               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 - Gauss1 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:  Gauss1            (Gauss1.dat)
8:  *
9:  * Procedure:     Nonlinear Least Squares Regression
10:  *
11:  * Description:   The data are two well-separated Gaussians on a
12:  *                decaying exponential baseline plus normally
13:  *                distributed zero-mean noise with variance = 6.25.
14:  *
15:  * Reference:     Rust, B., NIST (1996).
16:  *
17:  * Data:          1 Response  (y)
18:  *                1 Predictor (x)
19:  *                250 Observations
20:  *                Lower Level of Difficulty
21:  *                Generated Data
22:  *
23:  * Model:         Exponential Class
24:  *                8 Parameters (b1 to b8)
25:  *
26:  *                y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
27:  *                                    + b6*exp( -(x-b7)**2 / b8**2 ) + e
28:  *
29:  *
30:  *           Starting values                  Certified Values
31:  *
32:  *         Start 1     Start 2           Parameter     Standard Deviation
33:  *   b1 =    97.0        94.0         9.8778210871E+01  5.7527312730E-01
34:  *   b2 =     0.009       0.0105      1.0497276517E-02  1.1406289017E-04
35:  *   b3 =   100.0        99.0         1.0048990633E+02  5.8831775752E-01
36:  *   b4 =    65.0        63.0         6.7481111276E+01  1.0460593412E-01
37:  *   b5 =    20.0        25.0         2.3129773360E+01  1.7439951146E-01
38:  *   b6 =    70.0        71.0         7.1994503004E+01  6.2622793913E-01
39:  *   b7 =   178.0       180.0         1.7899805021E+02  1.2436988217E-01
40:  *   b8 =    16.5        20.0         1.8389389025E+01  2.0134312832E-01
41:  *
42:  * Residual Sum of Squares:                    1.3158222432E+03
43:  * Residual Standard Deviation:                2.3317980180E+00
44:  * Degrees of Freedom:                               242
45:  * Number of Observations:                           250
46:  */
47: Title "Gauss1";
48: Variables y,x;
49: Parameter b1 = 97.0;
50: Parameter b2 = 0.009;
51: Parameter b3 = 100.0;
52: Parameter b4 = 65.0;
53: Parameter b5 = 20.0;
54: Parameter b6 = 70.0;
55: Parameter b7 = 178.0;
56: Parameter b8 = 16.5;
57: Function   y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + b6*exp( -(x-b7)**2 / b8**2 );
58: plot;
59: 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.

Gauss1
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 = 4.7460231E+103
Final sum of deviations = -9.1298813E+051
Standard error of estimate = 4.42851E+050
Average deviation = 3.65195E+049
Maximum deviation for any observation = 6.62623E+051

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

Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
y        1.182746        152.0519         60.5314        41.70884
x               1             250           125.5        72.31298

----  Calculated Parameter Values  ----

Parameter  Initial guess   Final estimate
----------  -------------  ----------------
b1             97                97
b2          0.009             0.009
b3            100               100
b4             65                65
b5             20                20
b6             70                70
b7            178               178
b8           16.5              16.5

----  Analysis of Variance  ----

Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     7               0               0       0.00  1.00000
Error        242   4.746023E+103   1.961167E+101
Total        249        433167.1
```