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• 在數(shù)據(jù)中所有點(diǎn)之間繪制一條線

• 計(jì)算每條線的斜率

• 中位數(shù)斜率是 回歸斜率

用這種方法計(jì)算斜率非?？煽俊．?dāng)誤差呈正態(tài)分布且沒(méi)有異常值時(shí),，斜率與OLS非常相似,。

有幾種獲取截距的方法。如果 關(guān)心回歸中的截距,，那么知道 軟件在做什么是很合理的,。 

當(dāng)我對(duì)異常值和異方差性有擔(dān)憂時(shí)，請(qǐng)?jiān)谏戏结槍?duì)Theil-Sen進(jìn)行簡(jiǎn)單線性回歸的評(píng)論 ,。

我進(jìn)行了一次 模擬,，以了解Theil-Sen如何在異方差下與OLS比較。它是更有效的估計(jì)器。

library(simglm)
library(ggplot2)
library(dplyr)
library(WRS)

# Hetero
nRep <- 100
n.s <- c(seq(50, 300, 50), 400, 550, 750, 1000)
samp.dat <- sample((1:(nRep*length(n.s))), 25)
lm.coefs.0 <- matrix(ncol = 3, nrow = nRep*length(n.s))
ts.coefs.0 <- matrix(ncol = 3, nrow = nRep*length(n.s))
lmt.coefs.0 <- matrix(ncol = 3, nrow = nRep*length(n.s))
dat.s <- list()



ggplot(dat.frms.0, aes(x = age, y = sim_data)) +
  geom_point(shape = 1, size = .5) +
  geom_smooth(method = "lm", se = FALSE) +
  facet_wrap(~ random.sample, nrow = 5) +
  labs(x = "Predictor", y = "Outcome",
       title = "Random sample of 25 datasets from 15000 datasets for simulation",
       subtitle = "Heteroscedastic relationships")

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ggplot(coefs.0, aes(x = n, colour = Estimator)) +
  geom_boxplot(
    aes(ymin = q025, lower = q25, middle = q50, upper = q75, ymax = q975), data = summarise(
      group_by(coefs.0, n, Estimator), q025 = quantile(Slope, .025),
      q25 = quantile(Slope, .25), q50 = quantile(Slope, .5),
      q75 = quantile(Slope, .75), q975 = quantile(Slope, .975)), stat = "identity") +
  geom_hline(yintercept = 2, linetype = 2) + scale_y_continuous(breaks = seq(1, 3, .05)) +
  labs(x = "Sample size", y = "Slope",
       title = "Estimation of regression slope in simple linear regression under heteroscedasticity",
       subtitle = "1500 replications - Population slope is 2",
       caption = paste(
         "Boxes are IQR, whiskers are middle 95% of slopes",
         "Both estimators are unbiased in the long run, however, OLS has higher variability",
         sep = "\n"
       ))