Best 100 Fits for m=2 and n= 2

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 0.03700 0.427 0.451 0.687 0.174 2.848e-005 1.874e-003 0.244
2 0.03720 0.427 0.451 0.739 0.174 2.848e-005 1.874e-003 0.253
3 0.03898 0.635 0.326 0.375 0.174 2.310e-005 1.874e-003 0.256
4 0.03984 0.375 0.598 0.792 0.174 3.511e-005 1.520e-003 0.254
5 0.04055 0.427 0.451 0.792 0.174 2.848e-005 1.874e-003 0.262
6 0.04140 0.687 0.228 0.427 0.174 1.874e-005 2.310e-003 0.243
7 0.04182 0.375 0.598 0.739 0.174 3.511e-005 1.520e-003 0.242
8 0.04188 0.427 0.451 0.635 0.174 2.848e-005 1.874e-003 0.233
9 0.04240 0.375 0.749 0.792 0.174 4.329e-005 1.233e-003 0.263
10 0.04256 0.687 0.228 0.479 0.174 1.874e-005 2.310e-003 0.251
11 0.04262 0.375 0.598 0.844 0.174 3.511e-005 1.520e-003 0.266
12 0.04288 0.583 0.451 0.375 0.174 2.848e-005 1.520e-003 0.246
13 0.04346 0.687 0.228 0.375 0.174 1.874e-005 2.310e-003 0.234
14 0.04416 0.635 0.326 0.323 0.174 2.310e-005 1.874e-003 0.233
15 0.04494 0.687 0.228 0.531 0.174 1.874e-005 2.310e-003 0.257
16 0.04498 0.583 0.451 0.427 0.174 2.848e-005 1.520e-003 0.273
17 0.04503 0.375 0.749 0.844 0.174 4.329e-005 1.233e-003 0.278
18 0.04532 0.427 0.451 0.844 0.174 2.848e-005 1.874e-003 0.271
19 0.04653 0.479 0.326 0.844 0.174 2.310e-005 2.310e-003 0.246
20 0.04679 0.479 0.326 0.792 0.174 2.310e-005 2.310e-003 0.241
21 0.04696 0.479 0.326 0.896 0.174 2.310e-005 2.310e-003 0.250
22 0.04743 0.375 0.749 0.739 0.174 4.329e-005 1.233e-003 0.248
23 0.04748 0.635 0.228 0.583 0.174 1.874e-005 2.310e-003 0.236
24 0.04752 0.635 0.228 0.635 0.174 1.874e-005 2.310e-003 0.241
25 0.04757 0.427 0.326 1.000 0.174 2.310e-005 2.310e-003 0.225
26 0.04760 0.687 0.228 0.583 0.174 1.874e-005 2.310e-003 0.262
27 0.04784 0.479 0.326 0.948 0.174 2.310e-005 2.310e-003 0.254
28 0.04795 0.375 0.598 0.896 0.174 3.511e-005 1.520e-003 0.277
29 0.04802 0.635 0.228 0.687 0.174 1.874e-005 2.310e-003 0.244
30 0.04809 0.479 0.326 0.739 0.174 2.310e-005 2.310e-003 0.236
31 0.04829 0.635 0.228 0.531 0.174 1.874e-005 2.310e-003 0.231
32 0.04853 0.583 0.326 0.427 0.174 2.310e-005 1.874e-003 0.242
33 0.04876 0.635 0.326 0.427 0.174 2.310e-005 1.874e-003 0.275
34 0.04877 0.635 0.228 0.739 0.174 1.874e-005 2.310e-003 0.247
35 0.04877 0.531 0.598 0.479 0.174 3.511e-005 1.233e-003 0.270
36 0.04899 0.479 0.326 1.000 0.174 2.310e-005 2.310e-003 0.257
37 0.04946 0.427 0.326 0.948 0.174 2.310e-005 2.310e-003 0.222
38 0.04963 0.635 0.228 0.792 0.174 1.874e-005 2.310e-003 0.250
39 0.05012 0.375 0.598 0.687 0.174 3.511e-005 1.520e-003 0.229
40 0.05019 0.687 0.228 0.635 0.174 1.874e-005 2.310e-003 0.266
41 0.05027 0.427 0.598 0.687 0.174 3.511e-005 1.520e-003 0.270
42 0.05052 0.427 0.451 0.896 0.174 2.848e-005 1.874e-003 0.278
43 0.05054 0.635 0.228 0.844 0.174 1.874e-005 2.310e-003 0.252
44 0.05055 0.427 0.598 0.635 0.174 3.511e-005 1.520e-003 0.254
45 0.05057 0.635 0.228 0.479 0.174 1.874e-005 2.310e-003 0.225
46 0.05084 0.479 0.326 0.687 0.174 2.310e-005 2.310e-003 0.230
47 0.05134 0.583 0.326 0.479 0.174 2.310e-005 1.874e-003 0.256
48 0.05137 0.323 0.878 1.000 0.174 5.337e-005 1.000e-003 0.265
49 0.05143 0.635 0.228 0.896 0.174 1.874e-005 2.310e-003 0.254
50 0.05197 0.427 0.326 0.896 0.174 2.310e-005 2.310e-003 0.218
51 0.05201 0.687 0.326 0.323 0.174 2.310e-005 1.874e-003 0.266
52 0.05204 0.375 0.749 0.896 0.174 4.329e-005 1.233e-003 0.293
53 0.05222 0.687 0.228 0.323 0.174 1.874e-005 2.310e-003 0.221
54 0.05230 0.635 0.228 0.948 0.174 1.874e-005 2.310e-003 0.256
55 0.05253 0.323 0.878 0.948 0.174 5.337e-005 1.000e-003 0.252
56 0.05258 0.687 0.228 0.687 0.174 1.874e-005 2.310e-003 0.270
57 0.05273 0.739 0.228 0.323 0.174 1.874e-005 2.310e-003 0.249
58 0.05279 0.427 0.451 0.583 0.174 2.848e-005 1.874e-003 0.220
59 0.05313 0.635 0.228 1.000 0.174 1.874e-005 2.310e-003 0.258
60 0.05409 0.531 0.598 0.427 0.174 3.511e-005 1.233e-003 0.242
61 0.05426 0.375 0.598 0.948 0.174 3.511e-005 1.520e-003 0.287
62 0.05429 0.583 0.326 0.375 0.174 2.310e-005 1.874e-003 0.225
63 0.05432 0.427 0.878 0.635 0.163 5.337e-005 1.000e-003 0.246
64 0.05473 0.948 0.157 0.114 0.174 1.520e-005 2.310e-003 0.230
65 0.05474 0.687 0.228 0.739 0.174 1.874e-005 2.310e-003 0.273
66 0.05489 0.739 0.228 0.375 0.174 1.874e-005 2.310e-003 0.261
67 0.05522 0.948 0.157 0.166 0.174 1.520e-005 2.310e-003 0.256
68 0.05523 0.427 0.326 0.844 0.174 2.310e-005 2.310e-003 0.214
69 0.05528 0.479 0.749 0.531 0.163 4.329e-005 1.233e-003 0.251
70 0.05531 0.635 0.228 0.427 0.174 1.874e-005 2.310e-003 0.218
71 0.05541 0.427 0.959 0.687 0.163 6.579e-005 8.111e-004 0.256
72 0.05556 0.479 0.326 0.635 0.174 2.310e-005 2.310e-003 0.223
73 0.05567 0.427 0.451 0.948 0.174 2.848e-005 1.874e-003 0.285
74 0.05599 0.375 0.451 0.896 0.174 2.848e-005 1.874e-003 0.238
75 0.05603 0.427 0.598 0.739 0.174 3.511e-005 1.520e-003 0.286
76 0.05606 0.375 0.451 0.948 0.174 2.848e-005 1.874e-003 0.244
77 0.05629 0.948 0.228 0.114 0.174 1.874e-005 1.874e-003 0.270
78 0.05638 0.531 0.451 0.479 0.174 2.848e-005 1.520e-003 0.259
79 0.05647 0.635 0.451 0.375 0.174 2.848e-005 1.520e-003 0.283
80 0.05655 0.427 0.878 0.687 0.163 5.337e-005 1.000e-003 0.265
81 0.05664 0.323 0.878 0.948 0.163 5.337e-005 1.233e-003 0.252
82 0.05667 0.687 0.228 0.792 0.174 1.874e-005 2.310e-003 0.275
83 0.05689 0.323 0.878 1.000 0.163 5.337e-005 1.233e-003 0.265
84 0.05694 0.375 0.451 1.000 0.174 2.848e-005 1.874e-003 0.249
85 0.05702 0.531 0.451 0.427 0.174 2.848e-005 1.520e-003 0.237
86 0.05703 0.583 0.598 0.427 0.174 3.511e-005 1.233e-003 0.280
87 0.05710 0.375 0.451 0.844 0.174 2.848e-005 1.874e-003 0.231
88 0.05729 0.583 0.326 0.531 0.174 2.310e-005 1.874e-003 0.269
89 0.05733 0.375 0.992 0.844 0.163 8.111e-005 6.579e-004 0.255
90 0.05783 0.635 0.451 0.323 0.174 2.848e-005 1.520e-003 0.248
91 0.05839 0.687 0.228 0.844 0.174 1.874e-005 2.310e-003 0.278
92 0.05847 0.375 0.992 0.792 0.163 8.111e-005 6.579e-004 0.241
93 0.05851 0.323 0.598 1.000 0.184 3.511e-005 1.520e-003 0.248
94 0.05854 0.323 0.878 0.896 0.174 5.337e-005 1.000e-003 0.239
95 0.05890 0.479 0.749 0.583 0.163 4.329e-005 1.233e-003 0.275
96 0.05893 0.375 0.999 0.896 0.163 1.000e-004 5.337e-004 0.264
97 0.05898 0.739 0.228 0.271 0.174 1.874e-005 2.310e-003 0.231
98 0.05914 0.896 0.228 0.166 0.174 1.874e-005 1.874e-003 0.276
99 0.05925 0.739 0.228 0.427 0.174 1.874e-005 2.310e-003 0.271
100 0.05942 0.427 0.326 0.792 0.174 2.310e-005 2.310e-003 0.210
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