OK, so you apply linear regression to create a model for your data, and when you use that model to predict new values, the output values don't satisfy a constraint (namely, being positive). I can think of only a few different things that might be going on here:
- The new input values you are giving to the model are not within the allowable range for the problem. This is unlikely given your setup - presumably you know your situation well enough to determine what input values are allowed - but if this does happen to be the case, you need to change the way in which you obtain inputs.
- A linear model is not accurate over the full range between your original input data and new input data. Without more domain knowledge, it's impossible to tell what sort of model would be a better substitute. If this is a situation where you can come up with some sort of theoretical prediction about what general form of model should describe the data, you should use that form. If not... try an exponential I guess?
- A linear model is accurate, it's just not this particular one. You might have to do something like forcing the regression to include a particular point (e.g. the origin), for example. That would mean that you're not actually doing a full linear regression, but rather fitting a model with one fewer free parameter - e.g. in slope-intercept form, you're basically forcing the intercept to zero and only fitting the slope. Or the equivalent if using another point. This should be doable with some regression library that you can use. But if you use a linear model, it will predict negative values somewhere. You'll have to live with declaring those regions of parameter space to be outside the domain of the model (or possibly finding a way to make sense of negative values).
Based on the little information you've provided here, there's really not much more I can say. Maybe if you described your situation in more detail, I could offer more specific advice.
