Methods and guidelines for effective model calibration

Reference
Bard, Jonathon, 1974, Nonlinear parameter estimation: New York, Academic Press, 341p.
Beck, J.V. and Arnold, K.J., 1977, Parameter estimation in engineering and science: New York, 
John Wiley and Sons, 501p.

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90
APPENDIX D: CRITICAL VALUES FOR THE CORRELATION 
COEFFICIENT FOR NORMAL PROBABILITY GRAPHS, R
N
2
 
Table D1: Critical values of R
2
N
below which the hypothesis that the weighted residuals are inde-
pendent and normally distributed is rejected at the stated significance level (from Sha-
piro and Francia, 1972; Brockwell and Davis, 1987, p.304)
[ND, the number of observations (N-OBSERVATIONS in the UCODE documentation);
NPR, the number of prior information values (NPRIOR in the UCODE documentation)]
ND or Significance level ND or Significance level
ND+NPR 0.05 0.10 ND+NPR 0.05 0.10
35
0.943
0.952
81
0.970
0.975
83
0.971
0.976
50
0.953
0.963
85
0.972
0.977
51
0.954
0.964
87
0.972
0.977
53
0.957
0.964
89
0.972
0.977
55
0.958
0.965
57
0.961
0.966
91
0.973
0.978
59
0.962
0.967
93
0.973
0.979
95
0.974
0.979
61
0.963
0.968
97
0.975
0.979
63
0.964
0.970
99
0.976
0.980
65
0.965
0.971
67
0.966
0.971
131
0.980
0.983
69
0.966
0.972
200 0.987 
0.989
71
0.967
0.972
73
0.968
0.973
75
0.969
0.973
77
0.969
0.974
79
0.970
0.975
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References
Brockwell, P.J and Davis, R.A., 1989, Time series, Theory and methods: New York, Springer-Ver-
lag, 519 p.
Shapiro, S.S., and Francia, R.S., 1972, An approximate analysis of variance test for normality: 
Journal of the American Statistical Association, v. 67, p. 215-216.