Determine the the slope and its uncertainty?

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

Answer 1

[Jos (10584)]

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)])

[Lizan]

What does regress give you? Does it give you,

slope + error; slope - error;

I also find that polyfit does not give the same slope as in regress. Its confusing for me...

[Venkatessh]

regress gives you the 95% confidence interval of the coefficients (slope and y-intercept). I am not sure if you can get the errors by simply subtracting the confidence interval and even if you can bear in mind that it gives you a 95% estimate (~ 2-sigma) and not a 1-sigma uncertainty.

I am assuming by error you mean the uncertainty

Answer 2

[Ganessen Moothooveeren]

But still how to find the uncertainty in the slope using the polyfit function??

[Venkatessh]

In order to estimate the uncertainties of the coefficients obtained from polyfit function, you may follow the following steps:

[b, bint] = polyfit(x,y,1);
b_err = sqrt(diag((bint.R)\inv(bint.R'))./bint.normr.^2./bint.df);

where, b_err contains the uncertainty of the coefficients

[Ankan Biswas]

Hi Venkatessh, Can you explain the rationale behind your error calculation? Thanks in advance.