# Which type of regression has the best predictive power for extrapolating for smaller values?

I have a data set which deals with response variable in the order of 10-20. The scatter plot for such a regression appears linear, but the problem being when I predict for test cases using values very small compared to the trained sample the predicted response variables appear in negative values. Please note that the values of the data set predicted should not be negative.

Here is the 3d scatter plot of my data Is there a type of regression which has better predictive power which can perform such operations without such an error?

• Regarding "I predict for test cases using values very small compared to the trained sample". Extrapolating is always a hard problem, and not specifically an issue due to absolute magnitude. If your measurements were from 50 to 300, and you tried to predict down to where they should be 1.0 (or up to where they should be 10,000), then you'd have exactly the same problem. Do you have any model separate to the data measurement, which can be used to constrain predictions? – Neil Slater Mar 18 '17 at 9:04
• I do not have any more data I've used all I have. Is there a better regression or one which does this by the most accuracy in your experience ? – Rahul Aedula Mar 18 '17 at 13:30
• I'm not asking whether you have more data, but whether any model for your measurements exists beyond "must be positive"? E.g. if this represents some physical phenomenon, is there any theoretical model that the data should conform to, so that you are not just fitting statistical model, but have some basis in what you are measuring? If not, and you want a "better regression", please explain what regression model you have used - have you used linear regression based on minimising mean square error? – Neil Slater Mar 18 '17 at 13:36
• Yes as a matter of fact. It is a physical phenomenon. That's why I didn't mention about the data set. It's about Gravitational waves analysis. I'll spare you the details but yes the values have to be positive. Also as far as a theoretical model is concerned we have evaluated that the normal calculations for such a data set take too long hence we are using a regression to estimate such calculations quickly. Keep in mind we don't need high accuracy but it should still be very close to the value. It can't be negative – Rahul Aedula Mar 18 '17 at 13:59