rsquare

 PURPOSE:  calculate r square using data y and estimates yhat
 -------------------------------------------------------------------
 USAGE: R2 = rsquare(y,yhat)
 where: 
        y are the original values as vector or 2D matrix and
        yhat are the estimates calculated from y using a regression, given in
        the same form (vector or raster) as y
 -------------------------------------------------------------------------
 OUTPUTS:
        R2 is the r square value calculated using 1-SS_E/SS_T
 -------------------------------------------------------------------
 Note: NaNs in either y or yhat are deleted from both sets.

 Felix Hebeler, Geography Dept., University Zurich, Feb 2007

0001 function R2 = rsquare(y,yhat)
0002 % PURPOSE:  calculate r square using data y and estimates yhat
0003 % -------------------------------------------------------------------
0004 % USAGE: R2 = rsquare(y,yhat)
0005 % where:
0006 %        y are the original values as vector or 2D matrix and
0007 %        yhat are the estimates calculated from y using a regression, given in
0008 %        the same form (vector or raster) as y
0009 % -------------------------------------------------------------------------
0010 % OUTPUTS:
0011 %        R2 is the r square value calculated using 1-SS_E/SS_T
0012 % -------------------------------------------------------------------
0013 % Note: NaNs in either y or yhat are deleted from both sets.
0014 %
0015 % Felix Hebeler, Geography Dept., University Zurich, Feb 2007
0016 
0017 if nargin ~= 2
0018     error('This function needs some exactly 2 input arguments!');
0019 end
0020 
0021 % reshape if 2d matrix
0022 yhat=reshape(yhat,1,size(yhat,1)*size(yhat,2)); 
0023 y=reshape(y,1,size(y,1)*size(y,2));
0024 
0025 % delete NaNs
0026 while sum(isnan(y))~=0 || sum(isnan(yhat))~=0
0027     if sum(isnan(y)) >= sum(isnan(yhat)) 
0028         yhat(isnan(y))=[];
0029         y(isnan(y))=[];
0030     else
0031         y(isnan(yhat))=[]; 
0032         yhat(isnan(yhat))=[];
0033     end
0034 end
0035 
0036 % 1 - SSe/SSt
0037 R2 = 1 - ( sum( (y-yhat).^2 ) / sum( (y-mean(y)).^2 ) );
0038 
0039 % SSr/SSt
0040 % R2 = sum((yhat-mean(y)).^2) / sum( (y-mean(y)).^2 ) ;
0041 
0042 if R2<0 || R2>1
0043     error(['R^2 of ',num2str(R2),' : yhat does not appear to be a valid estimate of y from a regression.'])
0044 end