Best 100 Fits for m=1 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 0.04582 0.323 0.733 1.000 0.174 2.310e-003 4.329e-005 0.248
2 0.04726 0.323 0.733 0.948 0.174 2.310e-003 4.329e-005 0.240
3 0.04738 0.479 0.733 0.531 0.174 2.310e-003 2.848e-005 0.255
4 0.04755 0.375 0.733 0.792 0.174 2.310e-003 3.511e-005 0.255
5 0.04833 0.323 0.733 1.000 0.184 2.310e-003 3.511e-005 0.248
6 0.04857 0.375 0.733 0.844 0.184 2.310e-003 2.848e-005 0.267
7 0.04867 0.375 0.733 0.739 0.174 2.310e-003 3.511e-005 0.243
8 0.04873 0.739 0.371 0.271 0.174 1.874e-003 5.337e-005 0.255
9 0.04906 0.375 0.733 0.792 0.184 2.310e-003 2.848e-005 0.255
10 0.05018 0.375 0.733 0.844 0.174 2.310e-003 3.511e-005 0.267
11 0.05021 0.635 0.371 0.427 0.174 1.874e-003 6.579e-005 0.248
12 0.05078 0.583 0.371 0.635 0.184 1.874e-003 5.337e-005 0.252
13 0.05079 0.479 0.733 0.583 0.174 2.310e-003 2.848e-005 0.277
14 0.05117 0.583 0.371 0.687 0.184 1.874e-003 5.337e-005 0.257
15 0.05122 0.323 0.733 0.896 0.174 2.310e-003 4.329e-005 0.232
16 0.05154 0.583 0.371 0.583 0.184 1.874e-003 5.337e-005 0.246
17 0.05173 0.635 0.371 0.375 0.174 1.874e-003 6.579e-005 0.234
18 0.05183 0.375 0.733 0.896 0.184 2.310e-003 2.848e-005 0.278
19 0.05220 0.583 0.371 0.739 0.184 1.874e-003 5.337e-005 0.262
20 0.05279 0.323 0.733 0.948 0.184 2.310e-003 3.511e-005 0.240
21 0.05308 0.687 0.371 0.323 0.184 1.874e-003 4.329e-005 0.247
22 0.05314 0.687 0.371 0.375 0.184 1.874e-003 4.329e-005 0.265
23 0.05317 0.635 0.371 0.479 0.174 1.874e-003 6.579e-005 0.259
24 0.05355 0.583 0.371 0.531 0.174 1.874e-003 6.579e-005 0.239
25 0.05356 0.583 0.371 0.792 0.184 1.874e-003 5.337e-005 0.266
26 0.05411 0.531 0.371 0.844 0.174 1.874e-003 8.111e-005 0.241
27 0.05416 0.531 0.371 0.896 0.174 1.874e-003 8.111e-005 0.244
28 0.05421 0.583 0.371 0.531 0.184 1.874e-003 5.337e-005 0.239
29 0.05424 0.583 0.371 0.583 0.174 1.874e-003 6.579e-005 0.246
30 0.05440 0.531 0.371 0.792 0.174 1.874e-003 8.111e-005 0.237
31 0.05442 0.531 0.371 0.948 0.174 1.874e-003 8.111e-005 0.246
32 0.05479 0.583 0.371 0.479 0.174 1.874e-003 6.579e-005 0.230
33 0.05484 0.792 0.371 0.218 0.174 1.874e-003 5.337e-005 0.255
34 0.05484 0.531 0.371 1.000 0.174 1.874e-003 8.111e-005 0.249
35 0.05486 0.375 0.733 0.896 0.174 2.310e-003 3.511e-005 0.278
36 0.05494 0.375 0.733 0.739 0.184 2.310e-003 2.848e-005 0.243
37 0.05506 0.583 0.371 0.844 0.184 1.874e-003 5.337e-005 0.269
38 0.05512 0.375 0.733 0.687 0.174 2.310e-003 3.511e-005 0.229
39 0.05519 0.531 0.371 0.739 0.174 1.874e-003 8.111e-005 0.233
40 0.05586 0.583 0.371 0.635 0.174 1.874e-003 6.579e-005 0.252
41 0.05656 0.427 0.733 0.635 0.174 2.310e-003 3.511e-005 0.255
42 0.05659 0.583 0.371 0.896 0.184 1.874e-003 5.337e-005 0.273
43 0.05669 0.531 0.371 0.687 0.174 1.874e-003 8.111e-005 0.229
44 0.05698 0.687 0.371 0.323 0.174 1.874e-003 5.337e-005 0.247
45 0.05704 0.844 0.371 0.166 0.174 1.874e-003 4.329e-005 0.243
46 0.05710 0.583 0.733 0.427 0.174 2.310e-003 2.310e-005 0.280
47 0.05710 0.375 0.733 0.948 0.184 2.310e-003 2.848e-005 0.288
48 0.05717 0.427 0.733 0.687 0.174 2.310e-003 3.511e-005 0.271
49 0.05752 0.635 0.371 0.531 0.174 1.874e-003 6.579e-005 0.268
50 0.05788 0.583 0.371 0.687 0.174 1.874e-003 6.579e-005 0.257
51 0.05808 0.323 0.733 0.844 0.174 2.310e-003 4.329e-005 0.222
52 0.05810 0.583 0.371 0.948 0.184 1.874e-003 5.337e-005 0.275
53 0.05843 0.531 0.733 0.479 0.174 2.310e-003 2.310e-005 0.270
54 0.05874 0.427 0.733 0.687 0.184 2.310e-003 2.310e-005 0.271
55 0.05886 0.739 0.371 0.271 0.184 1.874e-003 4.329e-005 0.255
56 0.05917 0.427 0.733 0.635 0.174 2.310e-003 2.848e-005 0.255
57 0.05921 0.531 0.371 0.635 0.174 1.874e-003 8.111e-005 0.224
58 0.05922 0.479 0.733 0.479 0.174 2.310e-003 2.848e-005 0.233
59 0.05923 0.531 0.733 0.427 0.174 2.310e-003 2.310e-005 0.242
60 0.05930 0.427 0.733 0.635 0.184 2.310e-003 2.310e-005 0.255
61 0.05956 0.583 0.371 1.000 0.184 1.874e-003 5.337e-005 0.278
62 0.05956 0.583 0.371 0.427 0.174 1.874e-003 6.579e-005 0.220
63 0.05958 0.687 0.371 0.427 0.184 1.874e-003 4.329e-005 0.279
64 0.05984 0.479 0.371 1.000 0.174 1.874e-003 8.111e-005 0.221
65 0.05988 0.583 0.371 0.479 0.184 1.874e-003 5.337e-005 0.230
66 0.05999 0.583 0.371 0.739 0.174 1.874e-003 6.579e-005 0.262
67 0.06010 0.323 0.733 0.896 0.184 2.310e-003 3.511e-005 0.232
68 0.06020 0.531 0.371 0.948 0.184 1.874e-003 5.337e-005 0.246
69 0.06026 0.531 0.371 0.896 0.184 1.874e-003 5.337e-005 0.244
70 0.06033 0.531 0.371 1.000 0.184 1.874e-003 5.337e-005 0.249
71 0.06039 0.583 0.733 0.375 0.174 2.310e-003 2.310e-005 0.247
72 0.06042 0.375 0.733 0.948 0.174 2.310e-003 3.511e-005 0.288
73 0.06057 0.531 0.371 0.844 0.184 1.874e-003 5.337e-005 0.241
74 0.06065 0.739 0.371 0.323 0.174 1.874e-003 5.337e-005 0.280
75 0.06065 0.739 0.371 0.323 0.184 1.874e-003 4.329e-005 0.280
76 0.06085 0.375 0.977 0.844 0.174 2.848e-003 1.233e-005 0.267
77 0.06108 0.479 0.371 0.948 0.174 1.874e-003 8.111e-005 0.219
78 0.06124 0.635 0.371 0.479 0.184 1.874e-003 5.337e-005 0.259
79 0.06126 0.531 0.371 0.792 0.184 1.874e-003 5.337e-005 0.237
80 0.06131 0.479 0.733 0.635 0.174 2.310e-003 2.848e-005 0.297
81 0.06143 0.739 0.371 0.218 0.174 1.874e-003 5.337e-005 0.221
82 0.06162 0.427 0.733 0.583 0.174 2.310e-003 2.848e-005 0.237
83 0.06179 0.323 0.977 1.000 0.174 2.848e-003 1.520e-005 0.260
84 0.06193 0.687 0.371 0.271 0.174 1.874e-003 5.337e-005 0.223
85 0.06200 0.635 0.371 0.583 0.174 1.874e-003 6.579e-005 0.276
86 0.06206 0.635 0.371 0.531 0.184 1.874e-003 5.337e-005 0.268
87 0.06207 0.583 0.371 0.792 0.174 1.874e-003 6.579e-005 0.266
88 0.06224 0.635 0.371 0.427 0.184 1.874e-003 4.329e-005 0.248
89 0.06247 0.531 0.371 0.739 0.184 1.874e-003 5.337e-005 0.233
90 0.06260 0.375 0.977 0.896 0.174 2.848e-003 1.233e-005 0.282
91 0.06261 0.427 0.733 0.687 0.174 2.310e-003 2.848e-005 0.271
92 0.06264 0.479 0.371 0.896 0.174 1.874e-003 8.111e-005 0.216
93 0.06267 0.427 0.733 0.739 0.174 2.310e-003 3.511e-005 0.286
94 0.06281 0.687 0.371 0.375 0.174 1.874e-003 5.337e-005 0.265
95 0.06301 0.635 0.371 0.323 0.174 1.874e-003 6.579e-005 0.217
96 0.06320 0.531 0.371 0.583 0.174 1.874e-003 8.111e-005 0.218
97 0.06322 0.375 0.733 1.000 0.184 2.310e-003 2.848e-005 0.297
98 0.06349 0.635 0.371 0.427 0.184 1.874e-003 5.337e-005 0.248
99 0.06353 0.687 0.371 0.323 0.174 1.874e-003 6.579e-005 0.247
100 0.06388 0.427 0.733 0.739 0.184 2.310e-003 2.310e-005 0.286
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