How to implement without function.?

 polyfit(x,y,1)

How to implement the same thing without function..?

Answer 1

[Walter Roberson]

What you ask for is not possible.

http://www.mathworks.co.uk/matlabcentral/answers/38787-what-can-be-programmed-without-any-built-in-functions

Answer 2

[Jan]

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.