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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?


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You could fit the traditional linear model and look at residuals to select a better model. Are you able to share your data? – Max Jul 26 '12 at 19:39
I shared the data (I am looking for a better method.) Do you mean z=p1*x+p2*y+r? (r=residuals) – speecie Jul 26 '12 at 20:13
Where do your data come from? The best way is always to start from what you expect, you must have some idea of what the data represent and thus which model would in principle best fit them. Even if that models turns out not to be good, it's already a starting point. – Raskolnikov Jul 27 '12 at 12:16

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