The data is:

x1: time

x2: temp

y: quantity (dependent)

Each row of my y,x1,x2 data represents a known 'good' combination for a desired state. The goal of the model is to predict the quantity needed based on time and time to achieve a desired known good outcome. (i.e. at x2 temp for x2 amount of time, if I use y quantity I will achieve my desired outcome).

I'd like to be able to take the data and build a predictive model on it, but I am struggling with the right approach given that I know I need to account for an interaction and the curvilinear relationship.

I tried to use nlm in R, but the model seems too complex to be able to guess the starting values. I've tried giving it various values, but it seems to runaway to 0 or infinity. I also tried non-linear regressions in SPSS with the same approach.

I am thinking that the end model would look something like:

Code:

```
Y ~ e^(A+B*X1) + e^(C+D*X2) + e^(E+F*X1*X2)
Var-1 Var-2 Interaction
```

I tried to transform the data by doing curve fits on each variable to the growth model (e^(A+B*X1)) and then doing a multivariate linear regression on the transformed data, but the result doesn't seem right since I can't account for the interaction in the transformed data.

I'm new to non-linear multivariate regressions. I don't want to go the route of a decision tree, since my end goal is to build a predictive calculator on this, and I need a formula that I can program into software.

I have SPSS and R, but open to other tools. Any thoughts or guidance? I have my data here if anyone wants to take a look: https://drive.google.com/file/d/0B3Lw4Ug7AvqwUTg2dWROQ2k3bjA/view?usp=sharing