Uncertainties in polyfit having error in dependent variable (y)

Suppose I have data set... t=y(t)+- error, then what will be the error on the fitted line using polyfit...please.........

Answer 1

[Star Strider]

If you request the ‘S’-structure from polyfit, polyval will produce error bounds if you ask it for delta. See the documentation for details.

[Chris Martin]

My query was if y value is having some plus minus value then how to include that error in fitting along with uncertainties in polyfit. polyfit will give the uncertainties in fitting to y, but what what will be the uncertainties of polyfit to y+- something

[Star Strider]

It seems you want to do weighted fitting, probably inverse-variance fitting.

You cannot do weighted fitting with polyfit, at least to the best of my knowledge.

Since polynomial fitting is essentially a linear regression, you can use the core MATLAB lscov function to do weighted regression with a polynomial fit. (See the ‘Examples’ section.) I haven’t done that (I have the Statistics Toolbox that has its own functions for weighted fitting), but I would experiment with the X matrix in Example 1 and Example 2 as something like:

X = [ones(size(x))  x  x.^2  x.^3];

(with x and y as column vectors), and so on for as many powers of x as you want.