               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 - Eckerle4 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:  Eckerle4          (Eckerle4.dat)
8:  *
9:  * Description:   These data are the result of a NIST study involving
10:  *                circular interference transmittance.  The response
11:  *                variable is transmittance, and the predictor variable
12:  *                is wavelength.
13:  *
14:  * Reference:     Eckerle, K., NIST (197?).
15:  *                Circular Interference Transmittance Study.
16:  *
17:  * Data:          1 Response Variable  (y = transmittance)
18:  *                1 Predictor Variable (x = wavelength)
19:  *                35 Observations
20:  *                Higher Level of Difficulty
21:  *                Observed Data
22:  *
23:  * Model:         Exponential Class
24:  *                3 Parameters (b1 to b3)
25:  *
26:  *                y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2]  +  e
27:  *
28:  *           Starting values                  Certified Values
29:  *
30:  *         Start 1     Start 2           Parameter     Standard Deviation
31:  *   b1 =     1           1.5         1.5543827178E+00  1.5408051163E-02
32:  *   b2 =    10           5           4.0888321754E+00  4.6803020753E-02
33:  *   b3 =   500         450           4.5154121844E+02  4.6800518816E-02
34:  *
35:  * Residual Sum of Squares:                    1.4635887487E-03
36:  * Residual Standard Deviation:                6.7629245447E-03
37:  * Degrees of Freedom:                                32
38:  * Number of Observations:                            35
39:  */
40: Title "Eckerle4";
41: Variables y,x;
42: Parameter b1 = 1;
43: Parameter b2 = 10;
44: Parameter b3 = 500;
45: Function y = (b1/b2) * exp(-0.5*((x-b3)/b2)**2);
46: Plot;
47: Data;

Beginning computation...
Stopped due to: Both parameter and relative function convergence.

----  Final Results  ----

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

Eckerle4
Number of observations = 35
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Both parameter and relative function convergence.
Number of iterations performed = 14
Final sum of squared deviations = 1.4635887E-003
Final sum of deviations = 5.6490279E-002
Standard error of estimate = 0.00676292
Average deviation = 0.00441896
Maximum deviation for any observation = 0.018087
Proportion of variance explained (R^2) = 0.9971  (99.71%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9969  (99.69%)
Durbin-Watson test for autocorrelation = 0.974

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

Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
y        7.1E-005       0.3698049      0.07581049        0.121091
x             400             500             450        24.42425

----  Calculated Parameter Values  ----

Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
b1              1        1.55438272      0.01540805     100.88  0.00001
b2             10        4.08883219      0.04680302      87.36  0.00001
b3            500        451.541218      0.04680052    9648.21  0.00001

----  Analysis of Variance  ----

Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2       0.4970796       0.2485398    5434.09  0.00001
Error         32     0.001463589   4.573715E-005
Total         34       0.4985432
```