01-bootstrap.Rmd

# Bootstrap

```{r}
library(tidyverse)
df <- carData::Salaries
```

## Simple Linear Regression
```{r}
# set number of bootstraps
n_bootstrap <- 1000

# create empty dataframes for coefficients and r-squared
bootstrap_coef <- tibble(n_iter = NA,
                         .rows = n_bootstrap)
bootstrap_rsq <- tibble(n_iter = NA,
                         .rows = n_bootstrap)

# for loop for bootstrap
for (i in 1:n_bootstrap) {
  
  # randomly sample with replacement from the rows
  idx <- sample(1:nrow(df), nrow(df), replace = T)
  df_boot <- df[idx,]
  
  # run linear model
  model <- lm(salary ~ yrs.since.phd + yrs.service, df_boot)
  
  # extract estimates and r^2 value
  summary_model <- summary(model)
  t_stat <- summary_model$coefficients[, "t value"]
  df_denom <- summary_model$df[[2]]
  r_sq <- t_stat^2 / (t_stat^2 + df_denom)
  
  # write bootstrap iteration
  bootstrap_coef[i, 1] <- i
  bootstrap_rsq[i, 1] <- i
  
  # determine number of coefficients
  n_coef <- length(model$coefficients)
  
  # write estimate and r^2 to table for looping across variables
  for (j in 1:n_coef) {
    
    # bootstrap estimate confidence interval
    bootstrap_coef[i, names(model$coefficients[j])] <- model$coefficients[[j]]
    
    # bootstrap R^2 CI
    bootstrap_rsq[i, names(model$coefficients[j])] <- r_sq[j]
  }
}

# print estimate CI and R^2 CI for each variable
for (k in 2:n_coef+1) {
  
  # estimate CI
  cat("\n", colnames(bootstrap_coef[,k]), "\n")
  cat("\n estimate CI\n")
  bootstrap_ci <- quantile(as.matrix(bootstrap_coef[,k]), probs = c(0.025, .975))
  print(bootstrap_ci)
  
  # R^2 CI
  cat("\n R^2 CI\n")
  bootstrap_rsq_ci <- quantile(as.matrix(bootstrap_rsq[,k]), probs = c(0.025, .975))
  print(bootstrap_rsq_ci)
}

```