| Author |
 Topic  |
|
|
giordandue
Italy
Posts |
 Posted - 11/03/2007 : 12:39:56 PM
|
Origin Version (Select Help-->About Origin): 7.5
Operating System:Windows XP sp2
Hi,
I am encountering a strange problem: by fitting my data by Excel 2003 I am getting a best fitting with a power function, with a rather good correlation (y=0.0012x^-0.2 with R2=0.9). On the contrary, by using the fitting Wizard of OriginLab 7.5 and forcing a power allometric1 function (i.e. with similar form of the Excel one) I get another curve with a very poor correlation. y=0.000006x^-3.3 with R2=0.2 and extremely high chi^2/DoF.
I observe that such curve seems rather coincident with a curve of minimum which contain the majority of data on its left. Maybe I am wrong in something, but do you have some suggestion/interpretation? Thank you in advance for your help.. |
|
|
Mike Buess
USA
3037 Posts |
Posted - 11/03/2007 : 3:47:41 PM
|
Best if you could show us the data. Please paste the numbers to your next post.
Mike Buess
Origin WebRing Member |
 |
|
|
giordandue
Italy
Posts |
Posted - 11/03/2007 : 4:39:40 PM
|
Mike,
thank you for your answer. The data derive from about 2000 sampling by MonteCarlo method: please, could you suggest to me how to proceed to pass to you such a large amount of data? |
|
|
|
Mike Buess
USA
3037 Posts |
|
|
giordandue
Italy
Posts |
Posted - 11/03/2007 : 5:35:28 PM
|
Hereafter the data from probabilistic simulation. If it may be of some interest, in my graph I consider a max X value of 0.5 and a max Y value of 5.
0.058 0.289
0.007 15.078
0.003 194.734
0.009 43.547
0.022 1.012
0.025 0.946
0.006 21.36
0.005 70.89
0.111 0.199
0.055 0.909
0.03 1.432
0.012 13.076
0.015 4.59
0.008 51.348
0.03 2.21
0.031 1.075
0.168 0.042
0.055 0.35
0.006 18.998
0.003 57.991
0.046 0.534
0.002 138.711
0.068 0.61
0.097 0.205
0.132 0.044
0.011 28.687
0.077 0.158
0.002 157.992
0.032 0.826
0.012 6.377
0.005 225.437
0.023 8.94
0.029 1.78
0.028 6.87
0.022 10.705
0.031 0.631
0.043 0.944
0.056 0.601
0.008 9.937
0.038 0.998
0.006 39.881
0.028 2.56
0.007 10.988
0.064 0.317
0.038 0.452
0.017 1.683
0.008 63.441
0.098 0.169
0.052 1.094
0.006 85.979
0.004 59.259
0.019 0.855
0.043 0.461
0.009 5.992
0.033 1.825
0.027 1.343
0.025 6.38
0.043 0.999
0.025 1.057
0.006 95.743
0.007 29.281
0.033 3.038
0.081 0.339
0.052 0.476
0.016 14.848
0.01 24.884
0.034 1.464
0.147 0.149
0.012 2.794
0.059 0.504
0.018 3.493
0.034 0.855
0.037 1.086
0.042 0.852
0.041 0.834
0.018 3.05
0.061 1.02
0.032 1.554
0.008 10.094
0.043 0.578
0.006 22.579
0.013 6.661
0.022 1.899
0.012 10.749
0.03 1.715
0.108 0.122
0.005 65.446
0.074 0.578
0.004 86.065
0.009 20.409
0.057 1.387
0.004 153.808
0.029 2.723
0.029 1.982
0.02 2.615
0.021 3.548
0.03 0.989
0.026 2.039
0.042 0.913
0.003 58.645
0.025 2.099
0.081 0.42
0.005 291.67
0.007 9.013
0.002 235.581
0.009 25.181
0.004 80.332
0.019 1.071
0.072 0.352
0.003 287.087
0.036 1.234
0.042 0.757
0.031 0.934
0.02 4.691
0.028 3.523
0.04 1.127
0.027 1.524
0.005 216.947
0.024 2.029
0.094 0.12
0.032 2.064
0.021 1.208
0.024 1.954
0.045 1.14
0.078 0.356
0.035 0.365
0.129 0.082
0.023 2.532
0.112 0.349
0.019 5.229
0.009 7.567
0.003 1600.098
0.084 0.245
0.057 0.908
0.005 84.104
0.03 0.964
0.05 0.726
0.009 6.377
0.015 4.856
0.05 0.525
0.036 1.08
0.008 2.723
0.004 741.21
0.019 5.341
0.008 37.456
0.09 0.143
0.004 114.021
0.006 36.771
0.016 1.38
0.02 4.127
0.041 0.728
0.086 0.282
0.005 28.453
0.032 1.009
0.006 252.423
0.002 10430.025
0.022 2.885
0.021 2.109
0.014 15.063
0.024 5.491
0.019 3.511
0.034 0.825
0.004 281.823
0.048 0.585
0.099 0.251
0.12 0.09
0.007 11.649
0.007 49.547
0.021 14.713
0.059 0.524
0.055 0.909
0.021 2.38
0.028 2.032
0.034 2.588
0.026 1.473
0.035 0.985
0.015 5.866
0.033 2.409
0.022 5.422
0.065 0.225
0.006 50.251
0.003 307.871
0.03 2.106
0.077 0.527
0.008 18.096
0.028 0.793
0.051 0.909
0.029 1.107
0.005 11.371
0.025 2.653
0.024 2.508
0.036 0.832
0.026 1.564
0.048 0.481
0.042 0.773
0.059 0.459
0.07 0.415
0.119 0.068
0.022 3.832
0.004 188.241
0.005 38.827
0.003 114.887
0.012 17.588
0.037 1.273
0.186 0.028
0.008 7.597
0.093 0.708
0.016 16.763
0.004 80.925
0.023 3.464
0.005 58.146
0.019 14.608
0.006 14.223
0.132 0.161
0.045 0.568
0.006 67.094
0.07 0.631
0.015 2.415
0.078 0.269
0.095 0.206
0.002 321.558
0.01 5.288
0.013 47.186
0.01 18.316
0.045 0.862
0.028 1.353
0.007 46.399
0.022 2.014
0.013 28.961
0.064 0.635
0.012 7.862
0.118 0.184
0.026 10.779
0.004 42.136
0.035 2.999
0.006 14.851
0.01 62.042
0.006 11.535
0.012 3.463
0.172 0.074
0.097 0.232
0.17 0.091
0.021 1.318
0.005 17.129
0.01 8.909
0.02 4.115
0.056 1.601
0.018 10.893
0.014 6.547
0.004 1084.425
0.003 353.431
1E-3 53535.336
0.007 82.684
0.003 295.015
0.044 0.524
0.022 9.74
0.007 18.804
0.054 0.858
0.024 2.228
0.017 1.918
0.017 3.352
0.035 1.615
0.067 0.44
0.015 6.275
0.003 7871.167
0.022 4.999
1E-3 2158.602
0.028 2.358
0.03 0.902
0.011 4.247
0.006 13.691
0.011 27.349
0.048 0.698
0.057 0.985
0.015 4.325
0.012 24.078
0.035 2.381
0.018 4.506
0.01 23.597
0.021 3.64
0.01 7.719
0.005 19.708
0.012 7.199
0.026 0.631
0.005 18.951
0.025 3.891
0.007 100.25
0.023 5.132
0.01 22.943
0.006 22.629
0.011 9.257
0.065 1.636
0.044 0.751
0.006 45.402
0.05 0.698
0.005 12.38
0.016 4.827
0.014 9.764
0.01 4.679
0.002 475.119
0.005 43.034
0.005 25.19
1E-3 3314.86
0.065 0.708
0.005 195.621
0.054 0.765
0.049 3.043
0.003 213.715
0.01 12.648
0.053 0.632
0.01 9.56
0.055 1.513
0.003 50.847
0.006 19.414
0.08 0.163
0.078 0.322
0.015 10.353
0.052 0.993
0.017 5.07
0.006 26.642
0.012 21.995
0.008 13.319
0.005 316.898
0.004 50.945
0.008 9.128
0.016 5.816
0.014 8.621
0.004 509.842
0.012 22.036
0.043 0.704
0.02 4.008
0.025 5.575
0.01 48.518
0.008 63.432
0.035 1.408
0.005 64.692
0.003 43.12
0.094 0.171
0.006 8.477
0.202 0.046
0.015 3.689
0.008 11.767
0.018 3.749
0.026 2.643
0.004 787.536
0.025 1.646
0.052 1.088
0.005 31.881
0.016 7.426
0.031 1.829
0.035 1.506
0.07 0.643
0.004 115.279
0.011 7.292
0.016 3.328
0.009 3.127
0.015 4.28
0.066 0.72
0.14 0.058
0.073 0.513
0.029 3.703
0.006 18.959
0.092 0.486
0.035 2.809
0.033 0.949
0.024 1.567
0.01 5.26
0.008 9.207
0.024 2.898
0.053 0.942
0.01 12.216
0.026 3.917
0.018 8.005
0.02 6.814
0.055 0.389
0.032 0.825
0.046 0.669
0.024 5.1
0.009 5.925
0.025 1.612
0.014 27.879
0.019 10.181
1E-3 1071.759
0.008 5.338
0.013 15.383
0.112 0.187
0.051 0.588
0.052 0.393
0.014 5.091
0.026 4.417
0.028 1.388
0.02 3.138
0.006 66.977
0.014 17.943
1E-3 2359.938
0.104 0.145
0.051 1.213
0.09 0.206
0.012 6
0.033 0.699
0.006 58.452
0.036 0.886
0.049 0.465
0.011 50.428
0.002 74.752
0.017 7.575
0.012 35.041
0.015 2.884
0.01 4.453
0.028 3.626
0.01 22.484
0.003 297.339
0.006 88.009
0.008 12.335
0.013 16.146
0.05 0.618
0.002 323.543
0.018 11.886
0.029 2.312
0.057 0.333
0.01 18.805
0.029 1.909
0.014 7.079
0.102 0.112
0.008 161.613
0.012 53.068
0.01 16.573
0.003 105.895
0.005 32.155
0.019 3.872
0.005 89.994
0.102 0.296
0.012 15.552
0.015 3.749
0.044 0.964
0.014 6.228
0.01 8.586
0.038 1.427
0.023 2.013
0.01 17.235
0.059 0.42
0.013 7.646
0.048 0.63
0.042 0.851
0.01 13.216
0.01 7.136
0.01 8.227
0.039 1.267
0.048 0.716
0.026 2.005
0.014 5.842
0.021 2.033
0.061 0.265
0.023 1.308
0.012 44.523
0.006 19.685
0.033 1.66
0.007 17.615
0.005 78.592
0.013 41.549
0.019 8.432
0.019 1.574
0.048 0.713
0.003 131.754
0.004 439.566
0.008 34.856
0.005 23.779
0.016 6.069
1E-3 2422.099
0.014 7.012
0.027 1.589
0.018 2.334
0.017 5.707
0.141 0.025
0.023 2.403
0.004 616.705
0.021 3.957
0.005 78.589
0.032 2.109
0.016 15.487
0.008 55.745
0.012 1.931
0.021 3.593
0.01 8.487
0.025 7.882
0.042 1.651
0.003 132.871
0.017 1.478
0.023 0.968
0.067 0.672
0.002 297.019
0.01 9.733
0.003 175.691
1E-3 585.262
0.023 0.67
0.014 3.379
0.017 1.268
0.02 2.818
0.021 11.327
0.029 1.048
0.002 281.171
0.037 1.146
0.015 4.658
0.118 0.114
0.234 0.051
0.102 0.236
0.015 18.266
0.011 10.868
0.011 22.698
0.056 0.383
0.026 2.123
0.005 33.295
0.003 548.408
0.041 0.759
0.015 5.362
0.005 433.274
0.004 114.357
0.017 7.905
0.041 1.114
0.013 19.929
0.014 2.795
0.014 7.388
0.018 4.361
0.009 12.961
0.013 7.9
0.003 115.172
0.009 8.387
0.004 98.906
0.023 1.953
0.002 113.994
0.002 443.713
0.006 23.749
0.039 1.687
0.002 2990.839
0.006 119.956
0.067 0.15
0.124 0.122
0.027 3.891
0.032 0.567
0.064 0.546
0.019 7.915
0.026 1.751
0.005 36.986
0.022 1.878
0.009 18.752
0.034 1.127
0.025 2.32
0.013 21.326
0.009 10.179
0.005 49.879
0.01 16.889
0.005 86.884
0.006 57.7
0.053 1.256
0.052 0.567
0.017 7.041
1E-3 6321.175
0.002 1406.857
0.103 0.241
0.024 1.425
0.04 0.5
0.014 51.233
0.009 131.52
0.047 0.479
0.036 0.496
0.078 0.156
0.026 1.348
0.03 1.963
0.002 127.631
0.048 0.58
0.006 208.74
0.011 3.627
0.096 0.231
0.016 3.65
0.047 0.67
0.006 134.646
0.002 7771.702
0.122 0.14
0.006 71.765
0.046 0.429
0.002 562.317
0.009 53.56
0.027 2.55
0.023 0.65
0.028 3.057
0.005 387.746
0.199 0.078
0.165 0.099
0.016 4.121
0.004 110.979
0.047 0.804
0.044 0.414
0.007 57.875
0.006 29.89
0.011 7.995
0.005 65.263
1E-3 6587.633
0.02 2.794
0.004 76.427
0.005 27.473
0.038 0.65
0.052 1.976
0.041 0.645
0.016 5.825
0.078 0.141
0.069 0.217
0.027 5.226
0.002 739.294
0.066 0.548
0.003 77.085
0.021 4.795
0.102 0.132
0.284 0.044
0.059 0.347
0.037 0.913
0.064 0.317
0.009 23.631
0.032 2.073
0.009 6.026
0.012 24.948
0.018 9.82
0.051 0.496
0.058 0.469
0.024 3.291
0.058 0.476
0.07 0.437
0.021 2.338
0.003 166.308
0.028 1.727
0.007 19.709
0.01 21.828
0.026 1.266
0.013 3.521
0.021 3.524
0.012 3.228
0.01 18.305
0.082 0.341
0.024 4.033
0.005 31.36
0.07 0.256
0.031 3.095
0.027 1.584
0.012 11.398
0.015 2.843
0.01 3.112
0.082 0.12
0.009 40.015
0.02 1.522
0.043 0.732
0.011 2.967
0.014 3.593
0.055 0.54
0.014 2.603
0.025 2.074
0.004 55.881
0.009 12.816
0.037 1.267
0.007 9.627
0.083 0.428
0.023 1.99
0.028 2.859
0.1 0.183
0.089 0.312
0.025 3.432
0.041 3.842
0.003 81.205
0.017 4.94
1E-3 1187.817
0.016 2.942
0.111 0.168
0.017 6.412
0.008 80.853
0.004 54.647
0.002 123.452
0.004 41.069
1E-3 63460.473
0.036 0.766
0.013 16.514
0.078 0.252
0.015 3.748
0.026 1.069
0.004 92.121
0.039 0.305
0.015 2.944
0.049 0.211
0.003 323.036
0.008 14.676
0.014 1.493
0.036 1.799
0.025 3.493
0.008 48.764
0.026 7.766
0.033 1.692
0.007 47.86
0.014 7.795
0.004 352.388
0.06 1.147
0.034 0.413
0.014 2.241
0.026 6.347
0.013 6.991
0.034 3.536
0.077 0.201
0.035 0.905
0.013 26.905
0.008 44.952
0.008 10.088
0.002 7050.042
0.008 16.027
0.014 2.525
0.002 7717.988
0.011 7.619
0.038 1.559
0.003 125.826
0.024 2.363
0.007 42.377
0.009 10.367
0.039 1.159
0.005 146.852
0.009 18.029
0.027 1.545
0.023 1.574
0.004 131.422
0.002 1678.102
0.098 0.098
0.037 0.682
0.002 365.497
0.002 98.93
0.015 10.379
0.011 7.202
0.003 428.643
0.01 14.337
0.004 45.425
1E-3 639.941
0.009 50.963
0.007 54.487
0.005 81.75
0.002 173.029
0.033 1.591
0.018 3.847
0.01 102.097
0.018 11.949
0.042 0.927
0.011 6.054
0.007 17.614
0.052 0.518
0.014 10.551
0.011 93.581
0.02 1.034
0.089 0.185
0.027 1.305
0.027 2.159
0.003 60.933
0.004 17.498
0.002 4829.63
0.027 1.72
0.003 347.849
0.011 5.453
0.014 6.721
0.028 2.187
0.015 3.793
0.003 151.934
0.006 63.465
0.033 1.67
0.018 14.905
0.058 0.535
1E-3 1327.162
0.014 2.053
0.005 79.951
0.02 1.092
0.019 6.43
0.009 16.422
0.076 0.161
0.023 1.807
0.031 0.957
0.028 4.748
0.009 10.845
0.051 0.733
0.035 0.866
0.133 0.087
0.031 0.772
0.017 5.337
0.015 4.782
0.006 16.33
0.011 10.498
0.021 1.74
0.037 1.566
1E-3 4096.799
0.083 0.277
1E-3 507.151
0.009 12.681
0.006 42.233
0.017 1.859
0.014 7.736
0.004 88.461
0.008 13.75
0.026 4.106
0.023 9.991
0.003 856.995
0.014 30.56
0.011 7.115
0.03 1.515
0.009 12.393
0.003 162.3
0.015 7.867
1E-3 11676.744
0.015 11.186
0.005 131.309
0.021 4.309
0.012 8.752
0.054 0.607
0.026 8.007
0.018 4.619
0.018 1.8
0.04 0.528
0.166 0.098
0.095 0.089
0.033 3.645
0.008 39.894
0.017 3.763
0.007 63.966
0.022 1.841
0.024 3.039
0.006 35.584
0.008 83.229
0.045 0.559
0.023 3.311
0.003 1008.11
0.006 22.391
0.012 6.952
0.042 1.679
0.1 0.183
0.014 4.718
0.007 43.121
0.002 1690.556
0.009 18.514
0.031 0.792
0.004 112.668
0.026 0.8
0.005 28.58
0.029 1.37
0.003 82.509
0.025 7.036
0.014 11.58
1E-3 20587.075
0.016 4.624
0.025 2.378
0.039 2.78
0.011 18.543
0.003 123.12
0.034 1.083
0.145 0.109
0.061 1.666
0.006 134.773
0.009 86.82
0.003 189.921
0.043 3.627
0.043 1.235
0.014 1.135
0.006 179.463
0.011 21.825
0.016 6.976
0.047 0.273
0.056 0.554
0.025 1.885
0.002 310.126
0.016 3.594
0.052 0.501
0.008 13.202
0.024 1.547
0.041 2.044
0.035 1.24
0.004 33.901
0.201 0.077
0.006 57.853
0.046 0.76
0.021 6.641
0.057 0.473
0.187 0.067
0.012 8.037
0.055 0.443
0.032 4.286
0.036 0.696
0.019 9.37
0.004 65.221
0.011 10.196
0.031 0.617
0.005 53.425
0.031 5.439
0.005 18.546
0.017 4.61
1E-3 195089.329
0.028 5.529
0.025 3.647
0.011 6.861
0.011 7.641
1E-3 14145.366
0.017 2.378
0.062 0.232
0.017 16.783
0.002 510.206
0.094 0.242
0.002 184.607
0.014 10.066
0.004 86.824
0.002 4112.555
0.022 1.852
0.004 427.178
0.01 100.927
0.01 14.58
0.033 0.446
0.01 99.643
0.036 1.341
0.011 8.118
0.048 0.332
0.005 53.686
0.01 9.902
0.072 0.297
0.008 22.901
0.081 0.255
0.002 3596.156
0.05 0.525
0.075 0.309
0.007 142.78
0.07 0.349
0.005 57.023
0.009 22.906
0.032 1.428
0.054 0.481
0.027 0.717
0.002 1863.54
0.025 1.214
0.089 0.218
0.005 37.114
0.023 1.748
0.003 321.121
0.052 0.716
0.011 98.346
0.028 1.764
0.063 1.012
0.027 2.206
0.088 0.148
0.006 9.371
0.034 0.76
0.008 10.148
0.024 2.088
0.038 1.263
0.086 0.262
0.003 1679.344
0.019 4.878
0.039 2.764
0.012 2.676
0.013 24.504
0.002 544.541
0.012 10.559
0.043 2.172
0.009 86.926
0.02 3.787
0.013 14.797
0.018 7.017
0.03 5.846
0.011 12.765
0.009 9.473
0.047 1.208
0.202 0.067
0.021 5.726
0.026 4.957
0.036 0.83
0.011 6.406
0.047 0.571
0.022 5.79
0.013 9.858
0.01 20.23
0.01 25.215
0.009 5.323
0.012 15.363
0.025 2.224
0.008 16.438
0.025 1.834
0.058 0.331
0.167 0.093
0.155 0.091
0.027 0.765
0.073 0.195
0.009 20.543
0.026 11.763
0.04 2.018
0.002 1250.313
0.019 1.742
0.005 31.062
0.009 29.247
0.026 2.204
0.03 1.075
0.004 73.886
0.005 68.236
0.058 0.21
0.014 7.781
0.031 1.792
0.06 0.287
0.013 4.481
0.06 0.934
0.066 0.158
0.021 3.725
0.033 1.856
0.067 0.387
0.011 5.565
0.063 0.42
1E-3 28770.947
0.011 5.753
0.053 0.377
0.025 3.134
0.005 35.346
0.011 2.867
0.008 5.223
0.079 0.368
0.002 4829.624
0.038 0.798
0.006 23.902
1E-3 61591.864
0.017 4.781
0.014 2.814
0.003 100.76
0.008 12.925
0.017 4.84
0.035 3.515
0.031 1.471
0.02 1.007
0.007 12.579
0.007 24.724
0.003 684.78
0.027 1.513
0.017 2.032
0.053 1.528
0.016 2.975
0.053 0.126
0.033 1.668
0.108 0.152
0.003 589.349
1E-3 2939.878
0.053 0.557
0.008 17.004
0.03 1.416
0.01 11.249
0.019 12.893
0.017 7.794
0.003 63.435
0.005 39.159
0.009 9.989
0.003 81.4
0.008 77.128
0.004 39.177
0.009 8.236
0.039 0.935
0.041 0.302
0.025 1.926
0.006 80.035
0.004 477.021
0.007 14.243
0.017 5.335
0.004 440.58
0.036 0.867
0.119 0.227
0.026 4.785
0.032 1.06
0.06 0.245
0.016 3.322
0.031 1.831
0.078 0.308
0.007 127.521
0.015 11.399
0.009 8.76
0.025 7.033
0.131 0.074
0.009 13.999
0.015 1.984
0.084 0.24
0.007 24.312
0.044 0.463
0.016 3.49
0.089 0.233
0.049 0.676
0.069 0.449
0.013 13.126
0.02 1.255
0.009 4.205
0.022 8.468
0.011 3.699
0.033 3.317
0.047 1.948
0.011 35.222
0.011 18.336
0.038 0.676
0.071 0.67
0.061 0.237
0.054 0.717
0.011 5.997
0.032 0.56
0.02 2.382
0.02 1.668
0.028 6.692
0.01 5.918
0.031 2.576
0.007 32.265
0.038 3.281
0.024 1.746
0.018 2.594
0.004 270.499
0.066 0.403
0.037 1.853
0.035 0.581
0.018 13.045
0.021 10.413
0.041 2.743
0.053 0.303
0.014 1.786
0.165 0.074
0.037 1.51
0.015 3.275
0.019 2.898
0.009 12.11
1E-3 19974.228
0.026 5.218
0.014 8.192
0.006 154.947
0.023 2.254
0.018 5.249
0.004 74.98
0.005 98.793
0.049 0.558
0.012 6.132
0.011 4.62
0.038 0.926
0.065 0.259
0.021 2.484
0.011 20.121
0.057 0.638
0.044 1.328
0.007 16.114
0.01 8.438
0.003 410.362
0.012 8.428
0.005 71.806
0.012 2.856
0.027 1.754
0.017 29.296
1E-3 1538.344
0.055 1.09
0.027 1.878
0.009 12.249
0.01 10.726
0.005 28.39
0.028 4.341
0.029 5.13
0.007 12.794
0.084 0.255
0.031 4.264
0.029 5.335
0.012 4.398
0.015 7.351
0.059 0.495
0.006 219.586
0.007 41.128
0.048 0.287
0.015 7.929
0.041 0.713
0.011 44.635
0.094 0.221
0.012 10.442
0.009 8.491
0.066 0.37
0.023 0.518
0.041 1.076
0.069 0.186
0.026 2.908
0.029 0.742
0.035 1.772
0.064 0.413
0.002 406.088
0.041 0.869
0.018 1.437
0.02 1.384
0.116 0.152
0.039 1.269
0.024 8.031
0.021 2.07
0.043 1.187
0.002 1925.653
0.016 17.729
0.004 22.672
0.004 36.321
0.011 24.139
0.018 4.861
0.007 52.745
0.013 22.668
0.005 161.785
0.068 0.84
0.023 6.257
0.04 0.894
0.067 0.15
0.03 1.643
0.017 2.321
0.061 0.516
1E-3 969.762
0.006 42.647
0.019 3.354
0.011 6.33
0.013 4.17
0.127 0.236
0.003 284.009
0.004 23.639
0.01 4.536
0.002 230.876
0.096 0.324
0.012 14.658
0.033 0.489
0.041 0.627
0.056 0.633
0.018 16.276
0.003 661.781
0.034 0.929
0.015 12.543
0.013 4.793
0.008 30.243
0.081 0.176
0.037 0.4
0.05 0.969
0.002 2205.461
0.035 0.739
0.015 7.349
0.01 59.497
0.008 13.009
0.004 164.132
0.06 0.291
0.007 29.653
0.024 4.995
0.012 54.671
0.011 8.471
0.008 12.634
0.04 1.733
0.002 1626.837
0.017 2.238
0.045 0.312
0.071 0.253
0.008 7.099
0.032 0.962
0.155 0.102
0.011 4.205
0.003 75.296
0.014 5.11
0.012 6.916
1E-3 2554.642
0.014 4.843
0.006 25.135
0.026 1.634
0.015 4.763
0.008 6.687
0.002 350.868
0.03 1.37
0.003 1298.288
0.017 3.854
0.003 2070.343
0.011 5.038
0.004 50.222
0.008 77.677
0.008 31.377
0.056 0.215
0.035 0.312
0.002 8002.273
0.055 0.393
0.005 42.798
0.002 124.676
0.117 0.146
0.004 144.146
0.014 7.709
0.002 267.038
0.01 5.197
0.003 133.81
0.142 0.038
0.037 1.002
0.003 48.794
0.144 0.085
0.006 11.108
0.006 303.803
0.032 2.134
0.02 10.885
0.005 25.786
0.002 362.048
0.019 4.671
0.005 140.211
0.039 1.091
0.03 0.655
0.008 31.031
0.005 229.785
0.002 514.448
0.021 3.026
0.175 0.106
0.018 3.106
0.017 8.05
0.012 20.296
0.071 0.297
0.029 1.861
0.004 45.351
0.004 478.315
0.003 74.736
0.002 326.578
0.017 2.151
0.003 121.952
0.033 1.064
0.041 0.527
0.012 9.602
0.011 57.711
0.031 2.467
0.026 1.448
0.01 11.745
0.009 20.62
0.004 253.754
0.004 87.461
0.025 3.883
0.03 0.877
0.101 0.221
0.117 0.083
0.115 0.045
0.016 26.37
0.009 23.426
0.069 1.61
0.017 2.684
0.055 0.618
0.002 2570.924
1E-3 14544.362
0.005 29.883
0.076 0.367
0.005 35.138
0.032 0.648
0.077 0.496
0.079 0.148
0.062 0.863
1E-3 4512.11
0.007 28.627
0.007 369.603
0.174 0.072
0.006 65.299
0.008 15.635
0.086 0.269
0.009 74.339
0.038 0.957
0.01 6.15
0.033 1.01
0.175 0.041
0.011 6.485
0.017 1.254
0.059 0.184
0.022 1.678
0.023 1.762
0.101 0.206
0.034 3.767
0.007 14.237
0.02 12.982
0.025 2.543
0.054 0.494
0.251 0.044
0.003 193.402
0.018 9.349
0.008 5.217
0.006 10.828
0.013 9.54
0.006 189.086
0.025 3.014
0.006 113.401
0.021 4.539
1E-3 10648.624
0.036 1.049
0.012 5.374
0.006 88.46
0.01 15.763
0.012 1.729
0.016 5.755
0.056 0.301
0.072 0.15
0.006 350.237
0.065 0.519
0.022 4.156
0.015 9.361
0.008 9.403
0.041 0.266
0.027 3.159
0.052 0.484
0.025 1.486
0.008 18.957
0.049 0.502
0.075 0.179
0.01 271.382
0.013 12.464
0.015 2.629
0.014 10.695
0.049 1.496
0.08 0.225
0.051 1.088
0.015 5.846
0.02 1.591
0.034 0.657
0.068 0.306
0.036 1.26
0.009 3.66
0.036 1.99
0.068 0.516
0.043 0.561
0.06 0.201
0.003 273.206
0.054 0.644
0.003 62.589
0.025 1.761
0.032 2.482
0.006 17.923
1E-3 5011.25
0.044 0.566
0.045 0.932
1E-3 29726.101
0.012 25.997
0.049 0.617
0.101 0.159
0.038 2.45
0.015 9.554
0.022 2.23
0.007 49.563
0.01 6.648
0.002 14287.43
0.014 8.076
0.006 25.667
0.009 14.95
0.017 5.085
0.011 18.191
0.028 1.712
0.003 58.462
0.054 0.447
0.046 0.65
0.079 0.24
0.133 0.139
0.003 23.426
0.049 1.034
0.035 1.401
0.009 8.47
0.022 1.634
0.003 62.598
0.033 1.459
0.017 4.495
0.017 12.219
0.016 4.995
0.005 63.804
0.004 1145.19
0.035 0.993
0.025 5.239
0.053 0.343
0.02 4.944
0.021 5.865
0.003 668.441
0.052 0.376
0.185 0.059
0.035 1.915
0.002 3651.322
0.003 401.636
0.017 16.215
0.032 1.868
0.043 1.545
0.093 0.208
0.007 10.525
0.029 1.431
0.024 6.772
0.013 8.645
0.042 1.209
0.007 12.282
0.013 4.392
0.033 1.483
0.009 22.326
0.007 32.642
0.033 0.988
0.036 1.194
0.047 0.44
0.04 0.853
0.018 2.945
0.041 0.38
0.011 5.695
0.018 5.454
0.024 1.197
0.002 2320.154
0.005 23.081
0.053 0.578
0.004 2180.621
0.048 0.516
0.006 75.903
0.002 188.588
0.013 33.821
0.004 42.759
0.002 1075.909
0.011 13.666
0.042 0.273
0.007 9.079
0.028 1.39
0.025 3.253
0.066 0.507
0.012 25.562
0.006 271.42
0.022 4.33
0.006 23.228
0.004 115.66
0.013 3.726
0.013 3.129
0.006 12.977
0.024 2.231
0.144 0.096
0.125 0.347
0.031 0.969
0.023 13.998
0.058 0.383
0.107 0.143
0.015 9.778
0.024 2.692
0.006 22.675
0.02 20.769
0.022 1.192
0.004 153.529
0.233 0.035
0.059 0.361
1E-3 14490.853
0.064 0.426
0.01 8.438
0.042 0.713
0.003 104.754
0.03 2.318
0.028 1.831
0.024 12.027
0.004 75.581
0.009 38.33
0.008 5.951
0.009 15.533
0.008 10.408
0.011 17.55
0.002 181.423
0.011 8.924
0.028 3.757
0.028 1.147
0.018 5.861
0.078 0.35
0.02 2.086
0.058 0.286
0.066 0.097
0.03 0.668
0.017 3.828
0.01 29.099
0.047 1.043
1E-3 3878.747
0.02 4.304
0.007 5.767
0.025 4.784
0.005 37.069
0.041 1.284
0.012 5.996
0.012 5.997
0.011 6.685
0.019 1.744
0.1 0.209
0.002 1308.033
0.042 1.652
0.024 1.582
0.009 7.582
0.02 1.274
0.018 1.66
0.078 0.217
0.018 2.259
0.064 0.556
0.004 81.413
0.009 9.961
0.015 18.278
0.008 55.705
0.011 18.32
0.029 0.575
0.021 4.693
0.016 8.658
0.07 0.318
0.009 7.649
0.018 3.914
0.036 1.286
0.009 6.105
0.078 0.314
0.002 1647.701
0.006 53.739
0.004 34.454
0.038 2.242
0.005 42.973
0.004 471.056
0.004 60.737
0.006 20.027
0.01 31.71
0.019 7.061
0.007 33.713
0.014 2.543
0.039 1.252
0.02 3.706
0.004 278.894
0.013 4.543
0.071 0.255
0.163 0.057
0.146 0.099
0.003 870.237
0.034 0.495
0.002 1216.61
0.021 2.344
0.012 28.519
0.047 0.543
0.019 3.31
0.014 5.342
0.008 10.377
0.018 1.635
0.005 80.195
0.019 4.005
0.057 0.644
0.047 0.254
0.013 3.666
0.008 16.05
0.006 102.169
0.006 24.047
0.075 0.251
0.009 9.101
0.034 0.889
0.043 0.991
0.039 1.803
0.067 0.127
0.032 1.426
0.002 2330.755
0.098 0.205
0.111 0.157
0.095 0.546
0.076 0.727
0.063 0.46
0.012 8.056
0.029 2.2
0.153 0.106
0.055 0.429
0.018 5.193
0.093 0.217
0.056 0.486
0.012 5.343
0.04 1.343
0.023 1.643
0.061 0.434
0.061 0.142
0.017 5.836
0.058 0.519
0.02 4.969
0.014 5.212
0.006 102.841
0.003 89.628
0.047 0.403
0.026 3.429
0.074 0.209
0.033 0.409
0.015 13.081
0.046 0.61
0.006 64.317
0.004 1170.273
0.009 8.772
0.044 0.827
0.024 1.955
0.13 0.179
0.018 10.357
0.017 5.437
0.061 0.21
0.027 1.562
0.004 26.023
0.007 11.268
0.017 13.424
0.013 13.52
0.008 13.609
0.009 18.05
0.043 1.356
0.048 1.09
0.128 0.209
0.053 0.144
0.01 14.068
0.062 0.547
0.016 3.455
0.057 0.438
0.027 0.702
0.026 2.267
0.014 4.215
0.048 2.128
0.008 11.647
0.004 205.203
0.004 255.854
0.006 343.694
0.024 0.708
0.01 32.289
0.031 3.663
0.01 17.712
0.057 0.695
0.015 13.34
0.036 0.838
0.005 205.263
0.059 0.434
0.035 3.152
0.046 0.315
0.006 17.337
0.002 1199.284
0.026 1.586
0.022 2.89
0.011 10.691
0.169 0.135
0.038 1.443
0.012 11.695
0.03 0.238
0.007 102.112
0.005 52.267
0.017 8.589
0.131 0.174
0.042 0.534
0.003 1124.866
0.084 0.775
0.019 2.656
0.03 1.906
0.015 9.37
0.021 3.806
0.007 16.783
0.026 9.992
0.07 0.627
0.019 3.952
0.012 12.297
0.012 5.822
0.085 0.151
0.044 0.835
0.009 51.563
0.007 14.06
0.003 33.756
0.006 14.654
0.006 34.082
0.003 27.42
0.103 0.313
0.107 0.152
0.028 0.954
0.022 2.162
0.05 0.227
0.004 175.498
0.02 1.554
0.02 4.498
0.029 1.046
0.014 5.618
0.024 2.524
0.082 0.158
0.283 0.039
0.04 0.898
0.063 0.125
0.023 7.322
0.016 8.839
0.047 0.851
0.025 7.675
0.014 6.811
0.004 63.107
1E-3 40943.49
0.031 3.758
0.017 3.598
0.033 1.547
0.088 0.395
0.002 91.121
0.1 0.385
0.003 55.741
0.005 65.343
0.025 9.278
0.011 5.491
0.017 4.519
0.029 0.999
0.006 238.968
0.011 31.274
0.007 237.555
0.023 0.951
1E-3 5343.757
0.002 328.836
0.013 15.088
0.03 3.209
0.024 0.981
0.031 1.817
0.04 0.666
0.007 8.304
0.032 0.825
0.068 0.204
0.036 0.982
0.048 1.748
0.021 2.899
0.027 1.396
1E-3 264.571
0.055 1.282
0.028 0.915
0.085 0.171
0.108 0.155
0.019 2.645
0.013 4.414
0.149 0.082
0.069 0.303
0.006 38.014
0.139 0.073
0.018 3.037
0.032 2.152
0.008 15.134
0.002 280.398
0.006 20.124
0.044 2.17
0.035 1.127
0.004 124.365
0.01 10.294
0.031 5.495
0.018 3.32
0.024 1.632
0.004 106.064
0.078 0.443
0.022 3.824
0.007 25.06
0.028 3.732
0.082 0.274
0.006 41.783
0.037 0.474
0.013 4.315
0.064 1.555
0.003 3111.151
0.013 8.655
0.123 0.172
0.006 56.394
0.007 22.051
0.014 15.917
0.002 1353.701
0.02 9.658
0.013 13.885
0.013 14.761
0.047 0.809
0.106 0.162
0.072 0.323
|
|
|
|
Mike Buess
USA
3037 Posts |
Posted - 11/04/2007 : 11:13:54 AM
|
The first thing I noticed is that your data are unsorted. Of course that should not affect the fit itself but can affect how the fit curve is displayed. To confirm I sorted the worksheet by selecting the X column and then Analysis> Sort Worksheet> Ascending. Then I fit the entire curve to Allometric1 and obtained essentially the same results you got in Origin...
a=3e-6, b=-3.3, R^2=0.2, chi^2/dof=2.4e7
Next I noticed that your data have a large number of outliers (Y values [eg,53535.336] that are much greater than your stated Ymax=5). To determine their effect on the fit I used the Cluster Tool to remove all points with Y values greater than 100. This resulted in Graph3 which shows a significantly better fit...
a=0.017, b=-1.2, R^2=0.62, chi^2/dof=134
Third, most of your X values are repeated several times with different Y values. That does not necessarily affect the fit parameters but will certainly reduce the correlation coefficient and increase chi^2/dof. I used the LabTalk script at the bottom to average all Y values for each X. This resulted in Graph4 and a "very good" fit...
a=0.001, b=-2.1, R^2=0.98, chi^2/dof=1.9
Finally, in all of these fits the dependencies of both parameters were very close to unity (>0.98). This usually signifies an over-parametrized fitting function which is difficult to understand with only two parameters. Perhaps the Allometric1 function is inappropriate for your data.
...Oddly enough, high dependencies seem to be a characteristic of the Allometric1 function and happen even when fitting simulated data. Therefore, one cannot conclude that the function is inappropriate for your data.
sort -w %H col(A);
xsum=col(A)[1];
ysum=col(B)[1];
x0=xsum;
nn=1;
%W=%H;
win -t D;
for(i=2;i>1;i++) {
xx=%W_A[i];
yy=%W_B[i];
if(xx==0/0) break;
if(xx==x0) {
xsum+=xx;
ysum+=yy;
nn++;
} else {
ii=wks.maxrows;
col(A)[ii+1]=xsum/nn;
col(B)[ii+1]=ysum/nn;
nn=1;
x0=xx;
xsum=xx;
ysum=yy;
};
};
Mike Buess
Origin WebRing Member
Edited by - Mike Buess on 11/04/2007 11:18:31 AM
Edited by - Mike Buess on 11/04/2007 11:56:54 AM |
|
|
|
giordandue
Italy
Posts |
Posted - 11/04/2007 : 12:46:58 PM
|
Mike,
thank you very much for your detailed analysis and explanation.
Among other, it is quite interesting to observe that your last result (i.e. after the "average" session of y values for each x) is practically coincident with the result I got by Excel. Maybe, is it possible to derive that this last operation of averaging is applied by default in Excel? In effect, this may justify the big difference of two initial results (by Excel and Origin).
With reference to dependencies I may suppose that you are right considering that the parameters which compone X are involved in the analytical calculation of Y. I do not know that one answer exists, but in such a case which type of function could be generally more adequate?
Again thank you! |
|
|
|
Mike Buess
USA
3037 Posts |
Posted - 11/04/2007 : 1:34:01 PM
|
quote:
it is quite interesting to observe that your last result (i.e. after the "average" session of y values for each x) is practically coincident with the result I got by Excel.
Not really, if the Excel results you reported initially (a=0.0012, b=-0.2) are correct. Graph8 shows your sorted data and curves simulated from your Excel and Origin results. Excel's fit seems to ignore the low-X (high-Y) part of the curve which implies to me that it ignores the multiple Y values, which are more numerous at low-X.
quote:
I do not know that one answer exists, but in such a case which type of function could be generally more adequate?
I'm not sure either. As I added above the parameters in this function seem to be highly interdependent even when fitting a curve generated from given values of a and b. I don't know what to conclude from that fact.
Mike Buess
Origin WebRing Member |
|
|
|
giordandue
Italy
Posts |
Posted - 11/04/2007 : 2:47:17 PM
|
I am not understanding your last comment about the Excel fitting: in the following graph you can see such fitting curve and how it is well centered in the data cloud. As I observed in my previous message, please, let you notice that the equation is really close to the one you got by averaging the Y values for each X..
On the other side, in your graph8 the Origin function has different parameters than the values you reported in graph4 (these latter, near coincident with the Excel one..). Am I wrong?
 |
|
|
|
Mike Buess
USA
3037 Posts |
Posted - 11/04/2007 : 4:56:30 PM
|
quote:
in your graph8 the Origin function has different parameters than the values you reported in graph4 (these latter, near coincident with the Excel one..).
Both sets of parameters used for Graph8 were taken from your initial post...
"Graph8 shows your sorted data and curves simulated from your Excel and Origin results."
Furthermore, in that post you reported b=-0.2 from Excel rather than b=-2.0.
Mike Buess
Origin WebRing Member
Edited by - Mike Buess on 11/04/2007 7:32:35 PM |
|
|
|
giordandue
Italy
Posts |
Posted - 11/05/2007 : 02:57:27 AM
|
| Sorry for the initial mistake and thank you again for your help. |
|
|
| |
Topic |
|
fitting problem