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## NIST - MGH17 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:  MGH17             (MGH17.dat)
8:  *
9:  * Description:   This problem was found to be difficult for some very
10:  *                good algorithms.
11:  *
12:  *                See More, J. J., Garbow, B. S., and Hillstrom, K. E.
13:  *                (1981).  Testing unconstrained optimization software.
14:  *                ACM Transactions on Mathematical Software. 7(1):
15:  *                pp. 17-41.
16:  *
17:  * Reference:     Osborne, M. R. (1972).
18:  *                Some aspects of nonlinear least squares
19:  *                calculations.  In Numerical Methods for Nonlinear
20:  *                Optimization, Lootsma (Ed).
21:  *                New York, NY:  Academic Press, pp. 171-189.
22:  *
23:  * Data:          1 Response  (y)
24:  *                1 Predictor (x)
25:  *                33 Observations
26:  *                Average Level of Difficulty
27:  *                Generated Data
28:  *
29:  * Model:         Exponential Class
30:  *                5 Parameters (b1 to b5)
31:  *
32:  *                y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]  +  e
33:  *
34:  *           Starting values                  Certified Values
35:  *
36:  *         Start 1     Start 2           Parameter     Standard Deviation
37:  *   b1 =     50         0.5          3.7541005211E-01  2.0723153551E-03
38:  *   b2 =    150         1.5          1.9358469127E+00  2.2031669222E-01
39:  *   b3 =   -100        -1           -1.4646871366E+00  2.2175707739E-01
40:  *   b4 =      1          0.01        1.2867534640E-02  4.4861358114E-04
41:  *   b5 =      2          0.02        2.2122699662E-02  8.9471996575E-04
42:  *
43:  * Residual Sum of Squares:                    5.4648946975E-05
44:  * Residual Standard Deviation:                1.3970497866E-03
45:  * Degrees of Freedom:                                28
46:  * Number of Observations:                            33
47:  */
48: Title "MGH17";
49: Variables y,x;
50: // Note: Using Start 2 initial parameter values.
51: Parameter b1 = 0.5;
52: Parameter b2 = 1.5;
53: Parameter b3 = -1;
54: Parameter b4 = 0.01;
55: Parameter b5 = 0.02;
56: Function y = b1 + b2*exp(-x*b4) + b3*exp(-x*b5);
57: Plot;
58: Data;

Beginning computation...
Stopped due to: Relative function convergence.

----  Final Results  ----

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

MGH17
Number of observations = 33
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 21
Final sum of squared deviations = 5.4648947E-005
Final sum of deviations = 2.3375524E-011
Standard error of estimate = 0.00139705
Average deviation = 0.000949558
Maximum deviation for any observation = 0.00447599
Proportion of variance explained (R^2) = 1.0000  (100.00%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9999  (99.99%)
Durbin-Watson test for autocorrelation = 2.060

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

Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
y           0.406           0.936       0.6308182        0.189811
x               0             320             160         96.6954

----  Calculated Parameter Values  ----

Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
b1            0.5        0.37541006     0.002072315     181.15  0.00001
b2            1.5        1.93584782       0.2203171       8.79  0.00001
b3             -1       -1.46468805       0.2217575      -6.60  0.00001
b4           0.01      0.0128675365    0.0004486139      28.68  0.00001
b5           0.02       0.022122696    0.0008947203      24.73  0.00001

----  Analysis of Variance  ----

Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     4        1.152848       0.2882121  147668.68  0.00001
Error         28   5.464895E-005   1.951748E-006
Total         32        1.152903
```