#
#  Sýnidæmi í bootstrap, tekið úr quick-boot og endurbætt.
#

# Bootstrap 95% CI for R-Squared
library(boot)
# function to obtain R-Squared from the data
rsq <- function(formula, data, indices) {
  d <- data[indices,] # allows boot to select sample
  fit <- lm(formula, data=d)
  return(summary(fit)$r.square)
}
# bootstrapping with 1000 replications
results <- boot(data=mtcars, statistic=rsq,
   R=1000, formula=mpg~wt+disp)

# view results
results
plot(results)

# get 95% confidence interval 

boot.ci(results,type="bca")

#
# Ber saman við CI með Fisher-transformation
#
nn=nrow(mtcars)
r0=(summary(lm(mpg~wt+disp,data=mtcars))$r.square)^0.5
tanh(atanh(r0)-1.96*1/sqrt(nn-3))^2
tanh(atanh(r0)+1.96*1/sqrt(nn-3))^2


#
# Regression-dæmi
#

bs <- function(formula, data, indices) {
  d <- data[indices,] # allows boot to select sample
  fit <- lm(formula, data=d)
  return(coef(fit))
} 


# bootstrapping with 1000 replications
results <- boot(data=mtcars, statistic=bs,
   R=1000, formula=mpg~wt+disp)

# view results
results
plot(results, index=1) # intercept
plot(results, index=2) # wt
plot(results, index=3) # disp

# get 95% confidence intervals
boot.ci(results, type="bca", index=1) # intercept
boot.ci(results, type="bca", index=2) # wt
boot.ci(results, type="bca", index=3) # disp

#
# Ber saman við venjulega regression
#
summary(lm(mpg~wt+disp,data=mtcars))