I want to implement a regression analysis, but I have problems with finding a model for the given data. There are $149$ $(x,y,z)$-values. $y$ values are all positive, $x$ is between $[-10, 10]$ and $z$ is between $[-318, 2140].$
The data plots are below.
I tried an exponential model: $p_1 e^{-p_2 x} + p_3 y.$
I tried another exponential model: $p_3 e^{-4x} + p_2 e^{p_1y}.$
I also tried an logarithmic model: $p_1 \ln(p_2 y) + p_3 x.$ This was a straight line.
And $p_1 \ln(p_2 y) + p_3 e^{-p_4 x}.$
Is there any possibility to identify the right model? Or do you have an idea what I also can try?
