Hello.
I have found a curvilinear effect between two variables and have plotted the curvilinear effect between x and y. The relationship is in the shape of an inverted u (x & y are positively associated up until a certain point where they are then negatively associated). I am trying to figure out where exactly the relationship changes from a positive to a negative association. At the moment, I am just looking at the graph and "eyeballing" it to try and figure out the value.
Hello,
If I understand correctly, you can look at this as a regression problem and fit a second degree polynomial to your data then find the change point by setting the derivative of the fitted curve to zero. Polynomial fitting functions can be found in most programming languages.
As it is u-shaped, I doubt that it is a second degree polynomial. The derivative is zero for an interval, not at a single point. I suggest calculating the differences between consecutive values (you can do this very easily in Excel, for instance) and then you can easily identify the first occurrence of a negative from the list. You can use Excel functions to do that, as well.
Dear Skye,
I would try using the spline regression (some call it segmented or interrupted regression). I hope this reference may help you refine your search:
https://www.ibm.com/support/pages/spline-regression-aka-piecewise-polynomials-or-segmented-regression
Regards,
Valery
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