MATLAB: What does it means SE in the fitnlm function

fitnlmse

Hello everybody, I had the following problem. I wanted to make a nonlinear fit of some data. I used the function lsqcurvefit for this obtaining good results. Unfortunately the function didn't output also the errors o the parameters and the goodness of the fit. I turned then to teh function fitnlm t get the errors and the p-values. the output of the function in my case is the following:
mdl = 
Nonlinear regression model:
    y ~ 1/(p1*pi)*erf(2/p2*(xdata - p3)) + p4*xdata
Estimated Coeff:  ________Est___________________SE___________________tStat_________________p-Value
      p1        35.0596860208699        1.36289657792749    25.7243921429343    3.53913692983459e-11
      p2        126.391761700049        8.82277996474738    14.3256164389302    1.84776026703891e-08
      p3        21.7624312682344        1.37103425460148    15.8730033149756    6.27414889294585e-09
      p4    6.14006005505809e-05    1.57649921913032e-06     38.947434800794    3.87121533656818e-13
Number of observations: 15, Error degrees of freedom: 11
Root Mean Squared Error: 0.000254
R-Squared: 0.999,  Adjusted R-Squared 0.999
F-statistic vs. zero model: 2.1e+04, p-value = 2.86e-21
Now I don't understand exactly what stands SE for (Squared Errors?). Is it the error on the parameter? or it is the square of it? Or it is something else?
Thanks for the help
Regards
Gabriele

Best Answer

The ‘SE’ is the standared error of the estimate, essentially the expected standard deviation of the calculated value, since all estimated values have some measure of uncertainty. A good explanation is in the Formulas for the slope and intercept of a simple regression model: section of: Mathematics of Simple Regression. It is relevant itself, and is also used to calculate the confidence interval for the parameter. (This works the same way for linear and nonlinear regression, when least-squares regression is used for both.)
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