Best 100 Fits for m=3 and n= 1

Fit Result 36 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 0.04298 0.323 0.668 0.948 0.174 6.579e-008 5.337e-003 0.249
2 0.04304 0.323 0.668 1.000 0.174 6.579e-008 5.337e-003 0.259
3 0.04349 0.375 0.445 0.948 0.174 3.511e-008 6.579e-003 0.244
4 0.04389 0.375 0.445 0.896 0.174 3.511e-008 6.579e-003 0.238
5 0.04438 0.375 0.445 1.000 0.174 3.511e-008 6.579e-003 0.250
6 0.04498 0.479 0.516 0.531 0.174 4.329e-008 5.337e-003 0.250
7 0.04608 0.375 0.445 0.844 0.174 3.511e-008 6.579e-003 0.231
8 0.04608 0.687 0.270 0.323 0.174 1.874e-008 6.579e-003 0.246
9 0.04628 0.479 0.380 0.635 0.174 2.848e-008 6.579e-003 0.248
10 0.04660 0.583 0.321 0.427 0.174 2.310e-008 6.579e-003 0.242
11 0.04670 0.323 0.668 0.896 0.174 6.579e-008 5.337e-003 0.238
12 0.04712 0.375 0.592 0.792 0.174 5.337e-008 5.337e-003 0.253
13 0.04747 0.479 0.380 0.583 0.174 2.848e-008 6.579e-003 0.238
14 0.04793 0.583 0.321 0.479 0.174 2.310e-008 6.579e-003 0.257
15 0.04803 0.479 0.516 0.583 0.174 4.329e-008 5.337e-003 0.268
16 0.04829 0.375 0.592 0.739 0.174 5.337e-008 5.337e-003 0.241
17 0.04857 0.479 0.380 0.687 0.174 2.848e-008 6.579e-003 0.258
18 0.04884 0.583 0.445 0.375 0.174 3.511e-008 5.337e-003 0.245
19 0.04923 0.323 0.813 0.948 0.174 1.000e-007 4.329e-003 0.254
20 0.04969 0.323 0.813 1.000 0.174 1.000e-007 4.329e-003 0.266
21 0.05004 0.375 0.592 0.844 0.174 5.337e-008 5.337e-003 0.265
22 0.05047 0.531 0.321 0.531 0.174 2.310e-008 6.579e-003 0.237
23 0.05052 0.375 0.445 0.792 0.174 3.511e-008 6.579e-003 0.224
24 0.05084 0.375 0.516 0.896 0.184 4.329e-008 5.337e-003 0.259
25 0.05113 0.531 0.321 0.583 0.174 2.310e-008 6.579e-003 0.247
26 0.05119 0.375 0.516 0.844 0.184 4.329e-008 5.337e-003 0.250
27 0.05164 0.583 0.445 0.427 0.174 3.511e-008 5.337e-003 0.272
28 0.05210 0.323 0.516 1.000 0.174 4.329e-008 6.579e-003 0.230
29 0.05214 0.687 0.270 0.375 0.174 1.874e-008 6.579e-003 0.265
30 0.05223 0.427 0.380 0.792 0.174 2.848e-008 6.579e-003 0.238
31 0.05254 0.479 0.380 0.739 0.174 2.848e-008 6.579e-003 0.266
32 0.05264 0.427 0.380 0.844 0.174 2.848e-008 6.579e-003 0.244
33 0.05270 0.375 0.516 0.948 0.184 4.329e-008 5.337e-003 0.267
34 0.05275 0.427 0.744 0.687 0.174 8.111e-008 4.329e-003 0.272
35 0.05319 0.427 0.380 0.739 0.174 2.848e-008 6.579e-003 0.231
36 0.05325 0.323 0.813 0.896 0.174 1.000e-007 4.329e-003 0.241
37 0.05349 0.739 0.270 0.271 0.174 1.874e-008 6.579e-003 0.254
38 0.05390 0.583 0.321 0.531 0.174 2.310e-008 6.579e-003 0.269
39 0.05391 0.531 0.321 0.635 0.174 2.310e-008 6.579e-003 0.255
40 0.05392 0.427 0.380 0.896 0.174 2.848e-008 6.579e-003 0.249
41 0.05400 0.531 0.321 0.479 0.174 2.310e-008 6.579e-003 0.225
42 0.05422 0.479 0.380 0.531 0.174 2.848e-008 6.579e-003 0.226
43 0.05432 0.427 0.744 0.635 0.174 8.111e-008 4.329e-003 0.253
44 0.05449 0.323 0.592 1.000 0.184 5.337e-008 5.337e-003 0.247
45 0.05449 0.427 0.592 0.635 0.174 5.337e-008 5.337e-003 0.253
46 0.05463 0.427 0.592 0.687 0.174 5.337e-008 5.337e-003 0.269
47 0.05468 0.323 0.668 0.844 0.174 6.579e-008 5.337e-003 0.227
48 0.05471 0.375 0.516 0.792 0.184 4.329e-008 5.337e-003 0.241
49 0.05502 0.792 0.225 0.218 0.174 1.520e-008 6.579e-003 0.237
50 0.05515 0.375 0.592 0.896 0.174 5.337e-008 5.337e-003 0.276
51 0.05524 0.375 0.592 0.687 0.174 5.337e-008 5.337e-003 0.228
52 0.05548 0.479 0.516 0.479 0.174 4.329e-008 5.337e-003 0.229
53 0.05554 0.479 0.668 0.531 0.174 6.579e-008 4.329e-003 0.253
54 0.05572 0.427 0.380 0.948 0.174 2.848e-008 6.579e-003 0.254
55 0.05591 0.375 0.516 1.000 0.184 4.329e-008 5.337e-003 0.275
56 0.05614 0.427 0.380 0.687 0.174 2.848e-008 6.579e-003 0.223
57 0.05617 0.687 0.380 0.271 0.174 2.848e-008 5.337e-003 0.241
58 0.05618 0.583 0.321 0.375 0.174 2.310e-008 6.579e-003 0.224
59 0.05653 0.635 0.270 0.375 0.174 1.874e-008 6.579e-003 0.234
60 0.05657 0.323 0.516 0.948 0.174 4.329e-008 6.579e-003 0.224
61 0.05661 0.479 0.445 0.583 0.184 3.511e-008 5.337e-003 0.256
62 0.05703 0.479 0.445 0.635 0.184 3.511e-008 5.337e-003 0.270
63 0.05705 0.687 0.270 0.271 0.174 1.874e-008 6.579e-003 0.222
64 0.05706 0.844 0.225 0.166 0.174 1.520e-008 6.579e-003 0.232
65 0.05712 0.479 0.380 0.792 0.174 2.848e-008 6.579e-003 0.274
66 0.05741 0.323 0.744 1.000 0.184 8.111e-008 4.329e-003 0.265
67 0.05742 0.479 0.516 0.635 0.174 4.329e-008 5.337e-003 0.286
68 0.05744 0.635 0.270 0.427 0.174 1.874e-008 6.579e-003 0.248
69 0.05755 0.531 0.321 0.687 0.174 2.310e-008 6.579e-003 0.262
70 0.05760 0.375 0.445 0.739 0.174 3.511e-008 6.579e-003 0.216
71 0.05769 0.739 0.380 0.271 0.174 2.848e-008 5.337e-003 0.278
72 0.05779 0.427 0.380 1.000 0.174 2.848e-008 6.579e-003 0.259
73 0.05781 0.844 0.225 0.218 0.174 1.520e-008 6.579e-003 0.272
74 0.05845 0.531 0.668 0.479 0.174 6.579e-008 4.329e-003 0.266
75 0.05880 0.479 0.668 0.583 0.174 6.579e-008 4.329e-003 0.276
76 0.05909 0.531 0.516 0.479 0.174 4.329e-008 5.337e-003 0.266
77 0.05929 0.323 0.592 0.948 0.184 5.337e-008 5.337e-003 0.239
78 0.05955 0.427 0.744 0.739 0.174 8.111e-008 4.329e-003 0.291
79 0.05985 0.583 0.380 0.427 0.184 2.848e-008 5.337e-003 0.260
80 0.06023 0.323 0.744 0.948 0.184 8.111e-008 4.329e-003 0.254
81 0.06029 0.427 0.874 0.687 0.174 1.233e-007 3.511e-003 0.264
82 0.06039 0.792 0.225 0.271 0.174 1.520e-008 6.579e-003 0.263
83 0.06042 0.427 0.592 0.739 0.174 5.337e-008 5.337e-003 0.284
84 0.06053 0.427 0.445 0.739 0.184 3.511e-008 5.337e-003 0.253
85 0.06055 0.375 0.744 0.792 0.174 8.111e-008 4.329e-003 0.262
86 0.06075 0.375 0.744 0.739 0.174 8.111e-008 4.329e-003 0.246
87 0.06078 0.635 0.445 0.375 0.174 3.511e-008 5.337e-003 0.282
88 0.06090 0.583 0.321 0.583 0.174 2.310e-008 6.579e-003 0.280
89 0.06116 0.375 0.592 0.948 0.174 5.337e-008 5.337e-003 0.286
90 0.06132 0.427 0.445 0.687 0.184 3.511e-008 5.337e-003 0.243
91 0.06133 0.687 0.380 0.323 0.174 2.848e-008 5.337e-003 0.279
92 0.06138 0.531 0.321 0.739 0.174 2.310e-008 6.579e-003 0.269
93 0.06154 0.635 0.445 0.323 0.174 3.511e-008 5.337e-003 0.247
94 0.06164 0.687 0.270 0.427 0.174 1.874e-008 6.579e-003 0.279
95 0.06165 0.635 0.270 0.479 0.174 1.874e-008 6.579e-003 0.259
96 0.06167 0.531 0.380 0.531 0.184 2.848e-008 5.337e-003 0.259
97 0.06172 0.479 0.445 0.687 0.184 3.511e-008 5.337e-003 0.282
98 0.06176 0.479 0.380 0.844 0.174 2.848e-008 6.579e-003 0.280
99 0.06179 0.427 0.380 0.635 0.174 2.848e-008 6.579e-003 0.215
100 0.06214 0.375 0.516 0.739 0.184 4.329e-008 5.337e-003 0.231
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