R: Open/Closed Book Examination Data

scor {bootstrap} | R Documentation

## Open/Closed Book Examination Data

### Description

This is data form mardia, Kent and Bibby on 88 students who took examinations in 5 subjects. Some where with open book and other with closed book.

### Usage

    data(scor)

### Format

A data frame with 88 observations on the following 5 variables.

mec

  mechanics, closed book note

vec

  vectors, closed book note

alg

  algebra, open book note

ana

  analysis, open book note

sta

  statistics, open book note

### Details

The book uses this for bootstrap in principal component analysis.

### Source

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

### Examples

    str(scor)
    if(interactive())par(ask=TRUE)
    plot(scor)
    # The parameter of interest (theta) is the fraction of variance explained
    # by the first principal component.
    # For principal components analysis svd is better numerically than
    # eigen-decomposistion, but for bootstrapping the latter is _much_ faster.
    theta <- function(ind) {
       vals <- eigen(var(scor[ind,]), symmetric=TRUE, only.values=TRUE)$values
       vals[1] / sum(vals) }
    scor.boot <- bootstrap(1:88, 500, theta)
    sd(scor.boot$thetastar) # bootstrap standard error
    hist(scor.boot$thetastar)
    abline(v=theta(1:88), col="red2")
    abline(v=mean(scor.boot$thetastar), col="blue")

[Package bootstrap version 2019.6 Index]