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Asked by Lalit Patil
on 21 Jan 2013

polyfit(x,y,1)

How to implement the same thing without function..?

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Answer by Jan Simon
on 21 Jan 2013

I assume that this is a homework question. There are good reasons to look for a faster implementation than Matlab's `polyfit`, but you do not ask for speed.

At first you need to construct the Vandermonde matrix. There are a lot of different algorithms to get it, and Google or WikiPedia know more details.

At second the least squares problem must be solved. `V \ y` with the Vandermonde matrix V and the y values is sufficient. A QR decomposition is more stable, so I suggest to try it and ask again in case or problems.

Be sure to use properly scaled inputs for x: A mean of 0 and a standard deviation of 1 is a fair choice to support the numerical stability of the algorithm. It is easy to consider the scaling afterwards.

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