Consrder the Boston Housing data which are available from library ( MASS ) Boston attach ( Boston ) In Lab 4 we used these data with the 11 variables shown in Table 6.3 of Chapter 6. (a) Use the split of the 11 variables as in Q3 of Lab 4. Repeat (or report if completed in the lab) the calculations shown in Example 6.6, that is, list the values of the strengths of the correlations and show the four CC score plots corresponding to (u.j,v,j) forj = 1,..., 4. (b) Calculate a PCA of the 35\"] data. Use the first 5dimensional PCdata instead if the original Xll] data, and the 3112] data of part (a). Calculate and list the values of the strengths of the correlations and show the four CC score plots arising from the PC data and Em. (C) Now use all variables of the Boston Housing data other than chaa and add the extra variables 211 and letat to the previous 3m] data to increase these to 6 dimensional data. Use the EU] data of part (a). Calculate and list the values of the strengths of the six correlations and show the six CC score plots arising from data and 3m]. (d) Compare the results of parts (a) (c) and comment on the differences and why they could occur. (e) Carry out a hypothesis test for the data described in part (c) using the statistic Tk of Lecture 5 and the values of the correlation strengths obtained in part (c). Calculate the pvalues for each statistic and report these pvalues , (f) Using a 2% significance level, make a decision regarding the number of nonzero correlation coefficients of the population model based on your results in part (e) and comment