Best 100 Fits for m=1 and n= 3

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 0.03372 0.375 0.653 0.844 0.184 3.511e-004 2.848e-005 0.250
2 0.03533 0.375 0.653 0.896 0.184 3.511e-004 2.848e-005 0.258
3 0.03553 0.375 0.653 0.792 0.184 3.511e-004 2.848e-005 0.241
4 0.03710 0.583 0.432 0.479 0.184 2.848e-004 3.511e-005 0.254
5 0.03801 0.479 0.432 0.896 0.184 2.848e-004 4.329e-005 0.245
6 0.03804 0.583 0.432 0.427 0.184 2.848e-004 3.511e-005 0.240
7 0.03806 0.479 0.432 0.844 0.184 2.848e-004 4.329e-005 0.241
8 0.03853 0.479 0.432 0.948 0.184 2.848e-004 4.329e-005 0.249
9 0.03894 0.479 0.432 0.792 0.184 2.848e-004 4.329e-005 0.237
10 0.03896 0.375 0.653 0.948 0.184 3.511e-004 2.848e-005 0.266
11 0.03940 0.479 0.432 1.000 0.184 2.848e-004 4.329e-005 0.252
12 0.04097 0.479 0.432 0.739 0.184 2.848e-004 4.329e-005 0.232
13 0.04173 0.375 0.653 0.739 0.184 3.511e-004 2.848e-005 0.231
14 0.04207 0.583 0.432 0.531 0.184 2.848e-004 3.511e-005 0.265
15 0.04247 0.427 0.653 0.635 0.184 3.511e-004 2.310e-005 0.246
16 0.04257 0.687 0.432 0.323 0.184 2.848e-004 2.848e-005 0.265
17 0.04320 0.323 0.653 1.000 0.184 3.511e-004 3.511e-005 0.229
18 0.04331 0.427 0.653 0.687 0.184 3.511e-004 2.310e-005 0.260
19 0.04349 0.375 0.653 1.000 0.184 3.511e-004 2.848e-005 0.273
20 0.04421 0.896 0.260 0.166 0.184 2.310e-004 4.329e-005 0.247
21 0.04454 0.479 0.432 0.687 0.184 2.848e-004 4.329e-005 0.227
22 0.04457 0.531 0.653 0.479 0.184 3.511e-004 1.874e-005 0.269
23 0.04457 0.479 0.653 0.531 0.184 3.511e-004 2.310e-005 0.252
24 0.04467 0.479 0.653 0.583 0.184 3.511e-004 2.310e-005 0.270
25 0.04608 0.739 0.260 0.792 0.184 2.310e-004 5.337e-005 0.245
26 0.04609 0.739 0.260 0.739 0.184 2.310e-004 5.337e-005 0.243
27 0.04614 0.739 0.260 0.844 0.184 2.310e-004 5.337e-005 0.246
28 0.04621 0.739 0.260 0.687 0.184 2.310e-004 5.337e-005 0.242
29 0.04624 0.739 0.260 0.896 0.184 2.310e-004 5.337e-005 0.247
30 0.04636 0.739 0.260 0.948 0.184 2.310e-004 5.337e-005 0.248
31 0.04649 0.739 0.260 0.635 0.184 2.310e-004 5.337e-005 0.240
32 0.04650 0.739 0.260 1.000 0.184 2.310e-004 5.337e-005 0.249
33 0.04703 0.844 0.260 0.218 0.184 2.310e-004 4.329e-005 0.238
34 0.04704 0.739 0.260 0.583 0.184 2.310e-004 5.337e-005 0.237
35 0.04732 0.687 0.432 0.271 0.184 2.848e-004 2.848e-005 0.235
36 0.04778 0.844 0.260 0.271 0.184 2.310e-004 4.329e-005 0.253
37 0.04800 0.739 0.260 0.531 0.184 2.310e-004 5.337e-005 0.234
38 0.04816 0.531 0.653 0.427 0.184 3.511e-004 1.874e-005 0.244
39 0.04846 0.427 0.653 0.739 0.184 3.511e-004 2.310e-005 0.272
40 0.04862 0.583 0.432 0.583 0.184 2.848e-004 3.511e-005 0.275
41 0.04880 0.375 0.862 0.792 0.184 4.329e-004 1.520e-005 0.266
42 0.04885 0.531 0.432 0.583 0.184 2.848e-004 3.511e-005 0.243
43 0.04886 0.323 0.653 0.948 0.184 3.511e-004 3.511e-005 0.223
44 0.04908 0.427 0.653 0.583 0.184 3.511e-004 2.310e-005 0.232
45 0.04965 0.739 0.260 0.479 0.184 2.310e-004 5.337e-005 0.231
46 0.04985 0.531 0.432 0.531 0.184 2.848e-004 3.511e-005 0.234
47 0.05004 0.479 0.432 0.635 0.184 2.848e-004 4.329e-005 0.220
48 0.05015 0.531 0.432 0.635 0.184 2.848e-004 3.511e-005 0.251
49 0.05036 0.739 0.432 0.271 0.184 2.848e-004 2.848e-005 0.270
50 0.05052 0.583 0.432 0.375 0.184 2.848e-004 3.511e-005 0.223
51 0.05056 0.375 0.862 0.844 0.184 4.329e-004 1.520e-005 0.281
52 0.05060 0.896 0.260 0.218 0.184 2.310e-004 4.329e-005 0.270
53 0.05074 0.635 0.432 0.375 0.184 2.848e-004 3.511e-005 0.254
54 0.05089 0.323 0.862 1.000 0.184 4.329e-004 1.874e-005 0.269
55 0.05144 0.427 0.862 0.687 0.184 4.329e-004 1.233e-005 0.278
56 0.05194 0.844 0.260 0.323 0.184 2.310e-004 4.329e-005 0.262
57 0.05202 0.323 0.862 0.948 0.184 4.329e-004 1.520e-005 0.257
58 0.05204 0.323 0.862 0.948 0.184 4.329e-004 1.874e-005 0.257
59 0.05228 0.531 0.432 0.635 0.184 2.848e-004 4.329e-005 0.251
60 0.05232 0.635 0.432 0.375 0.184 2.848e-004 2.848e-005 0.254
61 0.05244 0.739 0.260 0.427 0.184 2.310e-004 5.337e-005 0.226
62 0.05244 0.375 0.653 0.687 0.184 3.511e-004 2.848e-005 0.220
63 0.05247 0.792 0.260 0.427 0.184 2.310e-004 5.337e-005 0.249
64 0.05254 0.427 0.862 0.635 0.184 4.329e-004 1.233e-005 0.258
65 0.05260 0.531 0.432 0.687 0.184 2.848e-004 3.511e-005 0.258
66 0.05271 0.792 0.260 0.479 0.184 2.310e-004 5.337e-005 0.253
67 0.05276 0.479 0.653 0.635 0.184 3.511e-004 2.310e-005 0.287
68 0.05280 0.792 0.432 0.218 0.184 2.848e-004 2.310e-005 0.266
69 0.05304 0.531 0.432 0.687 0.184 2.848e-004 4.329e-005 0.258
70 0.05307 0.792 0.260 0.375 0.184 2.310e-004 5.337e-005 0.244
71 0.05328 0.792 0.260 0.531 0.184 2.310e-004 5.337e-005 0.256
72 0.05329 0.531 0.432 0.583 0.184 2.848e-004 4.329e-005 0.243
73 0.05365 0.323 0.862 1.000 0.184 4.329e-004 1.520e-005 0.269
74 0.05368 0.323 0.862 0.896 0.184 4.329e-004 1.520e-005 0.246
75 0.05396 0.792 0.260 0.583 0.184 2.310e-004 5.337e-005 0.259
76 0.05427 0.375 0.862 0.739 0.184 4.329e-004 1.520e-005 0.250
77 0.05444 0.635 0.432 0.323 0.184 2.848e-004 2.848e-005 0.232
78 0.05466 0.792 0.260 0.635 0.184 2.310e-004 5.337e-005 0.261
79 0.05468 0.635 0.432 0.427 0.184 2.848e-004 3.511e-005 0.272
80 0.05478 0.531 0.432 0.739 0.184 2.848e-004 4.329e-005 0.264
81 0.05485 0.531 0.432 0.479 0.184 2.848e-004 3.511e-005 0.223
82 0.05505 0.583 0.432 0.635 0.184 2.848e-004 3.511e-005 0.283
83 0.05526 0.687 0.260 1.000 0.184 2.310e-004 5.337e-005 0.229
84 0.05527 0.427 0.653 0.792 0.184 3.511e-004 2.310e-005 0.283
85 0.05533 0.792 0.260 0.687 0.184 2.310e-004 5.337e-005 0.263
86 0.05549 0.531 0.432 0.739 0.184 2.848e-004 3.511e-005 0.264
87 0.05563 0.687 0.260 0.948 0.184 2.310e-004 5.337e-005 0.228
88 0.05563 0.792 0.260 0.323 0.184 2.310e-004 5.337e-005 0.236
89 0.05584 0.844 0.260 0.375 0.184 2.310e-004 4.329e-005 0.269
90 0.05585 0.531 0.653 0.531 0.184 3.511e-004 1.874e-005 0.292
91 0.05595 0.792 0.260 0.739 0.184 2.310e-004 5.337e-005 0.265
92 0.05597 0.583 0.653 0.427 0.184 3.511e-004 1.874e-005 0.281
93 0.05598 0.375 0.862 0.739 0.174 4.329e-004 1.874e-005 0.250
94 0.05609 0.687 0.260 0.896 0.184 2.310e-004 5.337e-005 0.227
95 0.05626 0.323 0.653 0.896 0.184 3.511e-004 3.511e-005 0.216
96 0.05653 0.792 0.260 0.792 0.184 2.310e-004 5.337e-005 0.266
97 0.05664 0.687 0.260 0.844 0.184 2.310e-004 5.337e-005 0.226
98 0.05672 0.375 0.862 0.792 0.174 4.329e-004 1.874e-005 0.266
99 0.05676 0.375 0.862 0.896 0.184 4.329e-004 1.520e-005 0.296
100 0.05698 0.531 0.432 0.792 0.184 2.848e-004 4.329e-005 0.269
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