Я пытаюсь найти коэффициенты функции, используя b-сплайн в R. Однако есть кое-что странное с результатом. Я использовал выходные коэффициенты R, чтобы найти y-шляпу, а затем квадратную ошибку, и это далеко. Я не знаю, что пошло не так с моими вычислениями и / или что я упустил в своем коде.
Вот мои данные (есть 1000 наблюдений):
structure(list(age = c(18, 24, 45, 43, 50, 54, 44, 30, 41, 52,
45, 34, 35, 39, 54, 51, 37, 50, 56, 37, 38, 40, 75, 40, 38, 49,
43, 34, 57, 18, 55, 51, 33, 34, 36, 56, 70, 25, 32, 27, 28, 27,
43, 50, 39, 52, 35, 57, 25, 33, 57, 71, 43, 23, 30, 22, 59, 28,
61, 34, 43, 54, 69, 41, 48, 49, 42, 37, 55, 21, 58, 31, 25, 32,
40, 44, 60, 23, 63, 44, 47, 61, 55, 24, 42, 25, 34, 53, 53, 70,
47, 46, 33, 34, 22, 74, 40, 45, 43, 33, 62, 37, 54, 34, 50, 46,
41, 63, 38, 35, 29, 66, 37, 39, 42, 51, 55, 51, 38, 49, 42, 43,
38, 59, 57, 25, 49, 41, 38, 61, 49, 52, 43, 60, 46, 21, 61, 32,
58, 35, 26, 32, 37, 22, 51, 44, 35, 60, 40, 35, 35, 47, 43, 33,
60, 38, 53, 55, 57, 64, 43, 35, 54, 45, 58, 48, 46, 46, 55, 51,
49, 34, 53, 40, 50, 37, 39, 52, 50, 48, 47, 27, 39, 44, 37, 52,
26, 39, 25, 31, 58, 30, 27, 40, 55, 35, 48, 29, 25, 40, 27, 44,
49, 22, 45, 33, 63, 49, 39, 25, 29, 37, 35, 46, 58, 39, 41, 29,
37, 62, 27, 37, 56, 36, 23, 46, 26, 43, 36, 54, 62, 40, 53, 48,
23, 34, 43, 55, 59, 60, 49, 45, 31, 34, 26, 22, 40, 41, 36, 38,
48, 47, 47, 35, 49, 40, 32, 57, 56, 73, 29, 49, 30, 29, 36, 39,
48, 45, 50, 42, 58, 48, 48, 45, 41, 27, 44, 32, 46, 52, 22, 53,
34, 38, 42, 25, 29, 28, 46, 55, 56, 41, 61, 47, 52, 27, 33, 58,
27, 52, 45, 22, 25, 25, 41, 54, 23, 36, 31, 52, 46, 45, 40, 33,
42, 41, 25, 24, 24, 51, 41, 42, 30, 55, 23, 60, 40, 41, 80, 53,
40, 35, 55, 24, 39, 30, 68, 54, 27, 34, 53, 48, 59, 30, 45, 39,
45, 43, 30, 57, 53, 42, 23, 58, 43, 33, 56, 37, 41, 33, 50, 43,
53, 37, 20, 26, 29, 57, 47, 54, 38, 23, 31, 43, 33, 48, 33, 52,
30, 44, 38, 51, 47, 28, 52, 23, 65, 27, 33, 49, 27, 48, 38, 58,
40, 46, 53, 25, 42, 40, 35, 50, 34, 48, 49, 41, 37, 58, 28, 33,
50, 38, 48, 30, 49, 44, 50, 58, 45, 44, 35, 59, 45, 51, 61, 45,
34, 33, 45, 50, 50, 39, 26, 49, 20, 31, 49, 56, 61, 56, 51, 42,
45, 30, 48, 33, 50, 31, 48, 35, 47, 45, 52, 46, 47, 49, 36, 51,
46, 37, 23, 43, 34, 58, 44, 61, 40, 37, 33, 38, 41, 30, 51, 39,
56, 44, 51, 35, 27, 47, 51, 41, 63, 61, 46, 33, 35, 28, 50, 41,
23, 45, 63, 59, 30, 30, 45, 42, 57, 52, 54, 30, 47, 38, 47, 39,
50, 47, 45, 44, 52, 42, 18, 56, 50, 50, 53, 38, 27, 56, 50, 56,
50, 49, 42, 50, 53, 28, 45, 24, 25, 38, 47, 38, 33, 39, 52, 46,
42, 61, 32, 42, 61, 27, 45, 58, 25, 34, 44, 40, 51, 50, 64, 54,
42, 31, 25, 32, 51, 75, 28, 28, 32, 53, 36, 43, 51, 35, 46, 38,
43, 39, 37, 59, 33, 23, 37, 40, 25, 27, 47, 52, 23, 33, 37, 34,
51, 40, 50, 64, 54, 50, 32, 37, 19, 32, 42, 26, 46, 18, 43, 62,
44, 40, 43, 32, 48, 35, 61, 47, 55, 28, 52, 27, 22, 20, 42, 29,
31, 59, 36, 32, 32, 25, 43, 44, 57, 49, 41, 38, 58, 59, 39, 60,
56, 44, 70, 27, 47, 41, 29, 42, 51, 47, 48, 39, 23, 31, 59, 19,
42, 35, 38, 45, 58, 26, 30, 54, 38, 44, 52, 73, 65, 28, 53, 53,
52, 27, 57, 32, 51, 43, 50, 53, 54, 24, 40, 30, 45, 55, 45, 44,
37, 41, 44, 52, 55, 43, 27, 43, 46, 30, 43, 48, 33, 29, 24, 52,
50, 24, 42, 53, 49, 46, 40, 41, 41, 36, 34, 24, 44, 33, 25, 40,
48, 56, 25, 44, 27, 58, 52, 60, 39, 51, 31, 45, 43, 45, 40, 46,
51, 47, 52, 31, 40, 26, 49, 38, 50, 63, 35, 29, 33, 29, 62, 45,
56, 58, 39, 49, 24, 61, 58, 47, 41, 71, 47, 38, 31, 56, 44, 33,
36, 31, 55, 48, 50, 42, 25, 55, 28, 30, 46, 48, 42, 23, 60, 34,
45, 28, 33, 58, 47, 24, 56, 56, 23, 56, 45, 58, 30, 46, 48, 50,
43, 37, 49, 31, 54, 52, 70, 30, 44, 34, 38, 28, 38, 39, 52, 34,
33, 45, 58, 38, 63, 38, 31, 53, 21, 38, 18, 28, 33, 32, 29, 28,
42, 28, 36, 47, 53, 48, 36, 55, 37, 68, 65, 37, 33, 19, 50, 22,
40, 45, 36, 37, 24, 66, 35, 33, 44, 48, 47, 41, 55, 74, 33, 62,
56, 29, 56, 47, 45, 44, 25, 45, 40, 56, 56, 47, 39, 38, 48, 44,
42, 55, 61, 39, 30, 49, 33, 31, 35, 55, 36, 37, 33, 48, 47, 60,
28, 28, 48, 29, 40, 32, 33, 40, 42, 36, 39, 44, 43, 44, 29, 49,
47, 46, 41, 52, 43, 38, 42, 56, 39, 29, 33, 33, 41, 44, 45, 58,
29, 42, 68, 47, 30, 39, 42, 49, 36, 44, 54, 42, 39, 30, 33, 28,
38, 30, 25, 52, 26, 54, 62, 57, 32, 60, 40, 49, 54, 48, 35, 46,
42, 58, 30, 27, 55, 50, 55, 40, 32, 27, 49, 50, 50, 44, 57, 72,
23, 31, 36, 63, 48, 46, 55, 44, 44, 32, 60, 42, 48, 36, 31, 54,
29, 46, 35, 50, 25, 33, 34, 51, 33, 59, 62, 28, 40, 52), wage = c(75.0431540173515,
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95.2307125669819, 87.9810327856054, 64.2743972206327, 128.680488220624,
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128.680488220624, 70.4760196469445, 76.8936025176112, 148.413159102577,
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111.720849360989, 103.90247060316, 118.884359339886, 151.591484239814,
101.82435207568, 99.6894636984864, 99.6894636984864, 99.6894636984864,
94.0727147457005, 152.216806827106, 104.921506533664, 65.1108537153447,
95.2307125669819, 173.879493310012, 193.411070530969, 114.475713290347,
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127.115743812184, 118.884359339886, 34.6074177301288, 114.475713290347,
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73.7757432746946, 130.982177377461, 75.0431540173515, 154.990260276812,
104.921506533664, 73.118306923864, 123.089699847943, 157.700527725737,
81.2832532842527, 107.256062128429, 78.9816745162994, 73.7757432746946,
94.0727147457005, 99.6894636984864, 176.989650489877, 73.7757432746946,
99.6894636984864, 94.0727147457005, 95.2307125669819, 127.115743812184,
99.6894636984864, 95.6888119067371, 109.833985642199, 118.884359339886,
176.989650489877, 61.1875264339915, 81.2832532842527, 256.400649562425,
81.2832532842527, 81.2832532842527, 55.7673905084923, 75.3556793180091,
130.982177377461, 43.7351116779821, 114.475713290347, 114.475713290347,
81.2832532842527, 68.5721657022738, 109.833985642199, 97.4932940453934,
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118.884359339886, 65.1108537153447, 109.833985642199, 104.921506533664,
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75.3556793180091, 104.921506533664, 95.2307125669819, 54.5981500331442,
89.2428846644714, 145.143601176911, 96.8667032433329, 130.982177377461,
84.0459576539924, 148.155046727428, 49.5553381215226, 141.77517233318,
115.375038556391, 65.1108537153447, 85.3839403789827, 101.82435207568,
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109.833985642199, 127.115743812184, 115.375038556391, 59.0970640815891,
76.8936025176112, 141.77517233318, 70.9095858696657, 200.543262324662,
97.4932940453934, 99.6894636984864, 186.876677628007, 81.2832532842527,
160.642475408263, 63.9666908300607, 87.9810327856054, 73.7757432746946,
145.143601176911, 141.77517233318, 76.8936025176112, 123.908567597957,
118.884359339886, 279.1974969917, 54.5981500331442, 154.68529299563,
180.030197076236, 118.884359339886, 87.9810327856054, 91.6992261117042,
59.0970640815891, 123.908567597957, 109.833985642199, 94.0727147457005,
117.146816914805, 65.1108537153447, 97.4932940453934, 118.019753340006,
141.77517233318, 116.176695171054, 75.3556793180091, 95.2307125669819,
111.720849360989, 103.90247060316, 147.116689159978, 87.9810327856054,
118.884359339886, 100.764272842107, 120.589436530402, 193.866878146586,
118.884359339886, 267.901086855275, 174.402876012275, 133.971500070695,
154.68529299563, 154.68529299563, 118.884359339886, 95.2307125669819,
109.833985642199, 111.720849360989, 134.705375118879, 85.9010443226556,
118.884359339886, 87.9810327856054, 92.8958447894966, 109.833985642199,
124.720446242886, 127.901232979118, 97.4932940453934, 198.350290464385,
92.8958447894966, 94.0727147457005, 148.413159102577, 79.8549003093467,
118.884359339886, 87.9810327856054, 94.0727147457005, 150.070476909424,
176.989650489877, 73.7757432746946, 125.12381572196, 277.79948020565,
107.903923866876, 60.7397785177603, 92.0363233010764, 109.833985642199,
66.9616443217359, 114.475713290347, 170.6951277113, 130.982177377461,
127.115743812184, 117.146816914805, 123.089699847943, 120.589436530402,
130.982177377461, 81.2832532842527, 36.6737041960799, 104.921506533664,
74.412963512917, 129.067820506745, 84.1000101164483, 185.918662879754,
105.927810775063, 163.515863976238, 63.1888610037461, 134.705375118879,
120.926701544426, 94.0727147457005, 132.487821126123, 133.232350826567,
145.143601176911, 118.884359339886, 150.330653495766, 278.964466695847,
98.2692308087927, 99.6894636984864, 94.0727147457005, 176.989650489877,
166.324941233877, 94.0727147457005, 139.703071527658, 78.3924668009837,
141.775856466307, 116.265324062503, 148.413159102577, 87.9810327856054,
90.4819133566401, 141.77517233318, 63.0927167348386, 65.1108537153447,
151.591484239814, 123.089699847943, 118.884359339886, 79.8549003093467,
104.004959912222, 55.5361044177385, 99.6894636984864, 99.6894636984864,
193.452606894109, 102.870246933215, 164.646988930328, 69.6190369046763,
99.6894636984864, 114.475713290347, 99.6894636984864, 95.2307125669819,
82.6796372966372, 116.943081320617, 54.5981500331442, 138.299126920883,
130.982177377461, 281.745970551857, 163.515863976238, 179.214858036271,
126.323880709786, 70.4760196469445, 118.019753340006, 71.3196387942183,
114.475713290347, 138.299126920883, 54.5981500331442, 94.0727147457005,
80.4302079458208, 89.2428846644714, 117.146816914805, 127.115743812184,
81.2832532842527, 52.4070640482002, 99.6894636984864, 63.1888610037461,
196.125272594255, 101.82435207568, 107.903923866876, 51.2396549228382,
99.6894636984864, 63.1888610037461, 148.413159102577, 99.6894636984864,
130.982177377461, 101.82435207568, 99.6894636984864, 79.8549003093467,
160.642475408263, 134.705375118879, 160.642475408263, 91.6992261117042,
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127.115743812184, 87.9810327856054, 144.47808766541, 160.409701962289,
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109.833985642199, 81.698421724729, 114.475713290347, 142.634472767972,
160.642475408263, 94.0727147457005, 54.5981500331442, 73.7757432746946,
160.642475408263, 148.413159102577, 87.9823064294987, 101.82435207568,
111.720849360989, 106.921814091211, 126.323880709786, 109.833985642199,
92.8958447894966, 54.5981500331442, 96.3706528322308, 114.475713290347,
94.0727147457005, 95.2307125669819, 139.00340805947, 81.2832532842527,
94.0727147457005, 87.9810327856054, 138.299126920883)), row.names = c(NA,
-1000L), class = c("tbl_df", "tbl", "data.frame"))
Вот моя функция использует узлы на 25,40 и 60
Call:
lm(formula = wage ~ bs(age, knots = c(25, 40, 60)), data = salary)
Coefficients:
(Intercept) bs(age, knots = c(25, 40, 60))1
56.423 8.631
bs(age, knots = c(25, 40, 60))2 bs(age, knots = c(25, 40, 60))3
46.314 69.927
bs(age, knots = c(25, 40, 60))4 bs(age, knots = c(25, 40, 60))5
65.584 29.341
bs(age, knots = c(25, 40, 60))6
27.058
Затем я вычислил ошибку y-hat и sqd
y_hat = (56.423+8.631*salary$age+46.314*(salary$age)^2+69.927*(salary$age)^3+65.584*(salary$age-25)^3+29.341*(salary$age-40)^3+27.058*(salary$age-60)^3)
sqd_error = (salary$wage - y_hat)^2
sqd_error
Вот что я получил (часть этого, так как это большой набор данных, у вас есть идея)
[1] 3.673488e+12 1.514171e+11 4.765440e+13 3.476206e+13 9.769555e+13
[6] 1.643685e+14 4.079991e+13 1.388170e+12 2.480692e+13 1.273657e+14
[11] 4.765459e+13 5.607993e+12 7.259031e+12 1.720632e+13 1.643683e+14
[16] 1.116993e+14 1.148553e+13 9.769283e+13 2.101982e+14 1.148543e+13
[21] 1.413636e+13 2.074496e+13 1.545190e+15 2.074396e+13 1.413716e+13
[26] 8.519755e+13 3.476289e+13 5.608069e+12 2.369560e+14 3.673471e+12
[31] 1.860756e+14 1.116990e+14 4.221360e+12 5.607848e+12 9.206242e+12
[36] 2.101994e+14 9.615010e+14 1.888253e+10 3.071311e+12 1.399047e+11
[41] 4.045521e+11 1.398721e+11 3.476335e+13 9.769558e+13 1.720677e+13
[46] 1.273651e+14 7.258070e+12 2.369541e+14 1.887217e+10 4.221217e+12