I have a set of paired X and Y values, where the X values vary from about 6 to about 100, and about half of the Y values are zero, and the rest are either positive or negative values. The absolute values of Y vary so much that a normal linear regression is useless. It very clearly looks like, however, that with increasing X leads there is an increasing probability that Y is positive, and this is what I want to prove. I don't know how to calculate the statistical significance of this, however. If there were no negative values, I could use a logistic regression, but in this case it is important to take into account also the negative values. See graph below. How can I go about in order to do a statistical test for this?