MATLAB: What is an accurate function for linear regression

Question

Hi All,

can anyone tell me an accurate function for linear regression (fitting a line to data). I am also interested in the slop, interception and R-square of the fitted line. I am only familiar with polifit

Thanks Aziz

Answer 1

Which Toolboxen do you have? There's fit in the Curve Fitting TB and LinearModel.fit in the Statistics Toolbox. polyfit is certainly just as accurate; for such simple fitting and wants, the coefficients are returned directly and Rsq is easily computed from the definition as 1-SSE/SST

ADDENDUM

>> x=1:10; x=x(:); y=randn(size(x));  % sample data
>> b=polyfit(x,y,1)                   % fit....
b =
  0.2412   -0.7021
>> plot(x,y,'-*)
>> yhat=polyval(b,x);      % evaluate
>> hold all
>> plot(x,yhat)
>> mn=mean(y);
>> dot(y-mn,y-mn)  % definition for SST, total sum squares
ans =
 28.1924
>> SST=var(y)*(length(y)-1)  % Use builtin VAR function
SST =
 28.1924
>> SSE=dot(y-yhat,y-yhat)
SSE =
 23.3944
>> Rsq=1-SSE/SST
Rsq =
  0.1702