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demoNLIN2

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demoNLIN2 Powered By Docstoc
					C1          C2          Visc
     0.01        1.10          3.81   F:            pr5/(1+exp(-pr1-pr2*X1-pr3*X2-pr4*X1*X2))
     0.01        1.20          3.82
     0.01        1.30          3.82   dF/dpr1       pr5*EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2)/(1+EXP(-pr1-pr2
     0.01        1.40          3.83   dF/dpr2       pr5*X1*EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2)/(1+EXP(-pr1
     0.02        1.10          3.84   dF/dpr3       pr5*X2*EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2)/(1+EXP(-pr1
     0.02        1.20          3.86   dF/dpr4       pr5*X1*X2*EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2)/(1+EXP(-
     0.02        1.30          3.86   dF/dpr5       1/(1+exp(-pr1-pr2*X1-pr3*X2-pr4*X1*X2))
     0.02        1.40          3.88
     0.03        1.10          3.88
     0.03        1.20          3.90
     0.03        1.30          3.91             0
     0.03        1.40          3.91             0
     0.04        1.10          3.91             0
     0.04        1.20          3.92             0
     0.04        1.30          3.94             4
     0.04        1.40          3.96
     0.05        1.10          3.94
     0.05        1.20          3.95
     0.05        1.30          3.97
     0.05        1.40          3.99
X1-pr3*X2-pr4*X1*X2))

-pr3*X2-pr4*X1*X2)/(1+EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2))^2
*X1-pr3*X2-pr4*X1*X2)/(1+EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2))^2
*X1-pr3*X2-pr4*X1*X2)/(1+EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2))^2
 pr2*X1-pr3*X2-pr4*X1*X2)/(1+EXP(-pr1-pr2*X1-pr3*X2-pr4*X1*X2))^2
-pr3*X2-pr4*X1*X2))
XLSTAT 2007.1 - Nonlinear regression - on 16/02/2007 at 20:25:56
Y / Quantitative: Workbook = demoNLIN2.xls / Sheet = Data / Range = Data!$C:$C / 20 rows and 1 column
X / Quantitative: Workbook = demoNLIN2.xls / Sheet = Data / Range = Data!$A:$B / 20 rows and 2 columns
Initial values: Workbook = / Sheet = / Range = / 0 row and 0 column
Stop conditions: Iterations = 200 / Convergence = 0,00001
Function: Y = pr5/(1+exp(-pr1-pr2*X1-pr3*X1-pr4*X1*X2))
Summary statistics



Summary statistics:

                Obs. with missing data    Minimum Maximum
 Variable Observations Obs. without missing data                   Mean Std. deviation
Visc              20           0       20     3.814  3.991          3.895     0.053
C1                20           0       20     0.010  0.050          0.030     0.015
C2                20           0       20     1.100  1.400          1.250     0.115


Correlation matrix:

Variables            C1       C2       Visc
C1                    1.000    0.000    0.957
C2                    0.000    1.000    0.258
Visc                  0.957    0.258    1.000


Nonlinear regression of variable Visc:

Goodness of fit statistics:

Observations 20.000
DF           15.000
R²            0.923
SSE           0.004
MSE           0.000
RMSE          0.017
Iterations  200.000


Model parameters:

Parameter       Value Standard error
pr1               0.759     3.683
pr2               2.605     6.333
pr3               0.316     1.297
pr4               0.143     5.637
pr5               5.555     7.047


Equation of the model:

Visc = 5,5549304622744/(1+exp(-0,75948640606628-2,60491734106518*C1-0,316326053376732*C1-0,14325208
 Predictions and residuals:

Observations            C1               C2         Visc   Pred(Visc) Residuals
 Obs1                    0.010            1.100      3.814     3.821     -0.007
 Obs2                    0.010            1.200      3.818     3.821     -0.004
 Obs3                    0.010            1.300      3.824     3.822      0.002
 Obs4                    0.010            1.400      3.829     3.822      0.007
 Obs5                    0.020            1.100      3.843     3.858     -0.014
 Obs6                    0.020            1.200      3.857     3.858     -0.001
 Obs7                    0.020            1.300      3.861     3.858      0.003
 Obs8                    0.020            1.400      3.885     3.859      0.026
 Obs9                    0.030            1.100      3.878     3.894     -0.016
 Obs10                   0.030            1.200      3.899     3.894      0.005
 Obs11                   0.030            1.300      3.911     3.895      0.016
 Obs12                   0.030            1.400      3.911     3.895      0.016
 Obs13                   0.040            1.100      3.913     3.929     -0.016
 Obs14                   0.040            1.200      3.918     3.930     -0.012
 Obs15                   0.040            1.300      3.935     3.931      0.004
 Obs16                   0.040            1.400      3.957     3.931      0.026
 Obs17                   0.050            1.100      3.945     3.965     -0.020
 Obs18                   0.050            1.200      3.946     3.965     -0.019
 Obs19                   0.050            1.300      3.969     3.966      0.002
 Obs20                   0.050            1.400      3.991     3.967      0.024



                                        Pred(Visc) / Visc

             4                                                                               0.03



                                                                                             0.02
           3.95

                                                                                             0.01
                                                                                  Residual
    Visc




            3.9
                                                                                                0



                                                                                             -0.01
           3.85


                                                                                             -0.02

            3.8
                  3.8            3.85              3.9        3.95         4                 -0.03
                                               Pred(Visc)
C:$C / 20 rows and 1 column
A:$B / 20 rows and 2 columns




Std. deviation




0,316326053376732*C1-0,14325208371119*C1*C2))
Residuals




  Observations

				
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