R语言多项式回归

fit2 <- lm(weight ~ height + I(height^2), data=women)

> fit2 <- lm(weight ~ height + I(height^2), data=women) 
> summary(fit2) 
 
Call: 
lm(formula=weight ~ height + I(height^2), data=women) 
Residuals: 
 Min 1Q Median 3Q Max 
-0.5094 -0.2961 -0.0094 0.2862 0.5971 
Coefficients: 
 Estimate Std. Error t value Pr(>|t|) 
(Intercept) 261.87818 25.19677 10.39 2.4e-07 *** 
Height -7.34832 0.77769 -9.45 6.6e-07 *** 
I(height^2) 0.08306 0.00598 13.89 9.3e-09 *** 
--- 
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
Residual standard error: 0.384 on 12 degrees of freedom 
Multiple R-squared: 0.999, Adjusted R-squared: 0.999 
F-statistic: 1.14e+04 on 2 and 12 DF, p-value: <2e-16 
> plot(women$height,women$weight, 
 xlab="Height (in inches)", 
 ylab="Weight (in lbs)") 
> lines(women$height,fitted(fit2))

新的预测等式为：

在p<0.001水平下，回归系数都非常显著。模型的方差解释率已经增加到了99.9%。二次项的 显著性（t=13.89，p<0.001）表明包含二次项提高了模型的拟合度。从图8-2也可以看出曲线确实 拟合得较好。