Писать много лень, да и некогда. В общем, проверил гипотезы
Parn (зависимость от дня недели) и мою (от фазы луны). От фазы луны зависимость должна возникнуть, тот, кто солит огурцы, знает, что огурцы, собранные на полнолуние, лучше не солить, воды в них много, будут потом мягкими. Для расчета добавил фиктивные двоичные нормированные переменные для дней недели (d1..d6) и синусовый период, принимающий значение -1 в новолуние и 1 в полнолуние (mds).
Игры с R
Код:
> summary(lm1<-lm(weight~poly(day,4)+d1+d3+d4+d5+d6+mds,data=MyW))
Call:
lm(formula = weight ~ poly(day, 4) + d1 + d3 + d4 + d5 + d6 +
mds, data = MyW)
Residuals:
Min 1Q Median 3Q Max
-2.65118 -0.55938 -0.02685 0.57784 2.97415
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 114.90432 0.07284 1577.389 < 2e-16 ***
poly(day, 4)1 -106.47489 0.90349 -117.849 < 2e-16 ***
poly(day, 4)2 7.61531 0.89633 8.496 2.6e-14 ***
poly(day, 4)3 -4.68008 0.90842 -5.152 8.6e-07 ***
poly(day, 4)4 2.33373 0.89863 2.597 0.0104 *
d1 0.27177 0.17470 1.556 0.1221
d3 -0.16756 0.17797 -0.942 0.3481
d4 -0.21818 0.17797 -1.226 0.2223
d5 0.04386 0.17800 0.246 0.8057
d6 0.06459 0.17476 0.370 0.7123
mds 0.19569 0.10670 1.834 0.0688 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.8949 on 140 degrees of freedom
Multiple R-squared: 0.9903, Adjusted R-squared: 0.9896
F-statistic: 1433 on 10 and 140 DF, p-value: < 2.2e-16
# Последовательно убираем предикторы и получаем
> summary(lm1<-lm(weight~poly(day,4)+mds,data=MyW))
Call:
lm(formula = weight ~ poly(day, 4) + mds, data = MyW)
Residuals:
Min 1Q Median 3Q Max
-2.8645 -0.5353 -0.0290 0.5652 3.2455
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 114.90658 0.07262 1582.344 < 2e-16 ***
poly(day, 4)1 -106.46512 0.90071 -118.202 < 2e-16 ***
poly(day, 4)2 7.67696 0.89274 8.599 1.19e-14 ***
poly(day, 4)3 -4.66665 0.90540 -5.154 8.20e-07 ***
poly(day, 4)4 2.41412 0.89434 2.699 0.00777 **
mds 0.19569 0.10638 1.839 0.06789 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.8923 on 145 degrees of freedom
Multiple R-squared: 0.99, Adjusted R-squared: 0.9897
F-statistic: 2882 on 5 and 145 DF, p-value: < 2.2e-16
> confint(lm1)
2.5 % 97.5 %
(Intercept) 114.76305332 115.0501062
poly(day, 4)1 -108.24533014 -104.6849116
poly(day, 4)2 5.91249061 9.4414330
poly(day, 4)3 -6.45614075 -2.8771670
poly(day, 4)4 0.64648918 4.1817550
mds -0.01457465 0.4059466
Мораль: разница в весе тушки между полнолунием и новолунием составляет порядка 400 грамм. От дня недели не зависит, потому как у меня сила воли такая, что можно сыр резать.
Кому интересно играть c данными, данные (в формате GNU R) прилагаю.
Много циферок
Код:
> MyW
date day weight trend d1 d2 d3 d4 d5 d6 mds
1 16.02.13 0 134.5 134.5000 0 0 0 0 0 1 -0.53042091
2 17.02.13 1 132.5 134.2337 -1 -1 -1 -1 -1 -1 -0.33923887
3 18.02.13 2 132.2 133.9630 1 0 0 0 0 0 -0.13272553
4 19.02.13 3 131.0 133.5686 0 1 0 0 0 0 0.07978611
5 20.02.13 4 130.5 133.1601 0 0 1 0 0 0 0.28869195
6 21.02.13 5 129.1 132.6196 0 0 0 1 0 0 0.48455087
7 22.02.13 6 129.4 132.1910 0 0 0 0 1 0 0.65851138
8 23.02.13 7 129.8 131.8727 0 0 0 0 0 1 0.80271164
9 24.02.13 8 130.5 131.6900 -1 -1 -1 -1 -1 -1 0.91063477
10 25.02.13 9 129.5 131.3984 1 0 0 0 0 0 0.97740339
11 26.02.13 10 128.4 130.9993 0 1 0 0 0 0 1.00000000
12 27.02.13 11 128.6 130.6799 0 0 1 0 0 0 0.97740339
13 28.02.13 12 128.8 130.4296 0 0 0 1 0 0 0.91063477
14 01.03.13 13 128.6 130.1860 0 0 0 0 1 0 0.80271164
15 02.03.13 14 127.6 129.8418 0 0 0 0 0 1 0.65851138
16 03.03.13 15 127.4 129.5167 -1 -1 -1 -1 -1 -1 0.48455087
17 04.03.13 16 126.7 129.1418 1 0 0 0 0 0 0.28869195
18 05.03.13 17 127.2 128.8833 0 1 0 0 0 0 0.07978611
19 06.03.13 18 127.3 128.6725 0 0 1 0 0 0 -0.13272553
20 07.03.13 19 127.0 128.4499 0 0 0 1 0 0 -0.33923887
21 08.03.13 20 126.7 128.2169 0 0 0 0 1 0 -0.53042091
22 09.03.13 21 126.5 127.9884 0 0 0 0 0 1 -0.69763152
23 10.03.13 22 125.1 127.6038 -1 -1 -1 -1 -1 -1 -0.83331392
24 11.03.13 23 125.0 127.2572 1 0 0 0 0 0 -0.93133618
25 12.03.13 24 123.6 126.7704 0 1 0 0 0 0 -0.98726835
26 13.03.13 25 122.8 126.2418 0 0 1 0 0 0 -0.99858270
27 14.03.13 26 123.9 125.9301 0 0 0 1 0 0 -0.96476787
28 15.03.13 27 124.7 125.7663 0 0 0 0 1 0 -0.88735208
29 16.03.13 28 123.3 125.4380 0 0 0 0 0 1 -0.76983398
30 17.03.13 29 123.8 125.2199 -1 -1 -1 -1 -1 -1 -0.61752461
31 18.03.13 30 123.5 124.9910 1 0 0 0 0 0 -0.43730732
32 19.03.13 31 123.2 124.7526 0 1 0 0 0 0 -0.23732670
33 20.03.13 32 122.6 124.4660 0 0 1 0 0 0 -0.02662052
34 21.03.13 33 122.1 124.1510 0 0 0 1 0 0 0.18528872
35 22.03.13 34 120.9 123.7183 0 0 0 0 1 0 0.38882417
36 23.03.13 35 122.4 123.5428 0 0 0 0 0 1 0.57478741
37 24.03.13 36 121.6 123.2841 -1 -1 -1 -1 -1 -1 0.73477415
38 25.03.13 37 122.5 123.1798 1 0 0 0 0 0 0.86155408
39 26.03.13 38 122.8 123.1292 0 1 0 0 0 0 0.94939761
40 27.03.13 39 122.6 123.0588 0 0 1 0 0 0 0.99433480
41 28.03.13 40 121.2 122.8113 0 0 0 1 0 0 0.99433480
42 29.03.13 41 122.0 122.7033 0 0 0 0 1 0 0.94939761
43 30.03.13 42 120.3 122.3834 0 0 0 0 0 1 0.86155408
44 31.03.13 43 119.4 121.9862 -1 -1 -1 -1 -1 -1 0.73477415
45 01.04.13 44 121.2 121.8816 1 0 0 0 0 0 0.57478741
46 02.04.13 45 120.6 121.7110 0 1 0 0 0 0 0.38882417
47 03.04.13 46 120.1 121.4965 0 0 1 0 0 0 0.18528872
48 04.04.13 47 120.0 121.2973 0 0 0 1 0 0 -0.02662052
49 05.04.13 48 120.3 121.1645 0 0 0 0 1 0 -0.23732670
50 06.04.13 49 119.0 120.8764 0 0 0 0 0 1 -0.43730732
51 07.04.13 50 118.9 120.6133 -1 -1 -1 -1 -1 -1 -0.61752461
52 08.04.13 51 119.7 120.4917 1 0 0 0 0 0 -0.76983398
53 09.04.13 52 118.4 120.2133 0 1 0 0 0 0 -0.88735208
54 10.04.13 53 117.5 119.8521 0 0 1 0 0 0 -0.96476787
55 11.04.13 54 117.5 119.5389 0 0 0 1 0 0 -0.99858270
56 12.04.13 55 117.4 119.2542 0 0 0 0 1 0 -0.98726835
57 13.04.13 56 117.5 119.0207 0 0 0 0 0 1 -0.93133618
58 14.04.13 57 119.1 119.0312 -1 -1 -1 -1 -1 -1 -0.83331392
59 15.04.13 58 118.3 118.9339 1 0 0 0 0 0 -0.69763152
60 16.04.13 59 117.3 118.7164 0 1 0 0 0 0 -0.53042091
61 17.04.13 60 116.9 118.4746 0 0 1 0 0 0 -0.33923887
62 18.04.13 61 116.1 118.1585 0 0 0 1 0 0 -0.13272553
63 19.04.13 62 116.5 117.9377 0 0 0 0 1 0 0.07978611
64 20.04.13 63 117.5 117.8794 0 0 0 0 0 1 0.28869195
65 21.04.13 64 116.5 117.6958 -1 -1 -1 -1 -1 -1 0.48455087
66 22.04.13 65 115.3 117.3769 1 0 0 0 0 0 0.65851138
67 23.04.13 66 115.1 117.0738 0 1 0 0 0 0 0.80271164
68 24.04.13 67 114.0 116.6646 0 0 1 0 0 0 0.91063477
69 25.04.13 68 115.0 116.4430 0 0 0 1 0 0 0.97740339
70 26.04.13 69 114.4 116.1710 0 0 0 0 1 0 1.00000000
71 27.04.13 70 115.2 116.0418 0 0 0 0 0 1 0.97740339
72 28.04.13 71 114.6 115.8498 -1 -1 -1 -1 -1 -1 0.91063477
73 29.04.13 72 114.6 115.6834 1 0 0 0 0 0 0.80271164
74 30.04.13 73 114.3 115.4993 0 1 0 0 0 0 0.65851138
75 01.05.13 74 114.3 115.3396 0 0 1 0 0 0 0.48455087
76 02.05.13 75 113.3 115.0681 0 0 0 1 0 0 0.28869195
77 03.05.13 76 113.9 114.9126 0 0 0 0 1 0 0.07978611
78 04.05.13 77 113.2 114.6846 0 0 0 0 0 1 -0.13272553
79 05.05.13 78 113.2 114.4870 -1 -1 -1 -1 -1 -1 -0.33923887
80 06.05.13 79 113.1 114.3023 1 0 0 0 0 0 -0.53042091
81 07.05.13 80 113.5 114.1955 0 1 0 0 0 0 -0.69763152
82 08.05.13 81 114.3 114.2094 0 0 1 0 0 0 -0.83331392
83 09.05.13 82 113.5 114.1150 0 0 0 1 0 0 -0.93133618
84 10.05.13 83 111.6 113.7802 0 0 0 0 1 0 -0.98726835
85 11.05.13 84 111.7 113.5033 0 0 0 0 0 1 -0.99858270
86 12.05.13 85 112.9 113.4230 -1 -1 -1 -1 -1 -1 -0.96476787
87 13.05.13 86 114.2 113.5264 1 0 0 0 0 0 -0.88735208
88 14.05.13 87 113.0 113.4563 0 1 0 0 0 0 -0.76983398
89 15.05.13 88 111.9 113.2491 0 0 1 0 0 0 -0.61752461
90 16.05.13 89 112.3 113.1228 0 0 0 1 0 0 -0.43730732
91 17.05.13 90 112.5 113.0399 0 0 0 0 1 0 -0.23732670
92 18.05.13 91 111.6 112.8482 0 0 0 0 0 1 -0.02662052
93 19.05.13 92 111.6 112.6820 -1 -1 -1 -1 -1 -1 0.18528872
94 20.05.13 93 114.5 112.9241 1 0 0 0 0 0 0.38882417
95 21.05.13 94 113.3 112.9741 0 1 0 0 0 0 0.57478741
96 22.05.13 95 112.2 112.8711 0 0 1 0 0 0 0.73477415
97 23.05.13 96 111.5 112.6885 0 0 0 1 0 0 0.86155408
98 24.05.13 97 112.0 112.5969 0 0 0 0 1 0 0.94939761
99 25.05.13 98 112.0 112.5174 0 0 0 0 0 1 0.99433480
100 26.05.13 99 110.6 112.2622 -1 -1 -1 -1 -1 -1 0.99433480
101 27.05.13 100 109.4 111.8812 1 0 0 0 0 0 0.94939761
102 28.05.13 101 109.3 111.5375 0 1 0 0 0 0 0.86155408
103 29.05.13 102 110.2 111.3595 0 0 1 0 0 0 0.73477415
104 30.05.13 103 109.4 111.0986 0 0 0 1 0 0 0.57478741
105 31.05.13 104 109.6 110.8991 0 0 0 0 1 0 0.38882417
106 01.06.13 105 109.6 110.7262 0 0 0 0 0 1 0.18528872
107 02.06.13 106 109.9 110.6162 -1 -1 -1 -1 -1 -1 -0.02662052
108 03.06.13 107 107.5 110.2014 1 0 0 0 0 0 -0.23732670
109 04.06.13 108 106.9 109.7619 0 1 0 0 0 0 -0.43730732
110 05.06.13 109 106.4 109.3144 0 0 1 0 0 0 -0.61752461
111 06.06.13 110 105.0 108.7400 0 0 0 1 0 0 -0.76983398
112 07.06.13 111 106.8 108.4818 0 0 0 0 1 0 -0.88735208
113 08.06.13 112 106.8 108.2579 0 0 0 0 0 1 -0.96476787
114 09.06.13 113 107.1 108.1037 -1 -1 -1 -1 -1 -1 -0.99858270
115 10.06.13 114 107.3 107.9968 1 0 0 0 0 0 -0.98726835
116 11.06.13 115 107.2 107.8907 0 1 0 0 0 0 -0.93133618
117 12.06.13 116 106.6 107.7189 0 0 1 0 0 0 -0.83331392
118 13.06.13 117 107.7 107.7164 0 0 0 1 0 0 -0.69763152
119 14.06.13 118 106.1 107.5012 0 0 0 0 1 0 -0.53042091
120 15.06.13 119 106.3 107.3413 0 0 0 0 0 1 -0.33923887
121 16.06.13 120 105.0 107.0296 -1 -1 -1 -1 -1 -1 -0.13272553
122 17.06.13 121 104.8 106.7328 1 0 0 0 0 0 0.07978611
123 18.06.13 122 105.1 106.5154 0 1 0 0 0 0 0.28869195
124 19.06.13 123 105.2 106.3403 0 0 1 0 0 0 0.48455087
125 20.06.13 124 106.2 106.3216 0 0 0 1 0 0 0.65851138
126 21.06.13 125 106.3 106.3188 0 0 0 0 1 0 0.80271164
127 22.06.13 126 105.8 106.2497 0 0 0 0 0 1 0.91063477
128 23.06.13 127 104.8 106.0567 -1 -1 -1 -1 -1 -1 0.97740339
129 24.06.13 128 104.9 105.9027 1 0 0 0 0 0 1.00000000
130 25.06.13 129 104.4 105.7027 0 1 0 0 0 0 0.97740339
131 26.06.13 130 104.4 105.5293 0 0 1 0 0 0 0.91063477
132 27.06.13 131 104.3 105.3656 0 0 0 1 0 0 0.80271164
133 28.06.13 132 104.5 105.2504 0 0 0 0 1 0 0.65851138
134 29.06.13 133 103.6 105.0307 0 0 0 0 0 1 0.48455087
135 30.06.13 134 103.6 104.8402 -1 -1 -1 -1 -1 -1 0.28869195
136 01.07.13 135 104.0 104.7284 1 0 0 0 0 0 0.07978611
137 02.07.13 136 102.8 104.4717 0 1 0 0 0 0 -0.13272553
138 03.07.13 137 102.0 104.1426 0 0 1 0 0 0 -0.33923887
139 04.07.13 138 102.3 103.8974 0 0 0 1 0 0 -0.53042091
140 05.07.13 139 102.7 103.7379 0 0 0 0 1 0 -0.69763152
141 06.07.13 140 102.9 103.6264 0 0 0 0 0 1 -0.83331392
142 07.07.13 141 102.7 103.5031 -1 -1 -1 -1 -1 -1 -0.93133618
143 08.07.13 142 103.1 103.4494 1 0 0 0 0 0 -0.98726835
144 09.07.13 143 102.6 103.3363 0 1 0 0 0 0 -0.99858270
145 10.07.13 144 102.3 103.1984 0 0 1 0 0 0 -0.96476787
146 11.07.13 145 101.0 102.9057 0 0 0 1 0 0 -0.88735208
147 12.07.13 146 101.4 102.7053 0 0 0 0 1 0 -0.76983398
148 13.07.13 147 99.9 102.3318 0 0 0 0 0 1 -0.61752461
149 14.07.13 148 100.2 102.0480 -1 -1 -1 -1 -1 -1 -0.43730732
150 15.07.13 149 100.9 101.8952 1 0 0 0 0 0 -0.23732670
151 16.07.13 150 102.3 101.9491 0 1 0 0 0 0 -0.02662052