Efron and Tibshirani discuss the scor (bootstrap) test score data on 88 students who took…

Question One [20 points, Rizzo 7.6] Efron and Tibshirani discuss the scor (bootstrap) test score data on 88

students who took examinations in five subjects [84, Table 7.1], [188, Table 1.2.1]. The first two tests (mechanics,

vectors) were closed book and the last three tests (algebra, analysis, statistics) were open book. Each row of the

data frame is a set of scores (xi1, …, xi5 ) for the ith student. Use a panel display to display the scatter plots for each

pair of test scores. Compare the plot with the sample correlation matrix. Then obtain bootstrap estimates of the

standard errors for each of the following estimates:

??????? = ???(??????, ??????), ??????? = ???(??????, ??????) ,??????? = ???(??????, ??????), ??????? = ???(??????, ??????)

Question Two [40 points, Rizzo 7.7] Refer to the previous question. Efron and Tibshirani discuss the following

example [84,Ch. 7]. The five-dimensional scores data have a 5×5 covariance matrix ?? with positive eigenvalues

??? > ??? . . > ???. In principal components analysis,

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