### Code for Bootstrapping lecture

### uses the package 'boot'
library(boot)
help(boot)



###Bootstrap the slope of a regression line using code

###import the same data
datum=read.csv(file.choose()) ### use example data from lecture 36 (first bootstap lecture)

head(datum)
results=lm(Y~X,data=datum) ### Run the Regression
summary(results)
coef(results)[2] ### Extract the Slopes

SlopeTracker=rep(0,1000) #### Create a list to track the slope estimates
SlopeTracker

length(datum$X) ### Determine the size of the original dataset
x=(1:100) ### Create a list of numbers equal to the size of the 
# original dataset
x

Test=sample(x,100,replace=TRUE) ### resample from x with replacement
### Creates a list of new sammples to include
Test
datumBoot=datum[Test,] ###Creates the new dataset
datumBoot
resultsTest=lm(Y~X,data=datumBoot) #ReRun the regression with the new dataset
summary(resultsTest)
coef(resultsTest)[2] ### Extract the new slope

#### Now repeat the above 1000 times
set.seed(123)   #run this code to make sure results are always the same
for(i in 1:1000){
  Test=sample(x,100,replace=TRUE) ### resample from x with replacement
  datumBoot=datum[Test,] ###Creates the new dataset
  resultsTest=lm(Y~X,data=datumBoot) #ReRun the regression with the new dataset
  SlopeTracker[i]=coef(resultsTest)[2] ### Record new slope in SlopeTracker
}

SlopeTracker=sort(SlopeTracker) ### Sort the list of estimates
SlopeTracker[25] ###Lower Confidence Limit
SlopeTracker[975] ### Upper Confidence Limit

### Compare to confint from regression
confint(results)

#25th and 975th estimate were used because these give 95% C.I.


######Bootstrap the slope of a regression line using the 'boot function'
##########################################################################

### import the data
datum=read.csv(file.choose())

### Calculate results using standard parametric tests
results=lm(Y~X,data=datum)
summary(results)
confint(results)

# Create Function that calculates slope of bootstrapped sample
lmFunc=function(bootData,repeats){ ### requires bootstrapped data-matrix and vector of numbers
	results=lm(Y~X,bootData[repeats,]) ### run regression
	beta=coef(results)[2] ###extract slope (intercept is first coefficient)
	return(beta)
}

boot.results=boot(datum,lmFunc,R=1000)
boot.results
boot.ci(boot.results)

boot.results$t ### prints the vector of bootstrapped parameter values (not sorted)

### compare to parametric results
results