Shape of confidence interval for predicted values in linear regression

bootstrap_linear_mod

# based on https://stats.stackexchange.com/q/85560/7482
if (!require("pacman")) install.packages("pacman")
pacman::p_load(dplyr, ggplot2)

boot_dat <- lapply(1:1000, function(i){
    inds <- sample.int(nrow(mtcars), replace = TRUE)
    lm(mpg ~ hp, data = mtcars[inds, c('mpg', 'hp')])
}) %>%
    lapply(function(x) setNames(as.data.frame(t(c(x$coeff))), c('intercept', 'slope'))) %>%
    bind_rows() %>%
    mutate(id = as.character(seq_len(n()))) %>%
    tbl_df()

ggplot(data = mtcars, aes(hp, mpg)) +
    geom_abline(data = boot_dat, aes(slope = slope, intercept = intercept, group = id), 
        color = 'grey60', alpha = .1) +
    geom_point() +
    geom_smooth(method = 'lm', color = 'red', fill = 'orange', alpha = .1) +
    theme_minimal()