Best 100 Fits for m=1 and n= 2

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 0.04106 0.427 0.749 0.635 0.184 4.329e-005 1.520e-005 0.258
2 0.04201 0.375 0.749 0.792 0.184 4.329e-005 1.874e-005 0.258
3 0.04248 0.375 0.598 1.000 0.195 3.511e-005 2.310e-005 0.253
4 0.04294 0.375 0.598 0.948 0.195 3.511e-005 2.310e-005 0.248
5 0.04321 0.375 0.749 0.739 0.184 4.329e-005 1.874e-005 0.246
6 0.04403 0.583 0.451 0.427 0.184 2.848e-005 2.848e-005 0.245
7 0.04501 0.375 0.598 0.896 0.195 3.511e-005 2.310e-005 0.242
8 0.04501 0.531 0.598 0.479 0.184 3.511e-005 1.874e-005 0.263
9 0.04505 0.531 0.598 0.427 0.184 3.511e-005 1.874e-005 0.241
10 0.04519 0.427 0.749 0.583 0.184 4.329e-005 1.520e-005 0.240
11 0.04526 0.375 0.749 0.844 0.184 4.329e-005 1.874e-005 0.270
12 0.04526 0.323 0.959 0.948 0.184 6.579e-005 8.111e-006 0.257
13 0.04535 0.375 0.598 0.896 0.184 3.511e-005 2.848e-005 0.242
14 0.04558 0.323 0.959 1.000 0.184 6.579e-005 8.111e-006 0.270
15 0.04559 0.427 0.598 0.739 0.195 3.511e-005 1.874e-005 0.257
16 0.04563 0.375 0.598 0.948 0.184 3.511e-005 2.848e-005 0.248
17 0.04576 0.479 0.598 0.531 0.184 3.511e-005 2.310e-005 0.245
18 0.04584 0.427 0.598 0.687 0.195 3.511e-005 1.874e-005 0.247
19 0.04593 0.479 0.598 0.583 0.184 3.511e-005 2.310e-005 0.260
20 0.04595 0.427 0.749 0.687 0.184 4.329e-005 1.520e-005 0.275
21 0.04624 0.635 0.598 0.323 0.184 3.511e-005 1.520e-005 0.252
22 0.04638 0.687 0.451 0.271 0.184 2.848e-005 2.310e-005 0.238
23 0.04653 0.375 0.598 0.844 0.184 3.511e-005 2.848e-005 0.235
24 0.04668 0.479 0.451 0.739 0.184 2.848e-005 3.511e-005 0.239
25 0.04688 0.479 0.451 0.792 0.184 2.848e-005 3.511e-005 0.245
26 0.04689 0.375 0.598 1.000 0.184 3.511e-005 2.848e-005 0.253
27 0.04725 0.583 0.451 0.479 0.184 2.848e-005 2.848e-005 0.260
28 0.04728 0.323 0.878 0.948 0.184 5.337e-005 1.233e-005 0.260
29 0.04740 0.531 0.749 0.479 0.184 4.329e-005 1.233e-005 0.274
30 0.04743 0.323 0.749 1.000 0.184 4.329e-005 2.310e-005 0.252
31 0.04756 0.427 0.878 0.635 0.184 5.337e-005 1.000e-005 0.259
32 0.04765 0.479 0.451 0.687 0.184 2.848e-005 3.511e-005 0.233
33 0.04781 0.479 0.451 0.844 0.184 2.848e-005 3.511e-005 0.249
34 0.04786 0.739 0.326 0.323 0.184 2.310e-005 3.511e-005 0.252
35 0.04789 0.323 0.878 0.896 0.184 5.337e-005 1.233e-005 0.248
36 0.04812 0.531 0.451 0.583 0.195 2.848e-005 2.310e-005 0.250
37 0.04837 0.427 0.598 0.792 0.195 3.511e-005 1.874e-005 0.267
38 0.04844 0.739 0.326 0.271 0.184 2.310e-005 3.511e-005 0.234
39 0.04858 0.323 0.749 0.948 0.184 4.329e-005 2.310e-005 0.243
40 0.04876 0.687 0.451 0.323 0.184 2.848e-005 2.310e-005 0.270
41 0.04907 0.375 0.598 0.844 0.195 3.511e-005 2.310e-005 0.235
42 0.04916 0.479 0.451 0.896 0.184 2.848e-005 3.511e-005 0.254
43 0.04920 0.427 0.878 0.687 0.184 5.337e-005 1.000e-005 0.279
44 0.04927 0.531 0.451 0.635 0.195 2.848e-005 2.310e-005 0.258
45 0.04966 0.375 0.598 0.792 0.184 3.511e-005 2.848e-005 0.227
46 0.04992 0.323 0.878 1.000 0.184 5.337e-005 1.233e-005 0.271
47 0.04997 0.844 0.326 0.166 0.184 2.310e-005 2.848e-005 0.235
48 0.05008 0.531 0.451 0.531 0.195 2.848e-005 2.310e-005 0.240
49 0.05033 0.583 0.451 0.375 0.184 2.848e-005 2.848e-005 0.228
50 0.05034 0.583 0.598 0.375 0.184 3.511e-005 1.874e-005 0.250
51 0.05035 0.323 0.959 0.896 0.184 6.579e-005 8.111e-006 0.243
52 0.05036 0.479 0.451 0.635 0.184 2.848e-005 3.511e-005 0.227
53 0.05036 0.479 0.451 0.896 0.195 2.848e-005 2.848e-005 0.254
54 0.05057 0.427 0.598 0.687 0.184 3.511e-005 2.310e-005 0.247
55 0.05061 0.479 0.451 0.844 0.195 2.848e-005 2.848e-005 0.249
56 0.05064 0.375 0.749 0.687 0.184 4.329e-005 1.874e-005 0.232
57 0.05066 0.479 0.451 0.948 0.195 2.848e-005 2.848e-005 0.258
58 0.05068 0.896 0.228 0.218 0.184 1.874e-005 4.329e-005 0.239
59 0.05074 0.479 0.451 0.948 0.184 2.848e-005 3.511e-005 0.258
60 0.05081 0.375 0.749 0.896 0.184 4.329e-005 1.874e-005 0.281
61 0.05084 0.427 0.598 0.635 0.195 3.511e-005 1.874e-005 0.236
62 0.05084 0.583 0.451 0.479 0.195 2.848e-005 2.310e-005 0.260
63 0.05108 0.531 0.749 0.427 0.184 4.329e-005 1.233e-005 0.246
64 0.05134 0.479 0.451 1.000 0.195 2.848e-005 2.848e-005 0.261
65 0.05148 0.427 0.598 0.635 0.184 3.511e-005 2.310e-005 0.236
66 0.05151 0.687 0.326 0.375 0.184 2.310e-005 3.511e-005 0.237
67 0.05162 0.792 0.451 0.218 0.184 2.848e-005 1.874e-005 0.268
68 0.05165 0.375 0.878 0.792 0.184 5.337e-005 1.233e-005 0.268
69 0.05165 0.479 0.598 0.635 0.184 3.511e-005 2.310e-005 0.274
70 0.05167 0.479 0.451 0.792 0.195 2.848e-005 2.848e-005 0.245
71 0.05174 0.896 0.228 0.271 0.184 1.874e-005 4.329e-005 0.248
72 0.05180 0.583 0.326 1.000 0.184 2.310e-005 4.329e-005 0.237
73 0.05189 0.583 0.326 0.948 0.184 2.310e-005 4.329e-005 0.235
74 0.05190 0.531 0.598 0.479 0.195 3.511e-005 1.520e-005 0.263
75 0.05201 0.531 0.451 0.687 0.195 2.848e-005 2.310e-005 0.266
76 0.05201 0.687 0.326 0.479 0.195 2.310e-005 2.848e-005 0.255
77 0.05210 0.583 0.326 0.896 0.184 2.310e-005 4.329e-005 0.233
78 0.05230 0.635 0.326 0.635 0.184 2.310e-005 4.329e-005 0.244
79 0.05232 0.323 0.749 0.896 0.184 4.329e-005 2.310e-005 0.235
80 0.05233 0.635 0.326 0.583 0.184 2.310e-005 4.329e-005 0.240
81 0.05241 0.479 0.451 1.000 0.184 2.848e-005 3.511e-005 0.261
82 0.05244 0.479 0.878 0.531 0.184 5.337e-005 8.111e-006 0.255
83 0.05247 0.583 0.326 0.844 0.184 2.310e-005 4.329e-005 0.231
84 0.05248 0.687 0.326 0.427 0.195 2.310e-005 2.848e-005 0.247
85 0.05249 0.687 0.326 0.427 0.184 2.310e-005 3.511e-005 0.247
86 0.05261 0.427 0.598 0.739 0.184 3.511e-005 2.310e-005 0.257
87 0.05268 0.427 0.598 0.844 0.195 3.511e-005 1.874e-005 0.275
88 0.05273 0.635 0.326 0.687 0.184 2.310e-005 4.329e-005 0.248
89 0.05278 0.479 0.749 0.531 0.184 4.329e-005 1.233e-005 0.259
90 0.05282 0.583 0.598 0.427 0.184 3.511e-005 1.874e-005 0.277
91 0.05284 0.635 0.451 0.375 0.195 2.848e-005 1.874e-005 0.260
92 0.05287 0.323 0.878 0.844 0.184 5.337e-005 1.233e-005 0.235
93 0.05296 0.323 0.749 1.000 0.195 4.329e-005 1.520e-005 0.252
94 0.05307 0.583 0.326 0.792 0.184 2.310e-005 4.329e-005 0.229
95 0.05309 0.687 0.326 0.531 0.195 2.310e-005 2.848e-005 0.261
96 0.05315 0.635 0.326 0.531 0.184 2.310e-005 4.329e-005 0.235
97 0.05329 0.375 0.959 0.792 0.184 6.579e-005 6.579e-006 0.261
98 0.05331 0.375 0.749 0.844 0.195 4.329e-005 1.520e-005 0.270
99 0.05340 0.635 0.326 0.739 0.184 2.310e-005 4.329e-005 0.251
100 0.05341 0.896 0.228 0.323 0.184 1.874e-005 4.329e-005 0.253
Go Back Top