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library(simglm)library(ggplot2)library(dplyr)library(WRS)# HeteronRep <- 100n.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")

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"? ? ? ?))