NIST/ITL StRD

Dataset Name:  MGH10             (MGH10.dat)

File Format:   ASCII

               Starting Values   (lines 41 to 43)

               Certified Values  (lines 41 to 48)

               Data              (lines 61 to 76)

Procedure:     Nonlinear Least Squares Regression

Description:   This problem was found to be difficult for some very

               good algorithms.

               See More, J. J., Garbow, B. S., and Hillstrom, K. E. 

               (1981).  Testing unconstrained optimization software.

               ACM Transactions on Mathematical Software. 7(1): 

               pp. 17-41.

Reference:     Meyer, R. R. (1970).  

               Theoretical and computational aspects of nonlinear 

               regression.  In Nonlinear Programming, Rosen, 

               Mangasarian and Ritter (Eds).  

               New York, NY: Academic Press, pp. 465-486.

Data:          1 Response  (y)

               1 Predictor (x)

               16 Observations

               Higher Level of Difficulty

               Generated Data

Model:         Exponential Class

               3 Parameters (b1 to b3)

               y = b1 * exp[b2/(x+b3)]  +  e

          Starting values                  Certified Values

        Start 1     Start 2           Parameter     Standard Deviation

  b1 =        2         0.02       5.6096364710E-03  1.5687892471E-04

  b2 =   400000      4000          6.1813463463E+03  2.3309021107E+01

  b3 =    25000       250          3.4522363462E+02  7.8486103508E-01

Residual Sum of Squares:                    8.7945855171E+01

Residual Standard Deviation:                2.6009740065E+00

Degrees of Freedom:                                13

Number of Observations:                            16

Data:  y               x

      3.478000E+04    5.000000E+01

      2.861000E+04    5.500000E+01

      2.365000E+04    6.000000E+01

      1.963000E+04    6.500000E+01

      1.637000E+04    7.000000E+01

      1.372000E+04    7.500000E+01

      1.154000E+04    8.000000E+01

      9.744000E+03    8.500000E+01

      8.261000E+03    9.000000E+01

      7.030000E+03    9.500000E+01

      6.005000E+03    1.000000E+02

      5.147000E+03    1.050000E+02

      4.427000E+03    1.100000E+02

      3.820000E+03    1.150000E+02

      3.307000E+03    1.200000E+02

      2.872000E+03    1.250000E+02