Best 100 Fits for m=5 and n= 5

Fit Result 1 for Cancer of the Lower GI Tract (1890s decade)

for European American Males (EAM)

CAL(g) vs. Cell Doubling (g)

Linear-Linear Plot Log-Linear Plot CLOSEUP of Log-Linear Plot Log-Log Plot

CAL(t) vs. Age (t)

Linear-Linear Plot Log-Linear Plot CLOSEUP of Log-Linear Plot Log-Log Plot

Goodness of Fit

The values of INC(h,t) vary more than a thousand-fold among the 18 age of death intervals recorded from maturity to old age (Fig.1). Statistical comparison of CAL(h,t) to INC(h,t) required a term that gave weight to all 18 intervals. Such a term is |log10 CAL(h,t) - log10 INC(h,t)| which is zero when the terms are identical, i.e. their ratio is equal to 1.0. The square root of the average of the square of these 18 terms is here employed as a goodness of fit parameter, GOF(h,t).

GOF(h,t) = {SUM [log10 CAL(h,t) - log10 INC(h,t)]2 /18}1/2

GOF(h,t) may have practical meaning for the general reader as it is akin to a standard deviation of |log10 CAL(h,t)-log10 INC(h,t)| averaged over all adult life. If GOF(h,t) = 0.1 then the 95% confidence limits of the average ratio of CAL(h,t) /INC(h,t) would be 10-0.2 and 100.2 or 0.63 and 1.58. If GOF(h,t) = 0.03 the 95% limits would be 0.93 and 1.07. A GOF(h,t) of greater than 0.1 indicates a poor fit of the model with stipulated parameters n and m or marked errors in the values of INC(h,t) arising from either sampling error or bias. Errors arising from small sample sizes do not contribute significantly to GOF(h,t) when large U.S. European-American cohorts are studied.

Table of Results

Fit RankGoodness of Fit GOF(h,t)F_promF_initfmuR_initiationR_promotionArea
1 0.04508 0.375 0.371 1.000 0.132 1.874e-003 3.511e-002 0.232
2 0.04786 0.948 0.150 0.114 0.132 1.520e-003 3.511e-002 0.242
3 0.04798 0.375 0.371 0.948 0.132 1.874e-003 3.511e-002 0.227
4 0.04946 0.739 0.371 0.271 0.132 1.874e-003 2.848e-002 0.264
5 0.05222 0.375 0.371 0.896 0.132 1.874e-003 3.511e-002 0.222
6 0.05750 0.792 0.371 0.218 0.132 1.874e-003 2.848e-002 0.249
7 0.05798 0.375 0.371 0.844 0.132 1.874e-003 3.511e-002 0.216
8 0.05814 0.896 0.150 0.166 0.132 1.520e-003 3.511e-002 0.237
9 0.06313 0.531 1.000 0.583 0.121 4.329e-003 1.233e-002 0.253
10 0.06348 0.583 0.733 0.479 0.132 2.310e-003 2.310e-002 0.275
11 0.06403 0.896 0.150 0.218 0.132 1.520e-003 3.511e-002 0.260
12 0.06422 0.635 0.733 0.427 0.132 2.310e-003 2.310e-002 0.283
13 0.06479 0.583 0.733 0.427 0.132 2.310e-003 2.310e-002 0.245
14 0.06490 0.948 0.150 0.166 0.132 1.520e-003 3.511e-002 0.282
15 0.06515 0.583 1.000 0.479 0.121 3.511e-003 1.520e-002 0.249
16 0.06529 0.479 1.000 0.739 0.121 5.337e-003 1.000e-002 0.263
17 0.06546 0.375 0.371 0.792 0.132 1.874e-003 3.511e-002 0.209
18 0.06614 0.687 0.371 0.323 0.132 1.874e-003 2.848e-002 0.269
19 0.06614 0.635 1.000 0.427 0.121 3.511e-003 1.520e-002 0.258
20 0.06647 0.479 1.000 0.687 0.121 5.337e-003 1.000e-002 0.248
21 0.06738 0.531 1.000 0.635 0.121 4.329e-003 1.233e-002 0.272
22 0.06754 0.792 0.371 0.271 0.132 1.874e-003 2.848e-002 0.308
23 0.06755 0.687 0.977 0.323 0.121 2.848e-003 1.874e-002 0.236
24 0.06905 0.323 0.733 1.000 0.132 2.310e-003 2.848e-002 0.245
25 0.06918 0.583 0.371 0.479 0.142 1.874e-003 2.848e-002 0.278
26 0.06941 0.531 0.371 0.531 0.142 1.874e-003 2.848e-002 0.260
27 0.06965 0.427 1.000 0.896 0.121 6.579e-003 8.111e-003 0.261
28 0.06984 0.583 0.371 0.427 0.142 1.874e-003 2.848e-002 0.256
29 0.07042 0.479 1.000 0.792 0.121 5.337e-003 1.000e-002 0.279
30 0.07053 0.427 1.000 0.844 0.121 6.579e-003 8.111e-003 0.249
31 0.07097 0.844 0.371 0.218 0.132 1.874e-003 2.848e-002 0.296
32 0.07103 0.687 0.371 0.271 0.132 1.874e-003 2.848e-002 0.228
33 0.07106 0.896 0.150 0.271 0.132 1.520e-003 3.511e-002 0.273
34 0.07107 0.531 1.000 0.531 0.121 4.329e-003 1.233e-002 0.233
35 0.07162 0.635 0.733 0.375 0.132 2.310e-003 2.310e-002 0.249
36 0.07163 0.739 0.371 0.323 0.132 1.874e-003 2.848e-002 0.310
37 0.07175 0.739 0.977 0.323 0.121 2.848e-003 1.874e-002 0.272
38 0.07207 0.583 1.000 0.531 0.111 1.520e-002 3.511e-003 0.255
39 0.07245 0.583 1.000 0.531 0.111 1.233e-002 4.329e-003 0.256
40 0.07251 0.531 0.371 0.479 0.142 1.874e-003 2.848e-002 0.242
41 0.07251 0.531 1.000 0.583 0.111 1.874e-002 2.848e-003 0.239
42 0.07267 0.531 1.000 0.583 0.111 2.310e-002 2.310e-003 0.238
43 0.07267 0.427 1.000 0.948 0.121 6.579e-003 8.111e-003 0.273
44 0.07289 0.583 1.000 0.531 0.121 4.329e-003 1.233e-002 0.268
45 0.07297 0.531 0.371 0.583 0.142 1.874e-003 2.848e-002 0.276
46 0.07306 0.583 1.000 0.531 0.121 3.511e-003 1.520e-002 0.273
47 0.07309 0.583 1.000 0.531 0.111 1.874e-002 2.848e-003 0.254
48 0.07316 0.583 1.000 0.427 0.121 3.511e-003 1.520e-002 0.225
49 0.07316 0.531 1.000 0.583 0.111 2.848e-002 1.874e-003 0.237
50 0.07328 0.583 1.000 0.479 0.111 1.000e-002 5.337e-003 0.236
51 0.07330 0.323 0.977 1.000 0.121 2.848e-003 2.310e-002 0.221
52 0.07331 0.687 0.977 0.375 0.121 2.848e-003 1.874e-002 0.271
53 0.07336 0.531 1.000 0.635 0.111 3.511e-002 1.520e-003 0.255
54 0.07338 0.531 1.000 0.635 0.111 2.848e-002 1.874e-003 0.255
55 0.07339 0.531 1.000 0.635 0.111 4.329e-002 1.233e-003 0.254
56 0.07342 0.531 1.000 0.635 0.111 5.337e-002 1.000e-003 0.254
57 0.07343 0.531 1.000 0.635 0.111 6.579e-002 8.111e-004 0.254
58 0.07343 0.531 1.000 0.635 0.111 8.111e-002 6.579e-004 0.254
59 0.07343 0.531 1.000 0.635 0.111 1.000e-001 5.337e-004 0.254
60 0.07343 0.531 1.000 0.635 0.111 1.233e-001 4.329e-004 0.254
61 0.07343 0.531 1.000 0.635 0.111 1.520e-001 3.511e-004 0.254
62 0.07343 0.531 1.000 0.635 0.111 1.874e-001 2.848e-004 0.254
63 0.07343 0.531 1.000 0.635 0.111 2.310e-001 2.310e-004 0.254
64 0.07343 0.531 1.000 0.635 0.111 2.848e-001 1.874e-004 0.254
65 0.07343 0.531 1.000 0.635 0.111 3.511e-001 1.520e-004 0.254
66 0.07343 0.531 1.000 0.635 0.111 4.329e-001 1.233e-004 0.254
67 0.07343 0.531 1.000 0.635 0.111 5.337e-001 1.000e-004 0.254
68 0.07343 0.531 1.000 0.635 0.111 6.579e-001 8.111e-005 0.254
69 0.07343 0.531 1.000 0.635 0.111 8.111e-001 6.579e-005 0.254
70 0.07343 0.531 1.000 0.635 0.111 1.000e+000 5.337e-005 0.254
71 0.07347 0.583 1.000 0.479 0.111 1.233e-002 4.329e-003 0.235
72 0.07355 0.531 1.000 0.583 0.111 1.520e-002 3.511e-003 0.240
73 0.07356 0.427 1.000 0.948 0.121 8.111e-003 6.579e-003 0.271
74 0.07360 0.531 1.000 0.583 0.111 3.511e-002 1.520e-003 0.237
75 0.07361 0.531 1.000 0.635 0.111 2.310e-002 2.310e-003 0.256
76 0.07368 0.427 0.371 0.844 0.132 1.874e-003 3.511e-002 0.252
77 0.07386 0.531 1.000 0.583 0.111 4.329e-002 1.233e-003 0.237
78 0.07400 0.531 1.000 0.583 0.111 5.337e-002 1.000e-003 0.237
79 0.07405 0.531 1.000 0.583 0.111 6.579e-002 8.111e-004 0.237
80 0.07406 0.479 0.977 0.687 0.132 2.848e-003 1.874e-002 0.266
81 0.07407 0.531 1.000 0.583 0.111 8.111e-002 6.579e-004 0.237
82 0.07408 0.531 1.000 0.583 0.111 1.000e-001 5.337e-004 0.237
83 0.07408 0.531 1.000 0.583 0.111 1.233e-001 4.329e-004 0.237
84 0.07409 0.531 1.000 0.583 0.111 1.520e-001 3.511e-004 0.237
85 0.07409 0.531 1.000 0.583 0.111 1.874e-001 2.848e-004 0.237
86 0.07409 0.531 1.000 0.583 0.111 2.310e-001 2.310e-004 0.237
87 0.07409 0.531 1.000 0.583 0.111 2.848e-001 1.874e-004 0.237
88 0.07409 0.531 1.000 0.583 0.111 3.511e-001 1.520e-004 0.237
89 0.07409 0.531 1.000 0.583 0.111 4.329e-001 1.233e-004 0.237
90 0.07409 0.531 1.000 0.583 0.111 5.337e-001 1.000e-004 0.237
91 0.07409 0.531 1.000 0.583 0.111 6.579e-001 8.111e-005 0.237
92 0.07409 0.531 1.000 0.583 0.111 8.111e-001 6.579e-005 0.237
93 0.07409 0.531 1.000 0.583 0.111 1.000e+000 5.337e-005 0.237
94 0.07423 0.427 0.371 0.896 0.132 1.874e-003 3.511e-002 0.259
95 0.07430 0.427 0.371 0.792 0.132 1.874e-003 3.511e-002 0.245
96 0.07442 0.583 1.000 0.531 0.111 2.310e-002 2.310e-003 0.253
97 0.07451 0.531 1.000 0.635 0.111 1.874e-002 2.848e-003 0.257
98 0.07452 0.844 0.733 0.218 0.121 2.310e-003 2.310e-002 0.268
99 0.07493 0.375 0.371 0.739 0.132 1.874e-003 3.511e-002 0.202
100 0.07537 0.427 1.000 0.896 0.121 8.111e-003 6.579e-003 0.259
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