Best 100 Fits for m=2 and n= 1

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 0.03547 0.375 0.445 1.000 0.184 3.511e-008 1.520e-003 0.246
2 0.03560 0.375 0.445 0.948 0.184 3.511e-008 1.520e-003 0.241
3 0.03663 0.479 0.380 0.635 0.184 2.848e-008 1.520e-003 0.246
4 0.03692 0.427 0.516 0.687 0.184 4.329e-008 1.233e-003 0.259
5 0.03697 0.427 0.516 0.635 0.184 4.329e-008 1.233e-003 0.246
6 0.03730 0.375 0.445 0.896 0.184 3.511e-008 1.520e-003 0.235
7 0.03758 0.479 0.380 0.687 0.184 2.848e-008 1.520e-003 0.255
8 0.03819 0.583 0.321 0.479 0.184 2.310e-008 1.520e-003 0.254
9 0.03829 0.323 0.744 0.948 0.184 8.111e-008 1.000e-003 0.257
10 0.03855 0.531 0.445 0.479 0.184 3.511e-008 1.233e-003 0.259
11 0.03904 0.323 0.744 1.000 0.184 8.111e-008 1.000e-003 0.268
12 0.03947 0.583 0.321 0.427 0.184 2.310e-008 1.520e-003 0.240
13 0.04003 0.479 0.380 0.583 0.184 2.848e-008 1.520e-003 0.236
14 0.04093 0.479 0.380 0.739 0.184 2.848e-008 1.520e-003 0.262
15 0.04098 0.375 0.445 0.844 0.184 3.511e-008 1.520e-003 0.229
16 0.04098 0.687 0.270 0.323 0.184 1.874e-008 1.520e-003 0.243
17 0.04219 0.375 0.592 0.792 0.184 5.337e-008 1.233e-003 0.254
18 0.04249 0.427 0.516 0.739 0.184 4.329e-008 1.233e-003 0.271
19 0.04263 0.323 0.744 0.896 0.184 8.111e-008 1.000e-003 0.245
20 0.04304 0.583 0.321 0.531 0.184 2.310e-008 1.520e-003 0.265
21 0.04317 0.375 0.592 0.844 0.184 5.337e-008 1.233e-003 0.266
22 0.04405 0.479 0.592 0.531 0.184 5.337e-008 1.000e-003 0.256
23 0.04418 0.687 0.270 0.375 0.184 1.874e-008 1.520e-003 0.260
24 0.04436 0.323 0.516 1.000 0.184 4.329e-008 1.520e-003 0.229
25 0.04473 0.635 0.380 0.323 0.184 2.848e-008 1.233e-003 0.244
26 0.04501 0.531 0.445 0.427 0.184 3.511e-008 1.233e-003 0.238
27 0.04503 0.739 0.270 0.271 0.184 1.874e-008 1.520e-003 0.252
28 0.04524 0.479 0.380 0.792 0.184 2.848e-008 1.520e-003 0.270
29 0.04525 0.375 0.668 0.792 0.184 6.579e-008 1.000e-003 0.263
30 0.04578 0.375 0.668 0.739 0.184 6.579e-008 1.000e-003 0.248
31 0.04602 0.427 0.516 0.583 0.184 4.329e-008 1.233e-003 0.231
32 0.04660 0.375 0.592 0.739 0.184 5.337e-008 1.233e-003 0.242
33 0.04664 0.531 0.445 0.531 0.184 3.511e-008 1.233e-003 0.277
34 0.04679 0.323 0.592 1.000 0.184 5.337e-008 1.233e-003 0.247
35 0.04688 0.375 0.445 0.792 0.184 3.511e-008 1.520e-003 0.222
36 0.04706 0.635 0.380 0.375 0.184 2.848e-008 1.233e-003 0.272
37 0.04754 0.375 0.592 0.896 0.184 5.337e-008 1.233e-003 0.276
38 0.04769 0.479 0.592 0.583 0.184 5.337e-008 1.000e-003 0.278
39 0.04776 0.323 0.592 0.948 0.184 5.337e-008 1.233e-003 0.239
40 0.04785 0.531 0.321 0.583 0.184 2.310e-008 1.520e-003 0.243
41 0.04854 0.635 0.225 0.844 0.184 1.520e-008 1.874e-003 0.247
42 0.04861 0.635 0.225 0.896 0.184 1.520e-008 1.874e-003 0.249
43 0.04863 0.635 0.225 0.792 0.184 1.520e-008 1.874e-003 0.244
44 0.04878 0.635 0.225 0.948 0.184 1.520e-008 1.874e-003 0.250
45 0.04892 0.531 0.321 0.531 0.184 2.310e-008 1.520e-003 0.234
46 0.04894 0.635 0.225 0.739 0.184 1.520e-008 1.874e-003 0.242
47 0.04902 0.635 0.225 1.000 0.184 1.520e-008 1.874e-003 0.252
48 0.04925 0.531 0.321 0.635 0.184 2.310e-008 1.520e-003 0.251
49 0.04930 0.479 0.380 0.531 0.184 2.848e-008 1.520e-003 0.224
50 0.04959 0.635 0.225 0.687 0.184 1.520e-008 1.874e-003 0.239
51 0.04960 0.583 0.321 0.583 0.184 2.310e-008 1.520e-003 0.275
52 0.04977 0.375 0.668 0.844 0.184 6.579e-008 1.000e-003 0.276
53 0.04977 0.479 0.380 0.844 0.184 2.848e-008 1.520e-003 0.276
54 0.04997 0.792 0.321 0.218 0.184 2.310e-008 1.233e-003 0.265
55 0.05000 0.427 0.380 0.844 0.184 2.848e-008 1.520e-003 0.240
56 0.05010 0.427 0.516 0.792 0.184 4.329e-008 1.233e-003 0.283
57 0.05016 0.323 0.516 0.948 0.184 4.329e-008 1.520e-003 0.222
58 0.05038 0.427 0.380 0.896 0.184 2.848e-008 1.520e-003 0.245
59 0.05047 0.739 0.187 0.739 0.184 1.233e-008 1.874e-003 0.244
60 0.05051 0.739 0.187 0.792 0.184 1.233e-008 1.874e-003 0.245
61 0.05051 0.739 0.187 0.687 0.184 1.233e-008 1.874e-003 0.242
62 0.05053 0.844 0.225 0.218 0.184 1.520e-008 1.520e-003 0.269
63 0.05054 0.792 0.187 0.427 0.184 1.233e-008 1.874e-003 0.250
64 0.05061 0.739 0.187 0.844 0.184 1.233e-008 1.874e-003 0.247
65 0.05062 0.427 0.380 0.792 0.184 2.848e-008 1.520e-003 0.234
66 0.05063 0.375 0.813 0.792 0.184 1.000e-007 8.111e-004 0.264
67 0.05065 0.531 0.270 1.000 0.184 1.874e-008 1.874e-003 0.243
68 0.05070 0.739 0.187 0.635 0.184 1.233e-008 1.874e-003 0.240
69 0.05074 0.739 0.187 0.896 0.184 1.233e-008 1.874e-003 0.248
70 0.05076 0.635 0.225 0.635 0.184 1.520e-008 1.874e-003 0.236
71 0.05089 0.739 0.187 0.948 0.184 1.233e-008 1.874e-003 0.249
72 0.05091 0.792 0.187 0.479 0.184 1.233e-008 1.874e-003 0.254
73 0.05102 0.792 0.187 0.375 0.184 1.233e-008 1.874e-003 0.244
74 0.05105 0.739 0.187 1.000 0.184 1.233e-008 1.874e-003 0.250
75 0.05112 0.531 0.270 0.948 0.184 1.874e-008 1.874e-003 0.241
76 0.05113 0.739 0.187 0.583 0.184 1.233e-008 1.874e-003 0.238
77 0.05118 0.323 0.592 0.896 0.184 5.337e-008 1.233e-003 0.230
78 0.05119 0.583 0.516 0.375 0.184 4.329e-008 1.000e-003 0.250
79 0.05135 0.375 0.813 0.844 0.184 1.000e-007 8.111e-004 0.280
80 0.05141 0.427 0.380 0.948 0.184 2.848e-008 1.520e-003 0.250
81 0.05160 0.792 0.187 0.531 0.184 1.233e-008 1.874e-003 0.257
82 0.05169 0.948 0.154 0.166 0.184 1.000e-008 1.874e-003 0.250
83 0.05185 0.531 0.321 0.687 0.184 2.310e-008 1.520e-003 0.258
84 0.05185 0.531 0.270 0.896 0.184 1.874e-008 1.874e-003 0.238
85 0.05193 0.427 0.668 0.687 0.184 6.579e-008 1.000e-003 0.276
86 0.05193 0.739 0.187 0.531 0.184 1.233e-008 1.874e-003 0.235
87 0.05194 0.739 0.270 0.323 0.184 1.874e-008 1.520e-003 0.275
88 0.05236 0.323 0.744 0.844 0.184 8.111e-008 1.000e-003 0.233
89 0.05239 0.792 0.187 0.583 0.184 1.233e-008 1.874e-003 0.260
90 0.05243 0.687 0.270 0.427 0.184 1.874e-008 1.520e-003 0.274
91 0.05246 0.583 0.321 0.375 0.184 2.310e-008 1.520e-003 0.223
92 0.05258 0.948 0.154 0.218 0.184 1.000e-008 1.874e-003 0.259
93 0.05259 0.427 0.668 0.635 0.184 6.579e-008 1.000e-003 0.258
94 0.05267 0.427 0.380 0.739 0.184 2.848e-008 1.520e-003 0.228
95 0.05269 0.635 0.225 0.583 0.184 1.520e-008 1.874e-003 0.232
96 0.05275 0.583 0.516 0.427 0.184 4.329e-008 1.000e-003 0.281
97 0.05284 0.427 0.380 1.000 0.184 2.848e-008 1.520e-003 0.254
98 0.05296 0.531 0.270 0.844 0.184 1.874e-008 1.874e-003 0.235
99 0.05312 0.896 0.154 0.323 0.184 1.000e-008 1.874e-003 0.243
100 0.05315 0.896 0.154 0.375 0.184 1.000e-008 1.874e-003 0.246
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