Regression

breadmonkey

Hello,

I really hope this makes sense:

I have a series of computer models with input x. I want the models to behave such that if I input x, the output is also x.

Now, what actually happens is that for input x, I get output y which is less than x and gets progressively less with each model in the series. The relationship is such that it can be represented well with a straight line - (i.e. the output varies linearly from x in model 1 to y in model 10).

So what I have done is used the output from the complete set of models all with input x to produce a line of best fit. So say x =100, I then use this line to try to predict the higher values of x I would have to input in order to get 100 as the output.

When I rerun the series of models, I'm back to a situation where I still don't have input = output = x but it's closer. I can then go though the loop again with a new regression and keep doing that until I converge on an acceptable solution.

My question is this: how can I use the data from the first two regression analyses to better predict for the third iteration? Could someone please point me in the right direction.

Carawaystick

Is this something you can do using the Euler method or Runge Kutta?



Generally, to improve your accuracy, if you have 3 points, you can use a quadratic curve, instead of a straight line, to get a second order approximation
4 points, a cubic curve for third order...

Do you know how close to x is close enough? given the numerical accuracy possible with a digital computer?