Best 100 Fits for m=1 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 0.03765 0.375 0.668 0.844 0.195 6.579e-008 1.520e-005 0.253
2 0.03782 0.375 0.592 0.948 0.195 5.337e-008 1.874e-005 0.245
3 0.03843 0.375 0.592 1.000 0.195 5.337e-008 1.874e-005 0.250
4 0.03846 0.375 0.668 0.792 0.195 6.579e-008 1.520e-005 0.244
5 0.03862 0.375 0.592 0.896 0.195 5.337e-008 1.874e-005 0.239
6 0.03919 0.427 0.668 0.635 0.195 6.579e-008 1.233e-005 0.249
7 0.03995 0.375 0.668 0.896 0.195 6.579e-008 1.520e-005 0.262
8 0.03998 0.479 0.516 0.635 0.195 4.329e-008 1.874e-005 0.250
9 0.04089 0.427 0.744 0.635 0.195 8.111e-008 1.000e-005 0.258
10 0.04098 0.427 0.668 0.687 0.195 6.579e-008 1.233e-005 0.263
11 0.04125 0.583 0.445 0.427 0.195 3.511e-008 1.874e-005 0.243
12 0.04127 0.479 0.445 0.844 0.195 3.511e-008 2.310e-005 0.245
13 0.04132 0.375 0.592 0.844 0.195 5.337e-008 1.874e-005 0.233
14 0.04144 0.479 0.445 0.792 0.195 3.511e-008 2.310e-005 0.241
15 0.04149 0.531 0.592 0.479 0.195 5.337e-008 1.233e-005 0.262
16 0.04172 0.531 0.516 0.479 0.195 4.329e-008 1.520e-005 0.247
17 0.04175 0.583 0.445 0.479 0.195 3.511e-008 1.874e-005 0.257
18 0.04182 0.479 0.445 0.896 0.195 3.511e-008 2.310e-005 0.249
19 0.04185 0.687 0.380 0.323 0.195 2.848e-008 1.874e-005 0.247
20 0.04185 0.479 0.516 0.583 0.195 4.329e-008 1.874e-005 0.239
21 0.04194 0.479 0.516 0.687 0.195 4.329e-008 1.874e-005 0.259
22 0.04211 0.323 0.874 0.948 0.195 1.233e-007 8.111e-006 0.261
23 0.04215 0.583 0.380 0.583 0.195 2.848e-008 2.310e-005 0.245
24 0.04235 0.375 0.744 0.792 0.195 8.111e-008 1.233e-005 0.258
25 0.04255 0.427 0.592 0.687 0.195 5.337e-008 1.520e-005 0.246
26 0.04267 0.479 0.445 0.739 0.195 3.511e-008 2.310e-005 0.236
27 0.04281 0.479 0.445 0.948 0.195 3.511e-008 2.310e-005 0.253
28 0.04298 0.583 0.380 0.635 0.195 2.848e-008 2.310e-005 0.251
29 0.04300 0.583 0.380 0.531 0.195 2.848e-008 2.310e-005 0.238
30 0.04361 0.375 0.668 0.739 0.195 6.579e-008 1.520e-005 0.234
31 0.04398 0.375 0.668 0.948 0.195 6.579e-008 1.520e-005 0.270
32 0.04402 0.323 0.874 0.896 0.195 1.233e-007 8.111e-006 0.249
33 0.04405 0.427 0.592 0.739 0.195 5.337e-008 1.520e-005 0.255
34 0.04408 0.479 0.445 1.000 0.195 3.511e-008 2.310e-005 0.256
35 0.04442 0.739 0.321 0.323 0.195 2.310e-008 2.310e-005 0.248
36 0.04454 0.323 0.874 1.000 0.195 1.233e-007 8.111e-006 0.272
37 0.04457 0.427 0.744 0.687 0.195 8.111e-008 1.000e-005 0.275
38 0.04463 0.323 0.813 0.948 0.195 1.000e-007 1.000e-005 0.254
39 0.04466 0.583 0.380 0.687 0.195 2.848e-008 2.310e-005 0.256
40 0.04471 0.479 0.592 0.583 0.195 5.337e-008 1.520e-005 0.259
41 0.04477 0.375 0.744 0.844 0.195 8.111e-008 1.233e-005 0.270
42 0.04481 0.531 0.592 0.427 0.195 5.337e-008 1.233e-005 0.241
43 0.04490 0.531 0.516 0.531 0.195 4.329e-008 1.520e-005 0.261
44 0.04501 0.323 0.922 0.948 0.195 1.520e-007 6.579e-006 0.262
45 0.04506 0.375 0.744 0.739 0.195 8.111e-008 1.233e-005 0.246
46 0.04506 0.427 0.592 0.635 0.195 5.337e-008 1.520e-005 0.235
47 0.04541 0.479 0.445 0.687 0.195 3.511e-008 2.310e-005 0.230
48 0.04574 0.583 0.516 0.427 0.195 4.329e-008 1.520e-005 0.263
49 0.04580 0.479 0.516 0.739 0.195 4.329e-008 1.874e-005 0.267
50 0.04583 0.427 0.668 0.583 0.195 6.579e-008 1.233e-005 0.234
51 0.04597 0.323 0.813 0.896 0.195 1.000e-007 1.000e-005 0.244
52 0.04598 0.323 0.668 1.000 0.195 6.579e-008 1.874e-005 0.232
53 0.04599 0.323 0.922 1.000 0.195 1.520e-007 6.579e-006 0.274
54 0.04604 0.635 0.516 0.323 0.195 4.329e-008 1.233e-005 0.247
55 0.04604 0.687 0.445 0.323 0.195 3.511e-008 1.520e-005 0.268
56 0.04614 0.323 0.744 1.000 0.195 8.111e-008 1.520e-005 0.251
57 0.04632 0.375 0.592 0.792 0.195 5.337e-008 1.874e-005 0.225
58 0.04646 0.323 0.813 1.000 0.195 1.000e-007 1.000e-005 0.264
59 0.04655 0.531 0.668 0.479 0.195 6.579e-008 1.000e-005 0.272
60 0.04670 0.583 0.380 0.739 0.195 2.848e-008 2.310e-005 0.260
61 0.04677 0.583 0.380 0.479 0.195 2.848e-008 2.310e-005 0.229
62 0.04683 0.687 0.380 0.375 0.195 2.848e-008 1.874e-005 0.264
63 0.04686 0.687 0.321 0.427 0.195 2.310e-008 2.310e-005 0.243
64 0.04689 0.479 0.592 0.531 0.195 5.337e-008 1.520e-005 0.244
65 0.04716 0.739 0.321 0.375 0.195 2.310e-008 2.310e-005 0.261
66 0.04731 0.427 0.668 0.739 0.195 6.579e-008 1.233e-005 0.276
67 0.04742 0.583 0.445 0.531 0.195 3.511e-008 1.874e-005 0.269
68 0.04775 0.896 0.270 0.166 0.195 1.874e-008 2.310e-005 0.251
69 0.04777 0.427 0.592 0.792 0.195 5.337e-008 1.520e-005 0.264
70 0.04779 0.427 0.744 0.583 0.195 8.111e-008 1.000e-005 0.241
71 0.04785 0.739 0.380 0.271 0.195 2.848e-008 1.874e-005 0.255
72 0.04790 0.687 0.321 0.479 0.195 2.310e-008 2.310e-005 0.250
73 0.04799 0.531 0.445 0.583 0.195 3.511e-008 1.874e-005 0.247
74 0.04810 0.531 0.445 0.531 0.195 3.511e-008 1.874e-005 0.237
75 0.04832 0.323 0.744 0.948 0.195 8.111e-008 1.520e-005 0.243
76 0.04844 0.687 0.321 0.375 0.195 2.310e-008 2.310e-005 0.233
77 0.04847 0.427 0.813 0.635 0.195 1.000e-007 8.111e-006 0.262
78 0.04848 0.479 0.744 0.531 0.195 8.111e-008 8.111e-006 0.260
79 0.04874 0.375 0.668 1.000 0.195 6.579e-008 1.520e-005 0.277
80 0.04875 0.531 0.516 0.427 0.195 4.329e-008 1.520e-005 0.229
81 0.04883 0.583 0.380 0.792 0.195 2.848e-008 2.310e-005 0.264
82 0.04884 0.844 0.270 0.218 0.195 1.874e-008 2.310e-005 0.241
83 0.04895 0.739 0.270 0.635 0.195 1.874e-008 2.848e-005 0.244
84 0.04900 0.739 0.270 0.687 0.195 1.874e-008 2.848e-005 0.246
85 0.04909 0.792 0.380 0.218 0.195 2.848e-008 1.520e-005 0.256
86 0.04909 0.739 0.270 0.583 0.195 1.874e-008 2.848e-005 0.242
87 0.04916 0.739 0.270 0.739 0.195 1.874e-008 2.848e-005 0.248
88 0.04921 0.635 0.445 0.375 0.195 3.511e-008 1.520e-005 0.258
89 0.04932 0.479 0.592 0.635 0.195 5.337e-008 1.520e-005 0.273
90 0.04932 0.323 0.922 0.896 0.195 1.520e-007 6.579e-006 0.249
91 0.04938 0.739 0.270 0.792 0.195 1.874e-008 2.848e-005 0.249
92 0.04950 0.479 0.516 0.531 0.195 4.329e-008 1.874e-005 0.228
93 0.04958 0.739 0.270 0.531 0.195 1.874e-008 2.848e-005 0.239
94 0.04960 0.687 0.445 0.271 0.195 3.511e-008 1.520e-005 0.238
95 0.04963 0.739 0.270 0.844 0.195 1.874e-008 2.848e-005 0.251
96 0.04970 0.583 0.516 0.375 0.195 4.329e-008 1.520e-005 0.241
97 0.04983 0.427 0.516 0.844 0.195 4.329e-008 1.874e-005 0.244
98 0.04986 0.427 0.516 0.792 0.195 4.329e-008 1.874e-005 0.238
99 0.04990 0.739 0.270 0.896 0.195 1.874e-008 2.848e-005 0.252
100 0.04993 0.687 0.321 0.531 0.195 2.310e-008 2.310e-005 0.256
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