非常高的残差平方和

Question

我遇到了拟合的平方残差和问题。残留物的平方和太高，这表明拟合不是很好。然而，从视觉上看，这具有非常高的剩余价值看起来很好......任何人都可以帮助我知道发生了什么事吗？

我的数据：

x=c(0.017359, 0.019206, 0.020619, 0.021022, 0.021793, 0.022366, 0.025691, 0.025780, 0.026355, 0.028858, 0.029766, 0.029967, 0.030241, 0.032216, 0.033657,
 0.036250, 0.039145, 0.040682, 0.042334, 0.043747, 0.044165, 0.044630, 0.046045, 0.048138, 0.050813, 0.050955, 0.051910, 0.053042, 0.054853, 0.056886,
0.058651, 0.059472, 0.063770,0.064567, 0.067415, 0.067802, 0.068995, 0.070742,0.073486, 0.074085 ,0.074452, 0.075224, 0.075853, 0.076192, 0.077002,
 0.078273, 0.079376, 0.083269, 0.085902, 0.087619, 0.089867, 0.092606, 0.095944, 0.096327, 0.097019, 0.098444, 0.098868, 0.098874, 0.102027, 0.103296,
 0.107682, 0.108392, 0.108719, 0.109184, 0.109623, 0.118844, 0.124023, 0.124244, 0.129600, 0.130892, 0.136721, 0.137456, 0.147343, 0.149027, 0.152818,
0.155706,0.157650, 0.161060, 0.162594, 0.162950, 0.165031, 0.165408, 0.166680, 0.167727, 0.172882, 0.173264, 0.174552,0.176073, 0.185649, 0.194492,
 0.196429, 0.200050, 0.208890, 0.209826, 0.213685, 0.219189, 0.221417, 0.222662, 0.230860, 0.234654, 0.235211, 0.241819, 0.247527, 0.251528, 0.253664,
 0.256740, 0.261723, 0.274585, 0.278340, 0.281521, 0.282332, 0.286166, 0.288103, 0.292959, 0.295201, 0.309456, 0.312158, 0.314132, 0.319906, 0.319924,
 0.322073, 0.325427, 0.328132, 0.333029, 0.334915, 0.342098, 0.345899, 0.345936, 0.350355, 0.355015, 0.355123, 0.356335, 0.364257, 0.371180, 0.375171,
0.377743, 0.383944, 0.388606, 0.390111, 0.395080, 0.398209, 0.409784, 0.410324, 0.424782 )


y= c(34843.40, 30362.66, 27991.80 ,28511.38, 28004.74, 27987.13, 22272.41, 23171.71, 23180.03, 20173.79, 19751.84, 20266.26, 20666.72, 18884.42, 17920.78, 15980.99, 14161.08, 13534.40, 12889.18, 12436.11,
12560.56, 12651.65, 12216.11, 11479.18, 10573.22, 10783.99, 10650.71, 10449.87, 10003.68,  9517.94,  9157.04,  9104.01,  8090.20,  8059.60,  7547.20,  7613.51,  7499.47,  7273.46,  6870.20,  6887.01,
6945.55,  6927.43,  6934.73,  6993.73,  6965.39,  6855.37,  6777.16,  6259.28,  5976.27,  5835.58,  5633.88,  5387.19,  5094.94,  5129.89,  5131.42,  5056.08,  5084.47,  5155.40,  4909.01,  4854.71,
4527.62,  4528.10,  4560.14,  4580.10,  4601.70,  3964.90,  3686.20,  3718.46,  3459.13,  3432.05,  3183.09,  3186.18,  2805.15,  2773.65,  2667.73,  2598.55,  2563.02,  2482.63,  2462.49,  2478.10,
2441.70,  2456.16,  2444.00,  2438.47,  2318.64,  2331.75,  2320.43,  2303.10,  2091.95,  1924.55, 1904.91,  1854.07,  1716.52,  1717.12,  1671.00,  1602.70,  1584.89,  1581.34,  1484.16,  1449.26,
1455.06,  1388.60,  1336.71,  1305.60,  1294.58,  1274.36,  1236.51,  1132.67,  1111.35,  1095.21,  1097.71,  1077.05,  1071.04,  1043.99,  1036.22,   950.26,   941.06,   936.37,   909.72,   916.45,
911.01, 898.94,   890.68,   870.99,   867.45,   837.39,   824.93,   830.61,   815.49,   799.77,   804.84,   804.88,   775.53,   751.95,   741.01,   735.86,   717.03,   704.57,   703.74,   690.63,
684.24,   650.30,   652.74,   612.95 )

然后使用nlsLM函数（minpack.lm包）进行拟合：

library(magicaxis)
library(minpack.lm)

sig.backg=3*10^(-3) 

mod <- nlsLM(y ~ a *( 1 + (x/b)^2 )^c+sig.backg,
             start = c(a = 0, b = 1, c = 0),
             trace = TRUE)

## plot data
magplot(x, y, main = "data", log = "xy", pch=16)
## plot fitted values
lines(x, fitted(mod), col = 2, lwd = 4 )

这个值是残留物：

> print(mod)
Nonlinear regression model
  model: y ~ a * (1 + (x/b)^2)^c + sig.backg
   data: parent.frame()
         a          b          c 
68504.2013     0.0122    -0.6324 
 residual sum-of-squares: 12641435

Number of iterations to convergence: 34 
Achieved convergence tolerance: 0.0000000149

平方和残差太高：12641435 ...

调整是这样还是有问题？这很糟糕？

Answer 1

这是有道理的，因为您的响应变量的平均值是38110960.如果您希望使用较小的数字，则可以扩展数据。

Answer 2

如果不知道平方的总和（可以从中计算R ^ 2），则残差平方和没有多大意义。如果您的数据具有较大的值，或者您添加了更多的数据点，无论您的拟合程度如何，它的值都会增加。此外，您可能希望查看残差与拟合数据的关系图，有一个明确的模式应该由您的模型解释，以确保您的错误是正常分布的。