dkm@sierpinski:~/5300$ R

R version 3.3.2 (2016-10-31) -- "Sincere Pumpkin Patch"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> crabs=read.csv('table-4-3.csv')
> attach(crabs)
> y
  [1] 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0
 [38] 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1
 [75] 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[112] 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1
[149] 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0
> y
  [1] 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0
 [38] 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1
 [75] 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[112] 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1
[149] 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0
> width
  [1] 28.3 22.5 26.0 24.8 26.0 23.8 26.5 24.7 23.7 25.6 24.3 25.8 28.2 21.0 26.0
 [16] 27.1 25.2 29.0 24.7 27.4 23.2 25.0 22.5 26.7 25.8 26.2 28.7 26.8 27.5 24.9
 [31] 29.3 25.8 25.7 25.7 26.7 23.7 26.8 27.5 23.4 27.9 27.5 26.1 27.7 30.0 28.5
 [46] 28.9 28.2 25.0 28.5 30.3 24.7 27.7 27.4 22.9 25.7 28.3 27.2 26.2 27.8 25.5
 [61] 27.1 24.5 27.0 26.0 28.0 30.0 29.0 26.2 26.5 26.2 25.6 23.0 23.0 25.4 24.2
 [76] 22.9 26.0 25.4 25.7 25.1 24.5 27.5 23.1 25.9 25.8 27.0 28.5 25.5 23.5 24.0
 [91] 29.7 26.8 26.7 28.7 23.1 29.0 25.5 26.5 24.5 28.5 28.2 24.5 27.5 24.7 25.2
[106] 27.3 26.3 29.0 25.3 26.5 27.8 27.0 25.7 25.0 31.9 23.7 29.3 22.0 25.0 27.0
[121] 23.8 30.2 26.2 24.2 27.4 25.4 28.4 22.5 26.2 24.9 24.5 25.1 28.0 25.8 27.9
[136] 24.9 28.4 27.2 25.0 27.5 33.5 30.5 29.0 24.3 25.8 25.0 31.7 29.5 24.0 30.0
[151] 27.6 26.2 23.1 22.9 24.5 24.7 28.3 23.9 23.8 29.8 26.5 26.0 28.2 25.7 26.5
[166] 25.8 24.1 26.2 26.1 29.0 28.0 27.0 24.5
> crabs
    color spine width satell weight y
1       3     3  28.3      8   3050 1
2       4     3  22.5      0   1550 0
3       2     1  26.0      9   2300 1
4       4     3  24.8      0   2100 0
5       4     3  26.0      4   2600 1
6       3     3  23.8      0   2100 0
7       2     1  26.5      0   2350 0
8       4     2  24.7      0   1900 0
9       3     1  23.7      0   1950 0
10      4     3  25.6      0   2150 0
11      4     3  24.3      0   2150 0
12      3     3  25.8      0   2650 0
13      3     3  28.2     11   3050 1
14      5     2  21.0      0   1850 0
15      3     1  26.0     14   2300 1
16      2     1  27.1      8   2950 1
17      3     3  25.2      1   2000 1
18      3     3  29.0      1   3000 1
19      5     3  24.7      0   2200 0
20      3     3  27.4      5   2700 1
21      3     2  23.2      4   1950 1
22      2     2  25.0      3   2300 1
23      3     1  22.5      1   1600 1
24      4     3  26.7      2   2600 1
25      5     3  25.8      3   2000 1
26      5     3  26.2      0   1300 0
27      3     3  28.7      3   3150 1
28      3     1  26.8      5   2700 1
29      5     3  27.5      0   2600 0
30      3     3  24.9      0   2100 0
31      2     1  29.3      4   3200 1
32      2     3  25.8      0   2600 0
33      3     2  25.7      0   2000 0
34      3     1  25.7      8   2000 1
35      3     1  26.7      5   2700 1
36      5     3  23.7      0   1850 0
37      3     3  26.8      0   2650 0
38      3     3  27.5      6   3150 1
39      5     3  23.4      0   1900 0
40      3     3  27.9      6   2800 1
41      4     3  27.5      3   3100 1
42      2     1  26.1      5   2800 1
43      2     1  27.7      6   2500 1
44      3     1  30.0      5   3300 1
45      4     1  28.5      9   3250 1
46      4     3  28.9      4   2800 1
47      3     3  28.2      6   2600 1
48      3     3  25.0      4   2100 1
49      3     3  28.5      3   3000 1
50      3     1  30.3      3   3600 1
51      5     3  24.7      5   2100 1
52      3     3  27.7      5   2900 1
53      2     1  27.4      6   2700 1
54      3     3  22.9      4   1600 1
55      3     1  25.7      5   2000 1
56      3     3  28.3     15   3000 1
57      3     3  27.2      3   2700 1
58      4     3  26.2      3   2300 1
59      3     1  27.8      0   2750 0
60      5     3  25.5      0   2250 0
61      4     3  27.1      0   2550 0
62      4     3  24.5      5   2050 1
63      4     1  27.0      3   2450 1
64      3     3  26.0      5   2150 1
65      3     3  28.0      1   2800 1
66      3     3  30.0      8   3050 1
67      3     3  29.0     10   3200 1
68      3     3  26.2      0   2400 0
69      3     1  26.5      0   1300 0
70      3     3  26.2      3   2400 1
71      4     3  25.6      7   2800 1
72      4     3  23.0      1   1650 1
73      4     3  23.0      0   1800 0
74      3     3  25.4      6   2250 1
75      4     3  24.2      0   1900 0
76      3     2  22.9      0   1600 0
77      4     2  26.0      3   2200 1
78      3     3  25.4      4   2250 1
79      4     3  25.7      0   1200 0
80      3     3  25.1      5   2100 1
81      4     2  24.5      0   2250 0
82      5     3  27.5      0   2900 0
83      4     3  23.1      0   1650 0
84      4     1  25.9      4   2550 1
85      3     3  25.8      0   2300 0
86      5     3  27.0      3   2250 1
87      3     3  28.5      0   3050 0
88      5     1  25.5      0   2750 0
89      5     3  23.5      0   1900 0
90      3     2  24.0      0   1700 0
91      3     1  29.7      5   3850 1
92      3     1  26.8      0   2550 0
93      5     3  26.7      0   2450 0
94      3     1  28.7      0   3200 0
95      4     3  23.1      0   1550 0
96      3     1  29.0      1   2800 1
97      4     3  25.5      0   2250 0
98      4     3  26.5      1   1967 1
99      4     3  24.5      1   2200 1
100     4     3  28.5      1   3000 1
101     3     3  28.2      1   2867 1
102     3     3  24.5      1   1600 1
103     3     3  27.5      1   2550 1
104     3     2  24.7      4   2550 1
105     3     1  25.2      1   2000 1
106     4     3  27.3      1   2900 1
107     3     3  26.3      1   2400 1
108     3     3  29.0      1   3100 1
109     3     3  25.3      2   1900 1
110     3     3  26.5      4   2300 1
111     3     3  27.8      3   3250 1
112     3     3  27.0      6   2500 1
113     4     3  25.7      0   2100 0
114     3     3  25.0      2   2100 1
115     3     3  31.9      2   3325 1
116     5     3  23.7      0   1800 0
117     5     3  29.3     12   3225 1
118     4     3  22.0      0   1400 0
119     3     3  25.0      5   2400 1
120     4     3  27.0      6   2500 1
121     4     3  23.8      6   1800 1
122     2     1  30.2      2   3275 1
123     4     3  26.2      0   2225 0
124     3     3  24.2      2   1650 1
125     3     3  27.4      3   2900 1
126     3     2  25.4      0   2300 0
127     4     3  28.4      3   3200 1
128     5     3  22.5      4   1475 1
129     3     3  26.2      2   2025 1
130     3     1  24.9      6   2300 1
131     2     2  24.5      6   1950 1
132     3     3  25.1      0   1800 0
133     3     1  28.0      4   2900 1
134     5     3  25.8     10   2250 1
135     3     3  27.9      7   3050 1
136     3     3  24.9      0   2200 0
137     3     1  28.4      5   3100 1
138     4     3  27.2      5   2400 1
139     3     2  25.0      6   2250 1
140     3     3  27.5      6   2625 1
141     3     1  33.5      7   5200 1
142     3     3  30.5      3   3325 1
143     4     3  29.0      3   2925 1
144     3     1  24.3      0   2000 0
145     3     3  25.8      0   2400 0
146     5     3  25.0      8   2100 1
147     3     1  31.7      4   3725 1
148     3     3  29.5      4   3025 1
149     4     3  24.0     10   1900 1
150     3     3  30.0      9   3000 1
151     3     3  27.6      4   2850 1
152     3     3  26.2      0   2300 0
153     3     1  23.1      0   2000 0
154     3     1  22.9      0   1600 0
155     5     3  24.5      0   1900 0
156     3     3  24.7      4   1950 1
157     3     3  28.3      0   3200 0
158     3     3  23.9      2   1850 1
159     4     3  23.8      0   1800 0
160     4     2  29.8      4   3500 1
161     3     3  26.5      4   2350 1
162     3     3  26.0      3   2275 1
163     3     3  28.2      8   3050 1
164     5     3  25.7      0   2150 0
165     3     3  26.5      7   2750 1
166     3     3  25.8      0   2200 0
167     4     3  24.1      0   1800 0
168     4     3  26.2      2   2175 1
169     4     3  26.1      3   2750 1
170     4     3  29.0      4   3275 1
171     2     1  28.0      0   2625 0
172     5     3  27.0      0   2625 0
173     3     2  24.5      0   2000 0
> fit=glm(y ~ width, family=binomial(link=logit))
> summary(fit)

Call:
glm(formula = y ~ width, family = binomial(link = logit))

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.0281  -1.0458   0.5480   0.9066   1.6942  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -12.3508     2.6287  -4.698 2.62e-06 ***
width         0.4972     0.1017   4.887 1.02e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 225.76  on 172  degrees of freedom
Residual deviance: 194.45  on 171  degrees of freedom
AIC: 198.45

Number of Fisher Scoring iterations: 4

> alpha=-12.3508
> beta=.4972
> med=-alpha/beta
> med
[1] 24.84071
> quartile1=med-1/beta
> quartile1
[1] 22.82944
> quartile3=med+1/beta
> quartile3
[1] 26.85197
> x0=26.5
> vcov(fit)
            (Intercept)       width
(Intercept)   6.9101576 -0.26684761
width        -0.2668476  0.01035012
> 6.910+x0^2*.01035+2*x0*-.2668
[1] 0.0378875
> 6.9101576+x0^2*.01035012+2*x0*-.2668476
[1] 0.03560657
> alpha+beta*x0
[1] 0.825
> ly0=alpha+beta*x0
> var_ly0=6.9101576+x0^2*.01035012+2*x0*-.2668476
> ly0+sqrt(var_ly0)*1.96
[1] 1.194846
> ly0-sqrt(var_ly0)*1.96
[1] 0.4551538
> ly0_ci_lower=ly0-sqrt(var_ly0)*1.96
> exp(ly0_ci_lower)/(1+exp(ly0_ci_lower))
[1] 0.6118639
> ly0_ci_upper=y0+sqrt(var_ly0)*1.96
> exp(ly0_ci_upper)/(1+exp(ly0_ci_upper))
[1] 0.7676067
> mean(width)
[1] 26.29884
> widthc=width-mean(width)
> width
  [1] 28.3 22.5 26.0 24.8 26.0 23.8 26.5 24.7 23.7 25.6 24.3 25.8 28.2 21.0 26.0
 [16] 27.1 25.2 29.0 24.7 27.4 23.2 25.0 22.5 26.7 25.8 26.2 28.7 26.8 27.5 24.9
 [31] 29.3 25.8 25.7 25.7 26.7 23.7 26.8 27.5 23.4 27.9 27.5 26.1 27.7 30.0 28.5
 [46] 28.9 28.2 25.0 28.5 30.3 24.7 27.7 27.4 22.9 25.7 28.3 27.2 26.2 27.8 25.5
 [61] 27.1 24.5 27.0 26.0 28.0 30.0 29.0 26.2 26.5 26.2 25.6 23.0 23.0 25.4 24.2
 [76] 22.9 26.0 25.4 25.7 25.1 24.5 27.5 23.1 25.9 25.8 27.0 28.5 25.5 23.5 24.0
 [91] 29.7 26.8 26.7 28.7 23.1 29.0 25.5 26.5 24.5 28.5 28.2 24.5 27.5 24.7 25.2
[106] 27.3 26.3 29.0 25.3 26.5 27.8 27.0 25.7 25.0 31.9 23.7 29.3 22.0 25.0 27.0
[121] 23.8 30.2 26.2 24.2 27.4 25.4 28.4 22.5 26.2 24.9 24.5 25.1 28.0 25.8 27.9
[136] 24.9 28.4 27.2 25.0 27.5 33.5 30.5 29.0 24.3 25.8 25.0 31.7 29.5 24.0 30.0
[151] 27.6 26.2 23.1 22.9 24.5 24.7 28.3 23.9 23.8 29.8 26.5 26.0 28.2 25.7 26.5
[166] 25.8 24.1 26.2 26.1 29.0 28.0 27.0 24.5
> widthc
  [1]  2.001156069 -3.798843931 -0.298843931 -1.498843931 -0.298843931
  [6] -2.498843931  0.201156069 -1.598843931 -2.598843931 -0.698843931
 [11] -1.998843931 -0.498843931  1.901156069 -5.298843931 -0.298843931
 [16]  0.801156069 -1.098843931  2.701156069 -1.598843931  1.101156069
 [21] -3.098843931 -1.298843931 -3.798843931  0.401156069 -0.498843931
 [26] -0.098843931  2.401156069  0.501156069  1.201156069 -1.398843931
 [31]  3.001156069 -0.498843931 -0.598843931 -0.598843931  0.401156069
 [36] -2.598843931  0.501156069  1.201156069 -2.898843931  1.601156069
 [41]  1.201156069 -0.198843931  1.401156069  3.701156069  2.201156069
 [46]  2.601156069  1.901156069 -1.298843931  2.201156069  4.001156069
 [51] -1.598843931  1.401156069  1.101156069 -3.398843931 -0.598843931
 [56]  2.001156069  0.901156069 -0.098843931  1.501156069 -0.798843931
 [61]  0.801156069 -1.798843931  0.701156069 -0.298843931  1.701156069
 [66]  3.701156069  2.701156069 -0.098843931  0.201156069 -0.098843931
 [71] -0.698843931 -3.298843931 -3.298843931 -0.898843931 -2.098843931
 [76] -3.398843931 -0.298843931 -0.898843931 -0.598843931 -1.198843931
 [81] -1.798843931  1.201156069 -3.198843931 -0.398843931 -0.498843931
 [86]  0.701156069  2.201156069 -0.798843931 -2.798843931 -2.298843931
 [91]  3.401156069  0.501156069  0.401156069  2.401156069 -3.198843931
 [96]  2.701156069 -0.798843931  0.201156069 -1.798843931  2.201156069
[101]  1.901156069 -1.798843931  1.201156069 -1.598843931 -1.098843931
[106]  1.001156069  0.001156069  2.701156069 -0.998843931  0.201156069
[111]  1.501156069  0.701156069 -0.598843931 -1.298843931  5.601156069
[116] -2.598843931  3.001156069 -4.298843931 -1.298843931  0.701156069
[121] -2.498843931  3.901156069 -0.098843931 -2.098843931  1.101156069
[126] -0.898843931  2.101156069 -3.798843931 -0.098843931 -1.398843931
[131] -1.798843931 -1.198843931  1.701156069 -0.498843931  1.601156069
[136] -1.398843931  2.101156069  0.901156069 -1.298843931  1.201156069
[141]  7.201156069  4.201156069  2.701156069 -1.998843931 -0.498843931
[146] -1.298843931  5.401156069  3.201156069 -2.298843931  3.701156069
[151]  1.301156069 -0.098843931 -3.198843931 -3.398843931 -1.798843931
[156] -1.598843931  2.001156069 -2.398843931 -2.498843931  3.501156069
[161]  0.201156069 -0.298843931  1.901156069 -0.598843931  0.201156069
[166] -0.498843931 -2.198843931 -0.098843931 -0.198843931  2.701156069
[171]  1.701156069  0.701156069 -1.798843931
> widthc2=widthc^2
> widthc2
  [1] 4.004626e+00 1.443122e+01 8.930769e-02 2.246533e+00 8.930769e-02
  [6] 6.244221e+00 4.046376e-02 2.556302e+00 6.753990e+00 4.883828e-01
 [11] 3.995377e+00 2.488453e-01 3.614394e+00 2.807775e+01 8.930769e-02
 [16] 6.418510e-01 1.207458e+00 7.296244e+00 2.556302e+00 1.212545e+00
 [21] 9.602834e+00 1.686996e+00 1.443122e+01 1.609262e-01 2.488453e-01
 [26] 9.770123e-03 5.765550e+00 2.511574e-01 1.442776e+00 1.956764e+00
 [31] 9.006938e+00 2.488453e-01 3.586141e-01 3.586141e-01 1.609262e-01
 [36] 6.753990e+00 2.511574e-01 1.442776e+00 8.403296e+00 2.563701e+00
 [41] 1.442776e+00 3.953891e-02 1.963238e+00 1.369856e+01 4.845088e+00
 [46] 6.766013e+00 3.614394e+00 1.686996e+00 4.845088e+00 1.600925e+01
 [51] 2.556302e+00 1.963238e+00 1.212545e+00 1.155214e+01 3.586141e-01
 [56] 4.004626e+00 8.120823e-01 9.770123e-03 2.253470e+00 6.381516e-01
 [61] 6.418510e-01 3.235839e+00 4.916198e-01 8.930769e-02 2.893932e+00
 [66] 1.369856e+01 7.296244e+00 9.770123e-03 4.046376e-02 9.770123e-03
 [71] 4.883828e-01 1.088237e+01 1.088237e+01 8.079204e-01 4.405146e+00
 [76] 1.155214e+01 8.930769e-02 8.079204e-01 3.586141e-01 1.437227e+00
 [81] 3.235839e+00 1.442776e+00 1.023260e+01 1.590765e-01 2.488453e-01
 [86] 4.916198e-01 4.845088e+00 6.381516e-01 7.833527e+00 5.284683e+00
 [91] 1.156786e+01 2.511574e-01 1.609262e-01 5.765550e+00 1.023260e+01
 [96] 7.296244e+00 6.381516e-01 4.046376e-02 3.235839e+00 4.845088e+00
[101] 3.614394e+00 3.235839e+00 1.442776e+00 2.556302e+00 1.207458e+00
[106] 1.002313e+00 1.336496e-06 7.296244e+00 9.976892e-01 4.046376e-02
[111] 2.253470e+00 4.916198e-01 3.586141e-01 1.686996e+00 3.137295e+01
[116] 6.753990e+00 9.006938e+00 1.848006e+01 1.686996e+00 4.916198e-01
[121] 6.244221e+00 1.521902e+01 9.770123e-03 4.405146e+00 1.212545e+00
[126] 8.079204e-01 4.414857e+00 1.443122e+01 9.770123e-03 1.956764e+00
[131] 3.235839e+00 1.437227e+00 2.893932e+00 2.488453e-01 2.563701e+00
[136] 1.956764e+00 4.414857e+00 8.120823e-01 1.686996e+00 1.442776e+00
[141] 5.185665e+01 1.764971e+01 7.296244e+00 3.995377e+00 2.488453e-01
[146] 1.686996e+00 2.917249e+01 1.024740e+01 5.284683e+00 1.369856e+01
[151] 1.693007e+00 9.770123e-03 1.023260e+01 1.155214e+01 3.235839e+00
[156] 2.556302e+00 4.004626e+00 5.754452e+00 6.244221e+00 1.225809e+01
[161] 4.046376e-02 8.930769e-02 3.614394e+00 3.586141e-01 4.046376e-02
[166] 2.488453e-01 4.834915e+00 9.770123e-03 3.953891e-02 7.296244e+00
[171] 2.893932e+00 4.916198e-01 3.235839e+00
> fitq=glm(y ~ widthc + widthc2, family=binomial(link=logit))
 
> summary(fitq)

Call:
glm(formula = y ~ widthc + widthc2, family = binomial(link = logit))

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.1185  -1.0441   0.5067   0.9483   1.5406  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  0.61851    0.21655   2.856  0.00429 ** 
widthc       0.53308    0.11685   4.562 5.07e-06 ***
widthc2      0.04047    0.04566   0.886  0.37537    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 225.76  on 172  degrees of freedom
Residual deviance: 193.63  on 170  degrees of freedom
AIC: 199.63

Number of Fisher Scoring iterations: 5

> library(epicalc)
Loading required package: foreign
Loading required package: survival
Loading required package: MASS

Attaching package: ‘MASS’

The following object is masked _by_ ‘.GlobalEnv’:

    crabs

Loading required package: nnet
> lrtest(fit,fitq)
Likelihood ratio test for MLE method 
Chi-squared 1 d.f. =  0.8254191 , P value =  0.3636005 

> x=seq(from=10, to=40, by=.1)
> logit=-12.3508+x*.4972
> pi_fit=exp(logit)/(1+exp(logit))
> plot(x, pi_fit,type='l')
> plot(width,y)
> plot(x, pi_fit,type='l')
> 

