How to force my robust regression to pass through y=1?

I have a very simple code with two vectors. I want to compute a robust regression on those values, but forcing the function to pass in y(0)=1. I tried to apply the polyfit function, but honestly I don't have much experience with Matlab. Does anyone have a simple solution for this, so I can extract my statistic results? Thanks

x=[1 1 1 1 1 1 28 28 28 28 28 28 56 56 56 56 56 56 84 84 84 84 84 84 112 112 112 112 112 112];
of_wt_veh=[1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 0.739660 0.697400 0.604162 0.748125 0.683022 0.761243 0.984600 0.675027 0.639655 0.662086 0.660443 0.845765 1.126925 0.709459 0.828230 0.604704 0.635310 0.783181 1.019504 0.640609 0.462813 0.616220 0.754486 0.6987264];

[b,stats] = robustfit(x,of_wt_veh);

scatter(x,of_wt_veh,'filled'); grid on; hold on
plot(x,b(1)+b(2)*x,'g','LineWidth',2)
legend('Data','Robust Regression')

Answer 1

[John D'Errico]

Use robustfit with no constant term. But subtract 1 from y.

That forces the fit to pass through y==1, at x==0.

b(1) = 1;
[b(2),stats] = robustfit(x,of_wt_veh - 1,[],[],'off');

The point is, if your fit has no constant term in a polynomial, then it goes through (0,0). EXACTLY. ALWAYS. So if you subtract 1 from y, then you want the fit to go through 0.

[Carlos Goncalves Moreira]

Great! Thanks a lot!

I have a follow-up question, perhaps you can also help me:

Do you know a way to compare two fits from two different sets of data and statistically test whether they are significantly different or not? I am been reading a lot about this but I only find information about how strong my fit is, but vague information about how can I statistally compare two fits to each other.

[John D'Errico]

Your followup is not a MATLAB question. :) But I'll offer a suggestion.

If you have two completely different models, with different meanings for the parameters, then you can say nothing. So assuming that you have the same model, fit to two different data sets. You cannot even compare a cubic and quadratic polynomial model in that sense, because of course they are different. There are tests that would allow you to TRY to decide if one model is better than another. But that was not your question.

The result of the two model will be a pair of vectors of parameters. With each vector of parameters, you can generate a covariance matrix.

Now, essentially subtract the two vectors. You should be able to find a statistical test that will tell if that difference vector is statistically different from the zero vector, because you will also effectively be able to compute a covariance matrix for the difference vector.

I won't go any further than that, because at this point, your question has nothing to do with MATLAB, and because I am not a statistician.

[Carlos Goncalves Moreira]

Thank you a lot!

Well, I meant my question in a way like 'How can I do (...) in Matlab?'. I was wondering whether there is a toolbox or any function a bit like 'robustfit' that is straightfoward and computes what I am looking for.

I appreciate your explanation! I will try to run what you suggest.

Cheers!

[Walter Roberson]

Carlos asks,

Does anyone know a solution for my question? Thanks.

[Walter Roberson]

kstest2() possibly.