R语言lm()的多项式回归

fit2 <- lm(weight ~ hight + I(height^2), data = women)
summary(fit2)
展开/折叠结果
Call:
lm(formula = weight ~ height + I(height^2), data = women)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.50941 -0.29611 -0.00941  0.28615  0.59706 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 261.87818   25.19677  10.393 2.36e-07 ***
height       -7.34832    0.77769  -9.449 6.58e-07 ***
I(height^2)   0.08306    0.00598  13.891 9.32e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3841 on 12 degrees of freedom
Multiple R-squared:  0.9995,	Adjusted R-squared:  0.9994 
F-statistic: 1.139e+04 on 2 and 12 DF,  p-value: < 2.2e-16

$\hat{Weight}=261.88-7.35 \times Height+0.083\times Height^2$

模型的方差解释了99.95%的方差。所有项均小于0.001,达到极显著水平。I()的作用是把一个表达式当作一个独立的项。

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