r - 线性回归 r 比较多个观察值与单个观察值

Question

根据我的 question 的回答，我应该为以下 2 个模型获得相同的截距值和回归系数。但它们不一样。到底是怎么回事？

我的代码有问题吗？还是原来的答案错了？

#linear regression average qty per price point vs all quantities

x1=rnorm(30,20,1);y1=rep(3,30)
x2=rnorm(30,17,1.5);y2=rep(4,30)
x3=rnorm(30,12,2);y3=rep(4.5,30)
x4=rnorm(30,6,3);y4=rep(5.5,30)
x=c(x1,x2,x3,x4)
y=c(y1,y2,y3,y4)
plot(y,x)
cor(y,x)
fit=lm(x~y)
attributes(fit)
summary(fit)

xdum=c(20,17,12,6)
ydum=c(3,4,4.5,5.5)
plot(ydum,xdum)
cor(ydum,xdum)
fit1=lm(xdum~ydum)
attributes(fit1)
summary(fit1)


> summary(fit)

Call:
lm(formula = x ~ y)

Residuals:
    Min      1Q  Median      3Q     Max 
-8.3572 -1.6069 -0.1007  2.0222  6.4904 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  40.0952     1.1570   34.65   <2e-16 ***
y            -6.1932     0.2663  -23.25   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.63 on 118 degrees of freedom
Multiple R-squared:  0.8209,    Adjusted R-squared:  0.8194 
F-statistic: 540.8 on 1 and 118 DF,  p-value: < 2.2e-16

> summary(fit1)

Call:
lm(formula = xdum ~ ydum)

Residuals:
      1       2       3       4 
-0.9615  1.8077 -0.3077 -0.5385 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  38.2692     3.6456  10.497  0.00895 **
ydum         -5.7692     0.8391  -6.875  0.02051 * 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.513 on 2 degrees of freedom
Multiple R-squared:  0.9594,    Adjusted R-squared:  0.9391 
F-statistic: 47.27 on 1 and 2 DF,  p-value: 0.02051

Answer 1

您没有以可比较的方式计算 xdum 和 ydum，因为 rnorm 只会近似于您指定的平均值，尤其是当您仅抽样 30 例。然而，这很容易修复:

coef(fit)
#(Intercept)           y 
#  39.618472   -6.128739 

xdum <- c(mean(x1),mean(x2),mean(x3),mean(x4))
ydum <- c(mean(y1),mean(y2),mean(y3),mean(y4))
coef(lm(xdum~ydum))
#(Intercept)        ydum 
#  39.618472   -6.128739