Best 100 Fits for m=5 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 0.04662 0.375 1.000 0.948 0.142 2.310e-003 1.233e-003 0.257
2 0.04772 0.375 1.000 0.896 0.142 2.310e-003 1.233e-003 0.245
3 0.04885 0.427 1.000 0.739 0.142 1.874e-003 1.233e-003 0.247
4 0.05069 0.375 1.000 1.000 0.142 2.310e-003 1.233e-003 0.268
5 0.05162 0.531 1.000 0.531 0.142 1.520e-003 1.233e-003 0.251
6 0.05308 0.427 1.000 0.792 0.142 1.874e-003 1.233e-003 0.261
7 0.05343 0.427 1.000 0.687 0.142 1.874e-003 1.233e-003 0.232
8 0.05556 0.375 1.000 0.844 0.142 2.310e-003 1.233e-003 0.233
9 0.05794 0.375 1.000 0.896 0.132 8.111e-003 1.000e-003 0.243
10 0.05865 0.375 1.000 0.844 0.132 8.111e-003 1.000e-003 0.231
11 0.05883 0.479 1.000 0.635 0.142 1.874e-003 1.233e-003 0.253
12 0.05891 0.479 1.000 0.687 0.142 1.874e-003 1.233e-003 0.271
13 0.05931 0.531 1.000 0.583 0.142 1.520e-003 1.233e-003 0.272
14 0.05934 0.375 1.000 0.948 0.132 2.310e-002 8.111e-004 0.251
15 0.05955 0.531 0.380 0.479 0.163 2.848e-008 1.874e-002 0.246
16 0.05967 0.479 1.000 0.635 0.132 6.579e-003 1.000e-003 0.251
17 0.06010 0.427 0.445 0.687 0.163 3.511e-008 1.874e-002 0.246
18 0.06064 0.479 1.000 0.583 0.132 6.579e-003 1.000e-003 0.234
19 0.06069 0.375 1.000 0.948 0.132 8.111e-003 1.000e-003 0.255
20 0.06081 0.375 0.744 0.792 0.163 8.111e-008 1.520e-002 0.254
21 0.06094 0.635 1.000 0.375 0.142 1.233e-003 1.233e-003 0.244
22 0.06094 0.375 1.000 1.000 0.132 2.310e-002 8.111e-004 0.263
23 0.06111 0.375 0.668 0.844 0.174 6.579e-008 1.520e-002 0.269
24 0.06112 0.583 1.000 0.427 0.132 5.337e-003 1.000e-003 0.237
25 0.06114 0.427 0.445 0.635 0.163 3.511e-008 1.874e-002 0.234
26 0.06138 0.427 1.000 0.844 0.142 5.337e-003 1.000e-003 0.274
27 0.06144 0.479 1.000 0.583 0.142 6.579e-004 1.520e-003 0.236
28 0.06156 0.375 0.516 0.844 0.163 4.329e-008 1.874e-002 0.252
29 0.06161 0.427 0.592 0.687 0.174 5.337e-008 1.520e-002 0.265
30 0.06173 0.687 1.000 0.323 0.132 4.329e-003 1.000e-003 0.243
31 0.06178 0.375 1.000 0.896 0.132 2.310e-002 8.111e-004 0.240
32 0.06179 0.427 1.000 0.739 0.132 1.874e-002 8.111e-004 0.242
33 0.06181 0.375 0.516 0.792 0.163 4.329e-008 1.874e-002 0.242
34 0.06186 0.427 1.000 0.844 0.142 1.874e-003 1.233e-003 0.275
35 0.06192 0.583 1.000 0.479 0.142 1.520e-003 1.233e-003 0.264
36 0.06226 0.375 0.744 0.844 0.163 8.111e-008 1.520e-002 0.269
37 0.06232 0.427 1.000 0.792 0.142 5.337e-003 1.000e-003 0.260
38 0.06247 0.323 1.000 1.000 0.142 1.000e-003 1.520e-003 0.224
39 0.06252 0.427 0.445 0.739 0.163 3.511e-008 1.874e-002 0.257
40 0.06272 0.323 0.813 1.000 0.163 1.000e-007 1.520e-002 0.258
41 0.06306 0.531 1.000 0.479 0.142 1.520e-003 1.233e-003 0.229
42 0.06315 0.427 1.000 0.792 0.132 1.874e-002 8.111e-004 0.256
43 0.06320 0.427 1.000 0.739 0.142 8.111e-004 1.520e-003 0.247
44 0.06347 0.375 0.668 0.896 0.174 6.579e-008 1.520e-002 0.282
45 0.06351 0.583 1.000 0.427 0.142 5.337e-004 1.520e-003 0.239
46 0.06355 0.531 1.000 0.531 0.132 1.520e-002 8.111e-004 0.247
47 0.06360 0.635 0.321 0.323 0.163 2.310e-008 1.874e-002 0.234
48 0.06361 0.792 0.270 0.218 0.163 1.874e-008 1.874e-002 0.255
49 0.06368 0.375 0.516 0.896 0.163 4.329e-008 1.874e-002 0.261
50 0.06381 0.531 0.380 0.531 0.163 2.848e-008 1.874e-002 0.263
51 0.06391 0.583 1.000 0.479 0.132 5.337e-003 1.000e-003 0.262
52 0.06397 0.375 0.668 0.792 0.174 6.579e-008 1.520e-002 0.255
53 0.06413 0.375 1.000 0.792 0.132 8.111e-003 1.000e-003 0.219
54 0.06446 0.531 0.380 0.427 0.163 2.848e-008 1.874e-002 0.227
55 0.06455 0.635 0.321 0.375 0.163 2.310e-008 1.874e-002 0.259
56 0.06461 0.427 0.592 0.635 0.174 5.337e-008 1.520e-002 0.248
57 0.06463 0.479 0.668 0.583 0.163 6.579e-008 1.520e-002 0.268
58 0.06484 0.479 1.000 0.635 0.142 6.579e-004 1.520e-003 0.254
59 0.06497 0.479 1.000 0.635 0.142 4.329e-003 1.000e-003 0.252
60 0.06505 0.375 0.744 0.739 0.163 8.111e-008 1.520e-002 0.239
61 0.06554 0.323 1.000 1.000 0.142 2.310e-003 1.233e-003 0.223
62 0.06555 0.375 1.000 1.000 0.132 8.111e-003 1.000e-003 0.266
63 0.06558 0.375 0.516 0.739 0.163 4.329e-008 1.874e-002 0.231
64 0.06559 0.479 1.000 0.687 0.142 4.329e-003 1.000e-003 0.270
65 0.06562 0.323 0.813 0.948 0.163 1.000e-007 1.520e-002 0.245
66 0.06564 0.531 1.000 0.479 0.132 5.337e-003 1.000e-003 0.228
67 0.06576 0.375 1.000 0.948 0.142 5.337e-003 1.000e-003 0.256
68 0.06582 0.427 0.592 0.739 0.174 5.337e-008 1.520e-002 0.281
69 0.06584 0.687 0.321 0.323 0.163 2.310e-008 1.874e-002 0.268
70 0.06604 0.375 1.000 0.844 0.142 8.111e-004 1.520e-003 0.234
71 0.06616 0.635 1.000 0.427 0.142 1.233e-003 1.233e-003 0.274
72 0.06622 0.375 1.000 0.896 0.142 5.337e-003 1.000e-003 0.244
73 0.06642 0.427 1.000 0.896 0.142 5.337e-003 1.000e-003 0.288
74 0.06643 0.479 1.000 0.687 0.132 6.579e-003 1.000e-003 0.269
75 0.06644 0.687 1.000 0.375 0.142 1.233e-003 1.233e-003 0.280
76 0.06660 0.427 1.000 0.792 0.142 8.111e-004 1.520e-003 0.262
77 0.06669 0.427 1.000 0.687 0.142 8.111e-004 1.520e-003 0.232
78 0.06673 0.531 0.516 0.479 0.174 4.329e-008 1.520e-002 0.262
79 0.06676 0.427 0.445 0.792 0.163 3.511e-008 1.874e-002 0.267
80 0.06713 0.531 1.000 0.531 0.132 5.337e-003 1.000e-003 0.250
81 0.06716 0.427 0.380 0.896 0.174 2.848e-008 1.874e-002 0.258
82 0.06716 0.323 1.000 1.000 0.132 1.000e-002 1.000e-003 0.221
83 0.06722 0.375 0.516 0.948 0.163 4.329e-008 1.874e-002 0.270
84 0.06723 0.427 1.000 0.687 0.132 6.579e-003 1.000e-003 0.230
85 0.06724 0.427 1.000 0.687 0.132 1.874e-002 8.111e-004 0.228
86 0.06728 0.375 0.744 0.896 0.163 8.111e-008 1.520e-002 0.284
87 0.06728 0.531 1.000 0.531 0.142 6.579e-004 1.520e-003 0.252
88 0.06729 0.583 0.592 0.427 0.163 5.337e-008 1.520e-002 0.270
89 0.06755 0.479 1.000 0.739 0.142 1.874e-003 1.233e-003 0.288
90 0.06756 0.427 0.380 0.844 0.174 2.848e-008 1.874e-002 0.251
91 0.06758 0.427 0.445 0.583 0.163 3.511e-008 1.874e-002 0.220
92 0.06767 0.531 1.000 0.583 0.132 1.520e-002 8.111e-004 0.268
93 0.06767 0.583 0.380 0.427 0.163 2.848e-008 1.874e-002 0.261
94 0.06770 0.427 0.380 0.948 0.174 2.848e-008 1.874e-002 0.263
95 0.06770 0.479 0.445 0.583 0.163 3.511e-008 1.874e-002 0.257
96 0.06779 0.479 0.668 0.531 0.163 6.579e-008 1.520e-002 0.245
97 0.06794 0.375 1.000 0.792 0.142 8.111e-004 1.520e-003 0.222
98 0.06808 0.323 0.668 1.000 0.174 6.579e-008 1.520e-002 0.256
99 0.06809 0.323 0.957 1.000 0.163 1.874e-007 1.233e-002 0.244
100 0.06814 0.375 1.000 0.896 0.142 8.111e-004 1.520e-003 0.246
Go Back Top