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The publication says beta was set to 5.5, not 11. So we The regression statistics for selecting beta are below, where "Cut" is the value of beta and "Adj R^2" is the value which should exceed a chosen threshold. When the threshold is set to the nominal value of 0.90 , beta=11 is the smallest value for which "Adj R^2" exceeds the threshold. The value of 5.5 would be selected if the threshold were set to 0.80.
Cut | p-value | Adj R^2 | Truncated Adj R^2 | slope | mean(k) | median(k) | max(k) |
|---|---|---|---|---|---|---|---|
1 | -1 | 0.12 | 0.871 | 0.841 | 949 | 939 | 1640 |
1.5 | -1 | -0.0707 | 0.854 | -0.11 | 508 | 486 | 1110 |
2 | -1 | 0.164 | 0.895 | -0.688 | 294 | 268 | 787 |
2.5 | -1 | 0.41 | 0.939 | -1.03 | 181 | 156 | 583 |
3 | -1 | 0.554 | 0.953 | -1.28 | 117 | 94.7 | 445 |
3.5 | -1 | 0.656 | 0.966 | -1.47 | 79 | 59.7 | 347 |
4 | -1 | 0.713 | 0.973 | -1.58 | 54.9 | 38.4 | 276 |
4.5 | -1 | 0.76 | 0.981 | -1.67 | 39.3 | 25.3 | 223 |
5 | -1 | 0.786 | 0.983 | -1.72 | 28.8 | 17 | 182 |
5.5 | -1 | 0.801 | 0.983 | -1.75 | 21.5 | 11.7 | 150 |
6 | -1 | 0.821 | 0.987 | -1.78 | 16.4 | 8.33 | 125 |
6.5 | -1 | 0.825 | 0.979 | -1.79 | 12.7 | 6.04 | 104 |
7 | -1 | 0.824 | 0.969 | -1.8 | 10 | 4.5 | 88.1 |
7.5 | -1 | 0.83 | 0.971 | -1.8 | 8.03 | 3.35 | 74.8 |
8 | -1 | 0.835 | 0.977 | -1.79 | 6.52 | 2.54 | 63.9 |
8.5 | -1 | 0.843 | 0.983 | -1.77 | 5.36 | 1.93 | 54.8 |
9 | -1 | 0.849 | 0.984 | -1.74 | 4.45 | 1.53 | 47.2 |
9.5 | -1 | 0.845 | 0.975 | -1.72 | 3.75 | 1.22 | 40.9 |
10 | -1 | 0.859 | 0.976 | -1.66 | 3.19 | 0.994 | 35.5 |
10.5 | -1 | 0.873 | 0.973 | -1.61 | 2.74 | 0.835 | 31 |
11 | -1 | 0.904 | 0.98 | -1.53 | 2.38 | 0.694 | 27.1 |
11.5 | -1 | 0.907 | 0.983 | -1.53 | 2.08 | 0.564 | 24.7 |
12 | -1 | 0.877 | 0.963 | -1.58 | 1.84 | 0.462 | 23.4 |
We reran the Sage code with that beta=5.5:
grey blue turquoise brown yellow green red black pink magenta
grey 971 0 0 0 0 0 0 0 0 0
blue 4 617 0 0 0 0 0 0 0 0
brown 0 0 602 0 0 0 0 0 0 0
turquoise 170 0 0 439 0 0 75 0 0 0
yellow 5 0 347 0 0 0 0 0 0 0
green 0 0 272 0 0 0 0 0 0 0
red 39 0 0 0 192 0 0 0 0 0
magenta 148 0 0 0 0 0 0 0 0 0
black 126 0 0 12 0 0 0 0 70 0
pink 58 0 0 0 0 106 0 0 0 0
purple 0 0 104 0 0 0 0 0 0 0
tan 80 0 0 0 0 0 0 0 0 0
greenyellow 18 0 0 0 0 0 0 71 0 0
salmon 59 0 0 0 0 0 0 0 0 0
cyan 56 0 0 0 0 0 0 0 0 0
midnightblue 0 0 0 0 0 0 0 0 0 55
lightcyan 45 0 0 0 0 0 0 0 0 0
lightgreen 44 0 0 0 0 0 0 0 0 0
grey60 44 0 0 0 0 0 0 0 0 0
lightyellow 39 0 0 0 0 0 0 0 0 0
coral 38 0 0 0 0 0 0 0 0 0
sienna 0 0 36 0 0 0 0 0 0 0
gold 36 0 0 0 0 0 0 0 0 0
peru 34 0 0 0 0 0 0 0 0 0
...
Unequal beta, module diff=14% | Identical beta, module diff=0.2% |
|---|---|
turquoise grey blue brown yellow green red pink magenta black purple | turquoise grey blue brown yellow green red black pink magenta purple |