顯着的二次項 - 線性迴歸 - R的

Question

我給出以下數據：

有人告訴我先適應二次模型。

> time = c(10,20,15,11,11,19,11,13,17,18,16,16,17,18,10) 
> experience = c(24,1,10,15,17,3,20,9,3,1,7,9,7,5,20) 
> fit = lm (time ~ experience + I(experience^2)) 
> summary(fit) 

Call: 
lm(formula = y ~ x + I(x^2)) 

Residuals: 
    Min  1Q Median  3Q  Max 
-1.8287 -0.8300 0.5054 0.7476 1.1713 

Coefficients: 
      Estimate Std. Error t value Pr(>|t|)  
(Intercept) 20.091108 0.724705 27.723 3e-12 *** 
x   -0.670522 0.154706 -4.334 0.000972 *** 
I(x^2)  0.009535 0.006326 1.507 0.157605  
--- 
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.091 on 12 degrees of freedom 
Multiple R-squared: 0.9162, Adjusted R-squared: 0.9022 
F-statistic: 65.59 on 2 and 12 DF, p-value: 3.465e-07 

一切似乎罰款在那裏。

我的模型是

y = 20.091-.671x+.0095x^2 

繪製它：

> x = seq(0,25, by = .1) 
> y = fit$coefficient[1]+fit$coefficient[2]*x+fit$coefficient[3]*x^2 
> lines(x,y) 

再次，一切似乎都很好。

但後來我被告知測試二次項在a = .1顯着性水平上是否顯着。

所以我做

> fit1 = lm (time ~ experience + I(experience^2)) 
> fit2 = lm(time~experience) 
> anova(fit2, fit1) 

Analysis of Variance Table 

Model 1: time ~ experience 
Model 2: time ~ experience + I(experience^2) 
    Res.Df RSS Df Sum of Sq  F Pr(>F) 
1  13 16.984       
2  12 14.280 1 2.7037 2.2719 0.1576 

所以對於二次項我的F值是2.27。對應於.1576的概率。因此，二次項在a = 0.112時顯着，但我的教授指出我們應該找到二次項對於我們的模型來說是微不足道的。我在這裏做錯了什麼？

Answer 1

你無法做的是構造正交多項式項。 R中的poly（）函數是爲此目的而設計的。

time = c(10,20,15,11,11,19,11,13,17,18,16,16,17,18,10) 
experience = c(24,1,10,15,17,3,20,9,3,1,7,9,7,5,20) 
fit = lm (time ~ poly(experience, degree=2)) 
summary(fit) 
#-------------- 
Call: 
lm(formula = time ~ poly(experience, degree = 2)) 

Residuals: 
    Min  1Q Median  3Q  Max 
-1.8287 -0.8300 0.5054 0.7476 1.1713 

Coefficients: 
           Estimate Std. Error t value Pr(>|t|)  
(Intercept)     14.8000  0.2817 52.544 1.48e-15 *** 
poly(experience, degree = 2)1 -12.3861  1.0909 -11.354 8.94e-08 *** 
poly(experience, degree = 2)2 1.6443  1.0909 1.507 0.158  
--- 
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.091 on 12 degrees of freedom 
Multiple R-squared: 0.9162, Adjusted R-squared: 0.9022 
F-statistic: 65.59 on 2 and 12 DF, p-value: 3.465e-07 

您的F統計量不是特定於二次項，而是真正將零模型與兩個項模型進行比較。