我试图在R中使用b样条来找到函数的系数。然而，结果有些奇怪。我用R输出系数来找到y-hat，然后是平方误差，这太离谱了。我不知道我的计算出了什么问题，也不知道我在代码中遗漏了什么。
这是我的数据(有1000个观测结果(：
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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这是我在25、40和60 时使用结的函数
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
然后我计算了y-hat和sqd误差
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
这是我得到的(部分原因是它是一个大数据集，你知道的(
[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
您的预测函数不使用与拟合函数相同的基，您只是使用多项式基。您应该在R中使用predict()函数，例如
fit <- lm(wage ~ bs(age, knots = c(25, 40, 60)), data = salary)
predict(fit)
如果你想在新的年龄进行预测，请使用
predict(fit, newdata = data.frame(age = 50:60))