram of values.
I have previously explored interquartile regression to identify the upper bound, but I'm wondering if there are any other approaches which I can apply which would enable me to identify the range of Y, depending on the X value. I assumed with heteroskedastic data like this that I would need to apply a transformation, but I'm not sure if this is the correct approach.
Could I just fit an interquartile regression to the upper and lower bounds and then provide an estimated value (with an error) for any value of Y that is predicted?
Following some suggestions from @whuber and @jbowman I have included some more graphics of the dataset. These are plots of the mean and standard deviation binned by groups of
8 (e.g. 1 - 8, 9 - 16), and a histogram of slices through the data at 4 intervals.
Histograms of slices through the data use a binwidth of 400. For example, for
1000, I included all values of
X that are 200 above or below so the slice ranges from
800 - 1200: