# How can I determine a relation, given the raw data for three variables?

I have a dataset relating two variables to a result, as shown in the image below.

In the image Variable 1 is held constant, and plotted against different values of Variable 2, and the result is shown. I have several entries for Variable 1 (though I can have as many intervals as I like. What I'm trying to do is determine an equation that gives Result as a function of Variable 1 and 2. i.e.

Result (Var1, Var2) where 0 >= Variable 1, Variable 2 <= 100


It seems like it should be a simple thing to do, but I'm not quite sure how to start.

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Are these plots of actual data? If so, you must have an enormous dataset which exhibits no appreciable scatter, making this purely a problem of mathematical discovery (and you might want to point Eureqa at it.) Otherwise, please describe your raw data. –  whuber Sep 4 '12 at 13:07
It sounds like you have a multiple regression situation. Note that "multivariate" usually refers to having >1 response variable, not >1 input variable. Also note that you seem to have 3 variables (2 covariates & 1 output variable), not 2. The data / fitted lines you display here are all cases where var1 is >0, is what you are trying to figure out what is likely to happen if var1 were <=0? –  gung Sep 4 '12 at 13:37
whuber. Thanks for the tip on Eureqa, I've just had a little play and it seems like a very useful tool! I couldn't find a way to give it multiple datasets though - i.e. it seems to only fit to 1 of the lines in the above graph. A slightly bigger version of the data set (not that big) is available here: goo.gl/NMptB –  user714852 Sep 4 '12 at 13:53
gung. Thank you for the clarification - I should have checked I was using the correct terminology. I've edited the question accordingly. var 1 and var 2 always take values between (and including) 0 and 100. I am attempting to find a relation that allows me to calculate Result for any value of Var1,Var2 because the data you see is smoothed experimental data. –  user714852 Sep 4 '12 at 13:58
We cannot do a whole lot with smoothed data: the smoothing has thrown away all the information needed to evaluate the goodness of fit and has also added smoothing artifacts. Please start over by sharing the particulars of the actual experimental data. –  whuber Sep 4 '12 at 15:11