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I have been given a table of values for 3 variables: the predictor variables X1 and X2 and the response variable Y. I am told that the response values were generated based on some non-linear function using the predictors X1 and X2. Eg, f = EXP(X1) + x1*X2 + (error term) and that I am to estimate this equation using Multiple Linear Regression.

The problem is, the data that have been generated don't show any immediately obvious transformations that I could apply. Matrix plot of the data

So, while I understand the need to transform the data, how am I supposed to know which transformations would be appropriate? Is there any systematic approach to problems like this? Or am I just supposed to keep guessing transformations like ln(1/X1^2), exp(X1*X2) etc until I hit on one that looks correct?

Thanks in advance.

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