Different Rsquares for fitlm and fit when using robust option

Hi all,

when using fit (curve fitting tool or programmatic) or fitlm, the resulting coefficients and Rsquare/ adjusted Rsquare are the same. However, using the "Robust" option (both time using the bisquare method), values for both Rsquare/ adjusted Rsquare AND the resulting coefficients (slope and offset of linear) are different. Does anyone have an explanation for this? Since the values are completely different (R² ~0.7 in fit function and ~0.2 in fitlm) I cannot just ignore this as a "minor difference in calculation"

I have included my data, but compare my results here:

USING FITLM:

Model = fitlm(XDATA, YDATA, 'Robust', 'on')

Model = 


Linear regression model (robust fit):
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate         SE        tStat       pValue  
                   _________    __________    ______    __________

    (Intercept)     0.027124      0.015805    1.7162      0.086706
    x1             0.0056166    0.00064793    8.6686    5.1589e-17


Number of observations: 540, Error degrees of freedom: 538
Root Mean Squared Error: 0.121
R-squared: 0.21,  Adjusted R-Squared 0.209
F-statistic vs. constant model: 143, p-value = 1.87e-29

USING FIT

opts = fitoptions( 'Method', 'LinearLeastSquares', 'Robust', 'on');
[Fitresult, GoodnessOfFit] = fit(XDATA, YDATA, fittype('poly1'), opts)

Fitresult = 

     Linear model Poly1:
     Fitresult(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =    0.005617  (0.004344, 0.006889)
       p2 =     0.02712  (-0.003923, 0.05817)

GoodnessOfFit = 

  struct with fields:

           sse: 7.8536
       rsquare: 0.7290
           dfe: 538
    adjrsquare: 0.7285
          rmse: 0.1208

Although the original question was different, the same problem occurred here (see latest entry):

https://de.mathworks.com/matlabcentral/answers/93865-how-do-i-compute-the-r-square-statistic-for-robustfit-using-statistics-toolbox-7-0-r2008b

Thanks for your help!

[Maximilian Rüppell]

Anyone?

[Martin Kaloudis]

I have exactly the same problem and have not yet found a solution, can anyone help?

Answer 1

[Simon Chou]

When robutness option is used, the regression will consider the outliers. Check this out

https://au.mathworks.com/help/curvefit/least-squares-fitting.html