Best 100 Fits for m=4 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 0.04376 0.375 0.733 0.844 0.132 2.310e-003 1.874e-002 0.260
2 0.04419 0.375 0.371 1.000 0.142 1.874e-003 2.310e-002 0.228
3 0.04561 0.375 0.733 0.896 0.132 2.310e-003 1.874e-002 0.274
4 0.04663 0.375 0.733 0.792 0.132 2.310e-003 1.874e-002 0.245
5 0.04677 0.427 0.371 0.896 0.142 1.874e-003 2.310e-002 0.254
6 0.04693 0.427 0.371 0.844 0.142 1.874e-003 2.310e-002 0.248
7 0.04782 0.427 0.371 0.948 0.142 1.874e-003 2.310e-002 0.260
8 0.04788 0.375 0.371 0.948 0.142 1.874e-003 2.310e-002 0.223
9 0.04885 0.427 0.371 0.792 0.142 1.874e-003 2.310e-002 0.241
10 0.04963 0.427 0.371 1.000 0.142 1.874e-003 2.310e-002 0.265
11 0.05032 0.375 0.733 0.948 0.132 2.310e-003 1.874e-002 0.288
12 0.05276 0.375 0.371 0.896 0.142 1.874e-003 2.310e-002 0.218
13 0.05279 0.531 0.371 0.531 0.132 1.874e-003 2.310e-002 0.259
14 0.05312 0.427 0.371 0.739 0.142 1.874e-003 2.310e-002 0.233
15 0.05318 0.531 0.371 0.479 0.132 1.874e-003 2.310e-002 0.242
16 0.05530 0.375 0.733 0.739 0.132 2.310e-003 1.874e-002 0.230
17 0.05637 0.375 0.733 1.000 0.132 2.310e-003 1.874e-002 0.302
18 0.05695 0.531 0.371 0.583 0.132 1.874e-003 2.310e-002 0.274
19 0.05702 0.792 0.150 0.531 0.132 1.520e-003 2.848e-002 0.238
20 0.05704 0.792 0.150 0.583 0.132 1.520e-003 2.848e-002 0.240
21 0.05715 0.792 0.150 0.635 0.132 1.520e-003 2.848e-002 0.242
22 0.05721 0.792 0.150 0.479 0.132 1.520e-003 2.848e-002 0.235
23 0.05722 0.687 0.733 0.323 0.132 2.310e-003 1.520e-002 0.253
24 0.05732 0.792 0.150 0.687 0.132 1.520e-003 2.848e-002 0.244
25 0.05751 0.792 0.150 0.739 0.132 1.520e-003 2.848e-002 0.245
26 0.05770 0.792 0.150 0.792 0.132 1.520e-003 2.848e-002 0.246
27 0.05779 0.792 0.150 0.427 0.132 1.520e-003 2.848e-002 0.231
28 0.05790 0.792 0.150 0.844 0.132 1.520e-003 2.848e-002 0.247
29 0.05809 0.792 0.150 0.896 0.132 1.520e-003 2.848e-002 0.248
30 0.05827 0.792 0.150 0.948 0.132 1.520e-003 2.848e-002 0.249
31 0.05827 0.531 0.977 0.583 0.132 2.848e-003 1.233e-002 0.272
32 0.05844 0.792 0.150 1.000 0.132 1.520e-003 2.848e-002 0.250
33 0.05866 0.531 0.977 0.531 0.132 2.848e-003 1.233e-002 0.250
34 0.05900 0.375 0.371 0.844 0.142 1.874e-003 2.310e-002 0.212
35 0.05915 0.792 0.150 0.375 0.132 1.520e-003 2.848e-002 0.227
36 0.05917 0.739 0.150 1.000 0.132 1.520e-003 2.848e-002 0.231
37 0.05929 0.583 0.371 0.427 0.132 1.874e-003 2.310e-002 0.257
38 0.05931 0.739 0.150 0.948 0.132 1.520e-003 2.848e-002 0.230
39 0.05943 0.739 0.371 0.271 0.142 1.874e-003 1.874e-002 0.268
40 0.05949 0.739 0.150 0.896 0.132 1.520e-003 2.848e-002 0.229
41 0.05972 0.739 0.150 0.844 0.132 1.520e-003 2.848e-002 0.228
42 0.06001 0.739 0.150 0.792 0.132 1.520e-003 2.848e-002 0.227
43 0.06025 0.427 0.371 0.687 0.142 1.874e-003 2.310e-002 0.225
44 0.06038 0.739 0.150 0.739 0.132 1.520e-003 2.848e-002 0.225
45 0.06055 0.375 1.000 1.000 0.132 3.511e-003 1.000e-002 0.260
46 0.06088 0.739 0.150 0.687 0.132 1.520e-003 2.848e-002 0.224
47 0.06148 0.375 1.000 0.948 0.132 3.511e-003 1.000e-002 0.249
48 0.06154 0.739 0.150 0.635 0.132 1.520e-003 2.848e-002 0.222
49 0.06162 0.427 1.000 0.844 0.121 8.111e-003 3.511e-003 0.251
50 0.06213 0.792 0.150 0.323 0.132 1.520e-003 2.848e-002 0.220
51 0.06224 0.531 0.371 0.427 0.132 1.874e-003 2.310e-002 0.223
52 0.06245 0.739 0.150 0.583 0.132 1.520e-003 2.848e-002 0.220
53 0.06257 0.427 1.000 0.896 0.121 8.111e-003 3.511e-003 0.264
54 0.06277 0.531 0.371 0.635 0.132 1.874e-003 2.310e-002 0.287
55 0.06292 0.427 1.000 0.792 0.121 4.329e-003 8.111e-003 0.247
56 0.06361 0.583 0.371 0.479 0.132 1.874e-003 2.310e-002 0.278
57 0.06371 0.739 0.150 0.531 0.132 1.520e-003 2.848e-002 0.218
58 0.06374 0.531 1.000 0.583 0.121 6.579e-003 4.329e-003 0.251
59 0.06411 0.739 0.733 0.271 0.132 2.310e-003 1.520e-002 0.246
60 0.06432 0.844 0.150 0.323 0.132 1.520e-003 2.848e-002 0.244
61 0.06484 0.844 0.150 0.271 0.132 1.520e-003 2.848e-002 0.235
62 0.06499 0.844 0.150 0.375 0.132 1.520e-003 2.848e-002 0.249
63 0.06521 0.427 1.000 0.739 0.121 4.329e-003 8.111e-003 0.233
64 0.06553 0.739 0.150 0.479 0.132 1.520e-003 2.848e-002 0.214
65 0.06554 0.427 1.000 0.844 0.121 4.329e-003 8.111e-003 0.260
66 0.06577 0.479 0.977 0.635 0.132 2.848e-003 1.233e-002 0.253
67 0.06592 0.844 0.150 0.427 0.132 1.520e-003 2.848e-002 0.254
68 0.06614 0.583 0.371 0.375 0.132 1.874e-003 2.310e-002 0.232
69 0.06618 0.427 1.000 0.792 0.121 8.111e-003 3.511e-003 0.239
70 0.06628 0.687 0.371 0.323 0.142 1.874e-003 1.874e-002 0.272
71 0.06648 0.427 0.733 0.739 0.132 2.310e-003 1.874e-002 0.273
72 0.06678 0.375 0.371 0.792 0.142 1.874e-003 2.310e-002 0.206
73 0.06683 0.844 0.150 0.479 0.132 1.520e-003 2.848e-002 0.257
74 0.06707 0.375 1.000 0.896 0.132 3.511e-003 1.000e-002 0.238
75 0.06723 0.427 1.000 0.948 0.121 8.111e-003 3.511e-003 0.276
76 0.06755 0.531 1.000 0.635 0.121 6.579e-003 4.329e-003 0.270
77 0.06761 0.531 1.000 0.531 0.121 3.511e-003 1.000e-002 0.241
78 0.06766 0.844 0.150 0.531 0.132 1.520e-003 2.848e-002 0.259
79 0.06772 0.427 0.733 0.687 0.132 2.310e-003 1.874e-002 0.254
80 0.06811 0.739 0.733 0.323 0.132 2.310e-003 1.520e-002 0.292
81 0.06820 0.739 0.150 0.427 0.132 1.520e-003 2.848e-002 0.210
82 0.06839 0.844 0.150 0.583 0.132 1.520e-003 2.848e-002 0.261
83 0.06845 0.479 0.977 0.583 0.132 2.848e-003 1.233e-002 0.235
84 0.06860 0.479 0.371 0.635 0.132 1.874e-003 2.310e-002 0.250
85 0.06863 0.792 0.150 0.271 0.132 1.520e-003 2.848e-002 0.211
86 0.06883 0.531 0.371 0.687 0.132 1.874e-003 2.310e-002 0.299
87 0.06903 0.844 0.150 0.635 0.132 1.520e-003 2.848e-002 0.263
88 0.06911 0.531 0.977 0.635 0.132 2.848e-003 1.233e-002 0.294
89 0.06945 0.479 0.371 0.583 0.132 1.874e-003 2.310e-002 0.238
90 0.06959 0.844 0.150 0.687 0.132 1.520e-003 2.848e-002 0.264
91 0.06966 0.479 0.371 0.687 0.132 1.874e-003 2.310e-002 0.261
92 0.06969 0.844 0.150 0.218 0.132 1.520e-003 2.848e-002 0.222
93 0.06975 0.375 0.733 0.687 0.132 2.310e-003 1.874e-002 0.215
94 0.06984 0.687 1.000 0.375 0.121 5.337e-003 5.337e-003 0.261
95 0.07008 0.844 0.150 0.739 0.132 1.520e-003 2.848e-002 0.265
96 0.07014 0.427 0.733 0.792 0.132 2.310e-003 1.874e-002 0.291
97 0.07051 0.844 0.150 0.792 0.132 1.520e-003 2.848e-002 0.266
98 0.07071 0.583 1.000 0.479 0.121 3.511e-003 1.000e-002 0.254
99 0.07074 0.427 0.371 0.635 0.142 1.874e-003 2.310e-002 0.216
100 0.07087 0.948 0.150 0.114 0.142 1.520e-003 2.310e-002 0.238
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