我正在使用R来拟合线性回归模型，然后我使用此模型来预测值，但它不能很好地预测边界值。你知道怎么解决吗？
ZLFPS是：
ZLFPS<-c(27.06,25.31,24.1,23.34,22.35,21.66,21.23,21.02,20.77,20.11,20.07,19.7,19.64,19.08,18.77,18.44,18.24,18.02,17.61,17.58,16.98,19.43,18.29,17.35,16.57,15.98,15.5,15.33,14.87,14.84,14.46,14.25,14.17,14.09,13.82,13.77,13.76,13.71,13.35,13.34,13.14,13.05,25.11,23.49,22.51,21.53,20.53,19.61,19.17,18.72,18.08,17.95,17.77,17.74,17.7,17.62,17.45,17.17,17.06,16.9,16.68,16.65,16.25,19.49,18.17,17.17,16.35,15.68,15.07,14.53,14.01,13.6,13.18,13.11,12.97,12.96,12.95,12.94,12.9,12.84,12.83,12.79,12.7,12.68,27.41,25.39,23.98,22.71,21.39,20.76,19.74,19.49,19.12,18.67,18.35,18.15,17.84,17.67,17.65,17.48,17.44,17.05,16.72,16.46,16.13,23.07,21.33,20.09,18.96,17.74,17.16,16.43,15.78,15.27,15.06,14.75,14.69,14.69,14.6,14.55,14.53,14.5,14.25,14.23,14.07,14.05,29.89,27.18,25.75,24.23,23.23,21.94,21.32,20.69,20.35,19.62,19.49,19.45,19,18.86,18.82,18.19,18.06,17.93,17.56,17.48,17.11,23.66,21.65,19.99,18.52,17.22,16.29,15.53,14.95,14.32,14.04,13.85,13.82,13.72,13.64,13.5,13.5,13.43,13.39,13.28,13.25,13.21,26.32,24.97,23.27,22.86,21.12,20.74,20.4,19.93,19.71,19.35,19.25,18.99,18.99,18.88,18.84,18.53,18.29,18.27,17.93,17.79,17.34,20.83,19.76,18.62,17.38,16.66,15.79,15.51,15.11,14.84,14.69,14.64,14.55,14.44,14.29,14.23,14.19,14.17,14.03,13.91,13.8,13.58,32.91,30.21,28.17,25.99,24.38,23.23,22.55,20.74,20.35,19.75,19.28,19.15,18.25,18.2,18.12,17.89,17.68,17.33,17.23,17.07,16.78,25.9,23.56,21.39,20.11,18.66,17.3,16.76,16.07,15.52,15.07,14.6,14.29,14.12,13.95,13.89,13.66,13.63,13.42,13.28,13.27,13.13,24.21,22.89,21.17,20.06,19.1,18.44,17.68,17.18,16.74,16.07,15.93,15.5,15.41,15.11,14.84,14.74,14.68,14.37,14.29,14.29,14.27,18.97,17.59,16.05,15.49,14.51,13.91,13.45,12.81,12.6,12,11.98,11.6,11.42,11.33,11.27,11.13,11.12,11.11,10.92,10.87,10.87,28.61,26.4,24.22,23.04,21.8,20.71,20.47,19.76,19.38,19.18,18.55,17.99,17.95,17.74,17.62,17.47,17.25,16.63,16.54,16.39,16.12,21.98,20.32,19.49,18.2,17.1,16.47,15.87,15.37,14.89,14.52,14.37,13.96,13.95,13.72,13.54,13.41,13.39,13.24,13.07,12.96,12.95,27.6,25.68,24.56,23.52,22.41,21.69,20.88,20.35,20.26,19.66,19.19,19.13,19.11,18.89,18.53,18.13,17.67,17.3,17.26,17.26,16.71,19.13,17.76,17.01,16.18,15.43,14.8,14.42,14,13.8,13.67,13.33,13.23,12.86,12.85,12.82,12.75,12.61,12.59,12.59,12.45,12.32)
QPZL<-c(36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16)
ZLDBFSAO<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2)
我的模特是：
fit32=lm(log(ZLFPS) ~ poly(QPZL,2,raw=T) + ZLDBFSAO)
results3 <- coef(summary(fit32))
first3<-as.numeric(results3[1])
second3<-as.numeric(results3[2])
third3<-as.numeric(results3[3])
fourth3<-as.numeric(results3[4])
fifth3<-as.numeric(results3[5])
#inverse model used for prediction of FPS
f1 <- function(x) {first3 +second3*x +third3*x^2 + fourth3*1}
您可以看到我的数据集here。此数据集包含我必须预测的值。每个QP的FPS变化是异质的。见数据集。我添加了一个新专栏。 拟合的数据集是不同的。
要测试模型，只需编写exp(f1(selected_QP))，其中选定的QP从16到36不等。请参阅给定的QP值数据集和模型应预测的FPS值。
您可以在线here运行模型。
当我在中间使用QP值时，假设在23到32之间，模型很好地预测了FPS值。否则，预测的误差值很大。