               NEWS NLREG has been selected as the "Editor"s Pick" by SoftSeek. NLREG is in use at hundreds of universities, laboratories, and government agencies around the world (over 20 countries). For a list of a few organizations using NLREG click here. If you have categorical variables, you may want to use a Decision Tree to model your data. Check out the DTREG Decision Tree Builder. You also should check out the News Rover program that automatically scans Usenet newsgroups, downloads messages of interest to you, decodes binary file attachments, reconstructs files split across multiple messages, and eliminates spam and duplicate files.  ## NIST - Gauss2 Dataset

```   1: /*
2:  * Statistical Reference Datasets  (Nonlinear Regression)
3:  * Statistical Engineering Division
4:  * National Institute of Standards and Technology
5:  * http://www.nist.gov/itl/div898/strd/
6:  *
7:  * Dataset Name:  Gauss2            (Gauss2.dat)
8:  *
9:  * Description:   The data are two slightly-blended Gaussians on a
10:  *                decaying exponential baseline plus normally
11:  *                distributed zero-mean noise with variance = 6.25.
12:  *
13:  * Reference:     Rust, B., NIST (1996).
14:  *
15:  * Data:          1 Response  (y)
16:  *                1 Predictor (x)
17:  *                250 Observations
18:  *                Lower Level of Difficulty
19:  *                Generated Data
20:  *
21:  * Model:         Exponential Class
22:  *                8 Parameters (b1 to b8)
23:  *
24:  *                y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
25:  *                                    + b6*exp( -(x-b7)**2 / b8**2 ) + e
26:  *
27:  *           Starting values                  Certified Values
28:  *
29:  *         Start 1     Start 2           Parameter     Standard Deviation
30:  *   b1 =    96.0        98.0         9.9018328406E+01  5.3748766879E-01
31:  *   b2 =     0.009       0.0105      1.0994945399E-02  1.3335306766E-04
32:  *   b3 =   103.0       103.0         1.0188022528E+02  5.9217315772E-01
33:  *   b4 =   106.0       105.0         1.0703095519E+02  1.5006798316E-01
34:  *   b5 =    18.0        20.0         2.3578584029E+01  2.2695595067E-01
35:  *   b6 =    72.0        73.0         7.2045589471E+01  6.1721965884E-01
36:  *   b7 =   151.0       150.0         1.5327010194E+02  1.9466674341E-01
37:  *   b8 =    18.0        20.0         1.9525972636E+01  2.6416549393E-01
38:  *
39:  * Residual Sum of Squares:                    1.2475282092E+03
40:  * Residual Standard Deviation:                2.2704790782E+00
41:  * Degrees of Freedom:                               242
42:  * Number of Observations:                           250
43:  */
44: Title "Gauss2";
45: Variables y,x;
46: Parameter b1 =  96.0;
47: Parameter b2 =   0.009;
48: Parameter b3 = 103.0;
49: Parameter b4 = 106.0;
50: Parameter b5 =  18.0;
51: Parameter b6 =  72.0;
52: Parameter b7 = 151.0;
53: Parameter b8 =  18.0;
54: Function  y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
55:               + b6*exp( -(x-b7)**2 / b8**2 );
56: Plot;
57: Data;

Beginning computation...
Stopped due to: Singular convergence.  Mutually dependent parameters?

----  Final Results  ----

NLREG version 4.0
This is a registered copy of NLREG that may not be redistributed.

Gauss2
Number of observations = 250
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Singular convergence.  Mutually dependent parameters?
Warning: All data points are on one side of the curve.
This indicates the model does not fit the data well.
Number of iterations performed = 1
Final sum of squared deviations = 1.2829118E+064
Final sum of deviations = -1.7400905E+032
Standard error of estimate = 7.28099E+030
Average deviation = 6.96036E+029
Maximum deviation for any observation = 1.03913E+032

----  Descriptive Statistics for Variables  ----

Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
y        1.182678        133.8252        60.53187        37.76226
x               1             250           125.5        72.31298

----  Calculated Parameter Values  ----

Parameter  Initial guess   Final estimate
----------  -------------  ----------------
b1             96                96
b2          0.009             0.009
b3            103               103
b4            106               106
b5             18                18
b6             72                72
b7            151               151
b8             18                18

----  Analysis of Variance  ----

Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     7               0               0       0.00  1.00000
Error        242   1.282912E+064   5.301288E+061
Total        249          355071
```