Determining functional relation of two dependant variables

[fsonnichsen]

I have a pair of correlated datasets that I collected in the lab for temperature and conductivity of a solution vs time. I want to determine the functional relation between the two. (see attached plot-an interesting lead/lag in the phase difference).
If I were trying to determine this relation using for example a carefully controlled temperature I would just use a regression against some order of polynomial on the temperature (the relation is almost linear). However in the present case the temperature varies in an undetermined fashion.
There is a lot of literature out there for doing this when one variable is independent but I cannot find something for both variables dependent on some other parameter (time here). What is the method for doing this and perhaps some texts describing this (or matlab/octave routines for that matter)
Thanks
Fritz

 

[andrewkirk]

I have seen plenty of analyses that estimate relations between variables from observations where both variables were random. I am not aware of any reason for wanting one of the variables to be controlled, other than that where that is the case one can choose values for that variable in such a way as to eliminate sparsely-covered regions in the range of interest. Is there any reason not to just use a technique such as loess together with cubic spline?