[R-br] Erro no ajuste usando nls()

[Elias Teixeira Krainski]

Mesmos resultados com Matlab R2015b:

 >> mc'

ans =

   Columns 1 through 17

     8.2834    7.7900    7.3243    7.8408    6.9411    8.0788 7.5859    
8.5045    7.7377    7.6300    7.4584    8.3254 8.4231    9.2183    
8.4298    8.1621    7.7530

   Columns 18 through 34

     8.5202    7.5397    8.4437    8.5259    8.5115    8.6919 7.8751    
8.7256    8.4112    8.4320    8.0465    8.0767 7.6655    6.8035    
7.0164    8.7062    7.7244

   Columns 35 through 51

     6.8070    6.9982    7.3664    7.2780    7.9291    7.8874 7.5017    
6.7873    7.0532    7.3677    7.2136    7.2331 6.5543    7.7349    
7.4804    7.8031    8.5610

   Columns 52 through 68

     7.7096    7.2965    7.4251    7.5591    7.4227    7.7352 7.4859    
7.5243    7.4444    6.5160    6.2838    7.3013 6.7309    7.1362    
6.7886    7.4702    7.3704

   Columns 69 through 85

     7.1180    7.1678    7.5752    7.1045    7.3966    7.1747 7.2116    
7.4036    6.9948    7.1491    7.6249    6.7693 7.0764    7.1518    
7.1104    7.7013    7.0376

   Columns 86 through 102

     6.8196    7.1667    7.5509    7.1804    6.8358    7.5356 6.3120    
5.8329    5.8187    6.8354    6.5233    6.1144 7.1026    6.9876    
5.8963    6.6491    6.1090

   Columns 103 through 112

     6.5956    6.6286    6.3461    6.5980    5.7874    6.3855 6.7979    
6.1270    6.7997    6.4785

 >> x'

ans =

   Columns 1 through 29

    269   270   271   272   273   274   275   276   277   278   279 
280   281   282   283   284   285   286   287   288   289   290 291   
292   293   294   295   296   297

   Columns 30 through 58

    298   299   300   301   302   303   304   305   306   307   308 
309   310   311   312   313   314   315   316   317   318   319 320   
321   322   323   324   325   326

   Columns 59 through 87

    327   328   329   330   331   332   333   334   335   336   337 
338   339   340   341   342   343   344   345   346   347   348 349   
350   351   352   353   354   355

   Columns 88 through 112

    356   357   358   359   360   361   362   363   364   365   366 
367   368   369   370   371   372   373   374   375   376   377 378   
379   380

 >> myfun = 'mc ~ 9.548 - b1 * (x - 268)^b2';
 >> b0 = [1;1];
 >> mnl = fitnlm(x, mc, myfun, b0);
 >> mnl

mnl =


Nonlinear regression model:
     mc ~ 9.548 - b1*(x - 268)^b2

Estimated Coefficients:
           Estimate       SE       tStat       pValue
           ________    ________    ______    __________

     b1    0.66888      0.10226    6.5412    1.9908e-09
     b2    0.30739     0.036839    8.3441    2.3263e-13


Number of observations: 112, Error degrees of freedom: 110
Root Mean Squared Error: 0.541
R-Squared: 0.432,  Adjusted R-Squared 0.427
F-statistic vs. zero model: 1.04e+04, p-value = 5.23e-126
 >>
 >> model2 = 'mc ~ b1 - b2 * (x - 268)^b3';
 >> ini2 = [8;0;1.4];
 >> mnl2 = fitnlm(x, mc, model2, ini2);
Warning: Rank deficient, rank = 2, tol =  1.038937e-10.
 > In nlinfit>LMfit (line 574)
   In nlinfit (line 276)
   In NonLinearModel/fitter (line 1123)
   In classreg.regr.FitObject/doFit (line 220)
   In NonLinearModel.fit (line 1430)
   In fitnlm (line 94)
 >> mnl2

mnl2 =


Nonlinear regression model:
     mc ~ b1 - b2*(x - 268)^b3

Estimated Coefficients:
           Estimate        SE         tStat       pValue
           _________    _________    _______    __________

     b1       8.0691      0.13723     58.802    2.1409e-84
     b2    0.0021746    0.0035616    0.61058       0.54275
     b3       1.4158      0.34368     4.1196    7.4165e-05


Number of observations: 112, Error degrees of freedom: 109
Root Mean Squared Error: 0.49
R-Squared: 0.537,  Adjusted R-Squared 0.528
F-statistic vs. constant model: 63.2, p-value = 6e-19
 >>