# Linear regression and measured values

1. Mar 7, 2015

### MechatronO

So I'm trying to identify a system that happens to be a synchronus generator via linear regression. I've got a model with the unknown coefficients A, B and C, and the measured variables I, w and T according to

I(w, T) = A*T + B*w + C

1. What I fear is that I could get multiple solutions that all are very similar in their error estimates. But, due to measurement errors, the one that shows the smallest error isn't the most accurate estimation in reality. Am I thinking correctly here?

2. I do have the possibility to run a number of tests with a fixed T, only varing W. Thus I can create a an approximate partial derivate of the function so

∂ I/∂w = B

Then I can have the value for B fixed, when searching for the values for A and C in a mesurement series with a varying T. Would this statistically decrease the risk for what is describe in (1)? I cannot get A with the same method, as I can't lock the value for w.

Any litterature and theory tips would be great so that I can learn more.

2. Mar 7, 2015

### FactChecker

That is unavoidable when there are unknown errors. Linear regression that fits well is probably as good as you can do unless you have better knowledge about the physics of the generator or the measurement errors. If you fix both T and W for several tests, you can get an idea of the magnitude of the measurement errors. That will tell you the most you can expect from even the best model.