8.13. In the radiotherapy data listed in Table 1.7 (see also the radiotherapy data on the website www.prenhall.com/statistics), the n = 98 observations on p = 6 variables rep- resent patients' reactions to radiotherapy. (a) Obtain the covariance and correlation matrices S and R for these data. (b) Pick one of the matrices S or R (justify your choice), and determine the eigenval- ues and eigenvectors. Prepare a table showing, in decreasing order of size, the per- cent that each eigenvalue contributes to the total sample variance. (c) Given the results in Part b, decide on the number of important sample principal components, Is it possible to summarize the radiotherapy data with a single reaction- index component? Explain. (d) Prepare a table of the correlation coefficients between each principal component you decide to retain and the original variables. If possible, interpret the components. 8.13. In the radiotherapy data listed in Table 1.7 (see also the radiotherapy data on the website www.prenhall.com/statistics), the n = 98 observations on p = 6 variables rep- resent patients' reactions to radiotherapy. (a) Obtain the covariance and correlation matrices S and R for these data. (b) Pick one of the matrices S or R (justify your choice), and determine the eigenval- ues and eigenvectors. Prepare a table showing, in decreasing order of size, the per- cent that each eigenvalue contributes to the total sample variance. (c) Given the results in Part b, decide on the number of important sample principal components, Is it possible to summarize the radiotherapy data with a single reaction- index component? Explain. (d) Prepare a table of the correlation coefficients between each principal component you decide to retain and the original variables. If possible, interpret the components