Why do regression coefficients obtained from Excel and Matlab differ?

Hi

I would like to run a regression on the following matrices: X(m,1) and Y(m,1). I wan to run a polynomial regression of order 15. I have used: 1. Method 1: b - polynomial order (I even increased precision with vpa, but that did not make any difference)

XM=ones(size(X,1),b);
for f=1:b
    H=vpa(X);
    XM(:,f+1)=H.^f;
end
Beta=pinv(XM'*XM)*(XM'*Y) 
ExpCont=XM*Beta

2. Method 2

BetaP=polyfit(X,Y,b)
ExpContP=polyval(BetaP,X)

Both methods resulted in the same result.

I have run regressions with the same input in Excel and Matlab. For an order 2 polynomial, the difference is insignificant. For higher order polynomials, the coefficients are not even close!!! Sometimes they even have opposite signs!!!! This results in a difference in the output.

Why are they different?

Answer 1

[dpb]

...want to run a polynomial regression of order 15.

very, Very, VERY, bad idea!!!

The differences are caused by numerical precision with such large powers owing to differences in how the normal equations are formed and solved.

For a practical solution, use something other than such a fitting form, say piecewise splines or the like.

Why do you think you need/want such a high-order polynomial, anyway?

[Marina]

Well, I am setting up a Monte Carlo simulation to find out the option price of an American call. Therefore, to increase the precision of the regression, I want to run several regressions of order 5, 10 and 15.

Well, bad idea?

[John D'Errico]

I'll amplify what dpb said. An insane idea.

High order polynomials like that will end up with virtually random coefficients due to numerical issues. Depending on how the data was shipped from one language to the other, you may have lost a bit or so in the least significant bits. That subtle difference is sufficient to see a difference when you compute that high order a polynomial. On top of that, the algorithm chosen by either system to compute the regression coefficients can easily have a huge impact on a problem like this.

By the way, the first method you showed was a TERRIBLE choice in terms of the numerics. Better would have been:

Beta = pinv(XM)*Y;

But even so, 15th degree is insane most of the time, and generally a complete waste of bits.

[Marina]

Thanks a lot:)