MATLAB: Determine the the slope and its uncertainty

MATLABregression

Hi,

I am trying to linearly fit a set of data points, find the slope and then compute the uncertainty of the slope, +, – uncertainty. How can I do this in MATLAB?

I have tried to look into regression and regress but are getting very confused.

Additional questions:

What is the outputs of Regress? Does it gives the slope of the linear fit? And the 95% confidence intervals? I noticed that b not the same as the polyfit?

Likewise, the polyfit does not give the same slope as regression. And Regression gives me matrix of result.. shouldn't slope just be one value. The inputs are just vectors of x,y data.

Thanks

Best Answer

Do you also want to fit an offset? Polyfit does that for you, but you have to tell regress explicitly,. Example:

x = 1:10 ; y = 10*x+3 ;
yr = y + rand(size(y))-0.5 ; % add noise
[b, bint] = regress(yr(:), [x(:) ones(numel(x),1)])

Related Solutions

MATLAB: Uncertainties and confidence intervals for both linear and nonlinear regression

I am not sure what do you mean by ‘the uncertainty of such parameters’?

The standard deviations of the estimated parameters are the square roots of the diagonals of the estimated variance-covariance matrix. In the nlinfit documentation, this is CovB.

The confidence interval (95% is the default) is the probability that the uncertainty of the parameter estimate includes zero. If it does (one of the confidence bounds is positive and the other negative), then that parameter is not needed in the regression model with the data you supplied to it. The confidence interval is therefore more meaningful than the variance or standard deviation.

MATLAB: Does POLYVAL produce error bounds with at least 50% of the predictions in MATLAB 6.5 (R13)

The bounds produced by POLYVAL surround an interval that is one standard error below and above the estimate. This standard error measures both the uncertainty in estimating the polynomial, and the additional uncertainty in predicting a new observation.

You can use the POLYCONF function in the Statistics Toolbox to compute a confidence interval for predicing a new observation. These intervals have the form

 p_hat(x) +/- T * SE

where p_hat (read this as "P Hat") is the estimated polynomial, SE is the standard error, and T is a quantile from the t distribution.

In the POLYVAL function we effectively set T=1. The confidence level of the resulting intervals depends on the number of error degrees of freedom (d.f.). It has a low value equal to 50% when there is 1 d.f., and it rises to 68% as the d.f. get larger. Here's an illustration using a range of d.f. values:

errordf = [1 2 3 10 50 10000];
tcdf(1,errordf) - tcdf(-1,errordf)
 ans =
     0.5000    0.5774    0.6090    0.6591    0.6779    0.6827

This is the reason for the claim in the file help.

Best Answer

Related Solutions

MATLAB: Uncertainties and confidence intervals for both linear and nonlinear regression

MATLAB: Does POLYVAL produce error bounds with at least 50% of the predictions in MATLAB 6.5 (R13)

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