NIST/non-linear/Roszman1.dat

0001 NIST/ITL StRD
0002 Dataset Name:  Roszman1          (Roszman1.dat)
0003
0004 File Format:   ASCII
0005                Starting Values   (lines 41 to 44)
0006                Certified Values  (lines 41 to 49)
0007                Data              (lines 61 to 85)
0008
0009 Procedure:     Nonlinear Least Squares Regression
0010
0011 Description:   These data are the result of a NIST study involving
0012                quantum defects in iodine atoms.  The response
0013                variable is the number of quantum defects, and the
0014                predictor variable is the excited energy state.
0015                The argument to the ARCTAN function is in radians.
0016
0017 Reference:     Roszman, L., NIST (19??).
0018                Quantum Defects for Sulfur I Atom.
0019
0020
0021
0022
0023
0024
0025 Data:          1 Response  (y = quantum defect)
0026                1 Predictor (x = excited state energy)
0027                25 Observations
0028                Average Level of Difficulty
0029                Observed Data
0030
0031 Model:         Miscellaneous Class
0032                4 Parameters (b1 to b4)
0033
0034                pi = 3.141592653589793238462643383279E0
0035                y =  b1 - b2*x - arctan[b3/(x-b4)]/pi  +  e
0036
0037
0038           Starting Values                  Certified Values
0039
0040         Start 1     Start 2           Parameter     Standard Deviation
0041   b1 =      0.1         0.2         2.0196866396E-01  1.9172666023E-02
0042   b2 =     -0.00001    -0.000005   -6.1953516256E-06  3.2058931691E-06
0043   b3 =   1000        1200           1.2044556708E+03  7.4050983057E+01
0044   b4 =   -100        -150          -1.8134269537E+02  4.9573513849E+01
0045
0046 Residual Sum of Squares:                    4.9484847331E-04
0047 Residual Standard Deviation:                4.8542984060E-03
0048 Degrees of Freedom:                                 21
0049 Number of Observations:                             25
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060 Data:   y           x
0061        0.252429    -4868.68
0062        0.252141    -4868.09
0063        0.251809    -4867.41
0064        0.297989    -3375.19
0065        0.296257    -3373.14
0066        0.295319    -3372.03
0067        0.339603    -2473.74
0068        0.337731    -2472.35
0069        0.333820    -2469.45
0070        0.389510    -1894.65
0071        0.386998    -1893.40
0072        0.438864    -1497.24
0073        0.434887    -1495.85
0074        0.427893    -1493.41
0075        0.471568    -1208.68
0076        0.461699    -1206.18
0077        0.461144    -1206.04
0078        0.513532     -997.92
0079        0.506641     -996.61
0080        0.505062     -996.31
0081        0.535648     -834.94
0082        0.533726     -834.66
0083        0.568064     -710.03
0084        0.612886     -530.16
0085        0.624169     -464.17