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### Multiple linear regression with volumic constraint

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```Hi all,

I have really appreciated the help from the people writing in this forum for some problems solving a linear regression with constraint (multiphased or segmented regression). Since my actual problem a linked with multiple segmented linear regresison, here's the link for a discussion defining a previous problem I had, actually defining/coding the regression.

I am programming a GUI for leveling agricultural field, without using the guide. My gui shows a 3-dimensional representation of the field and his «best-fit-plane», found by linear regression using lsqlin. The user can separate the field into multiple sections, so that the best-fit-plane become a segmented plane, i.e. two planes with a common intersection, where each plane is the best-fit-plane for his section.

My new problem: I want to change my regression or add a new function for changing the cut/fill ratio of the field. This ratio is the total volume higher than the best-fit plane divided by the total volume under the best-fit plane. I think that least-squares regression method will get a ratio of 1, but does anybody have any idea of how to change this ratio in the regression or hoe to change the planes equations after the regression is made?

I thought about it and I propose changing only the third coefficient of the plane equations, i.e the coefficient c in z=ax+by+c. However, programming it that way, I think I will lose the "best-fit" words for my "best fit plane". Is there another way for adding this constraint in the regression or programming it after?

Thanks a lot!
```
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```Hey,
Does anybody have an idea please? I would truly appreciate it!
```
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7/24/2012 9:09:24 PM