using a function that is similar to polyfit but with two linear terms

Hi,

I am looking for a matlab function that is working similar to polyfit, but where I can use two different input function but instead of having just one linear term, I need two. At the moment the regression looks as follows:

y=b0+b1*x+error

and the code to compute R^2 is the following:

x= changePriceWithoutNaN;
y=changeFWithoutNaN;
p = polyfit(x,y,1);
f = polyval(p,x);
plot(x,y,'o',x,f,'-')

yfit = polyval(p,x);
yfit =  p(1) * x + p(2);
yresid = y - yfit;
SSresid = sum(yresid.^2);
SStotal = (length(y)-1) * var(y);
rsq_full = 1 - SSresid/SStotal

Instead of having just one linear term, the term I am looking for is the following:

y=b0+b1*x+b2*z+error

Is there anybody how knows a function that is solving a least squared optimazation in the way to coe above does? Importat is that I do not look for a quadratic solution and therefore from what I can see polyfit(x,y,2) is not an option

What is z?

Are you doing a mixed effects fitting?

Answer 1

There are several multi-dimensional polynomial fitters on the FEX, e.g.,

http://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

http://www.mathworks.com/matlabcentral/fileexchange/13719-2d-weighted-polynomial-fitting-and-evaluation

thanks but from what I can see both are still quadratic, but I am looking only for a linear regression incl. least squared optimization in a way that the parameters b0, b1 and b2 are optimized, the linear equation is the following:

y=b0+x*b1+z*b2

I don't see the problem. Both FEX files handle two-dimensional polynomials of order N. There's no reason why can't choose N=1.

I am not fully sure if I get the description there right but there problem that I have is that there are two linear components which I need to cover. in addition I am not sure how excatly I need to do that. can I just download one of them in instead this code:

              x= dataT(:,2);
              %is the implied volatility
              y=dataT(:,10);

              p = polyfit(x,y,2)

using something like that:

x= dataT(:,2);
%is the implied volatility
y=dataT(:,10);
z=dataT(:,15);
p = polyfitn(x,y,z,3)

is that way the the z not quadratic? As said, the regression must stay linear, I do not want any quadratic components

As said, the regression must stay linear, I do not want any quadratic components

And as I keep telling you, if you want to have only linear terms, then tell that to polyfitn:

 p = polyfitn([x,y],z,1);

Answer 2

Locks, it seems like you are interested in multiple linear regression. If you have the stats toolbox you can use the REGRESS function to do that. If you don't then you can use a simple '\' as follows:

x = dataT(:,2);
%is the implied volatility
y = dataT(:,10);
z = dataT(:,15);
p = [x z ones(length(dataT))]\y

p will have the 3 coeff you desire. We are essentially solving a linear system in a least square sense.

thanks!

I have the Financial Toolbox, but it seems to me that I have to regress function as well, although I have never bought the stats toolbox.

However, I tried to program it, but I always get an error, here is the code:

Y= changePriceWithoutNaN; %change option price
x1=changeFWithoutNaN;
x2=changeLastAdjustmentWithoutNaN

X= [ones(size(x1)) x1 x2];

p2=regress(X,Y)

X is 1804x3 double

Y is 1804x1 double

and the error message I get is:

Error using regress (line 62)
Y must be a vector and must have the same number of rows as X.

Error in regressionAnalysisSAD_fullsample (line 83)
p2=regress(X,Y)

I do not understand that, from what I can see they have the same numbers of rows

What does

X\Y

return?

gives me an error message:

EDU>> X/Y
Error using  / 
Matrix dimensions must agree.

Locks,

1) Regress takes the response first and then the predictors. Here is the documentation for regress:

http://www.mathworks.com/help/stats/regress.html

>> p=regress(Y,X)

2) Statistics Toolbox is required for Financial Toolbox, therefore you will have it already installed. You can check the output of 'VER' to verify it.

3) Use backslash '\' not forwardslash '/', they are different in MATLAB in what they do. http://www.mathworks.com/help/matlab/ref/mldivide.html

>> X\Y

4) You can also use LinearModel.fit function (recommended over regress) It does the same thing but has the added advantage of obtaining the fit statistics automatically: http://www.mathworks.com/help/stats/linearmodel.fit.html

>> X= [x1 x2];
>> LinearModel.fit(x,y) %Ones not required, automatically added.

thanks, this is working, I get the following result:

Number of observations: 1804, Error degrees of freedom: 1801 Root Mean Squared Error: 1.69 R-squared: 0.97, Adjusted R-Squared 0.97 F-statistic vs. constant model: 2.9e+04, p-value = 0

how can I show the r^2 and r^2 adjusted numbers with 4 fractional digits?

IS there a way to see the coefficients b0, b1 and b2 I am also looking for?

mdl = LinearModel.fit(x,y)   
mdl.Coefficients.Estimate

If you are using the last approach. I recommend you read the documentation. This is all covered along with examples. If you are using earlier methods the estimates are the outputs.

mdl.Rsquared