The accompanying table reports data on percentages of sand, silt, and clay at 20 sites. [The data are from Nielsen, Biggar, and Erh (1973), as presented by Andrews and Herzberg XXXXXXXXXXThe depths 1,...

The accompanying table reports data on percentages of sand, silt, and clay at 20 sites. [The data are from Nielsen, Biggar, and Erh (1973), as presented by Andrews and Herzberg (1985). The depths 1, 2, and 3 correspond to depths 1, 6, and 12 in Andrews and Herzberg.] Use sand, silt, and clay percentages at the three depths as nine columns

(a) From the nature of the variables, is there any reason to expect a collinearity problem if these nine variables were to be used as independent variables in multiple regression analysis?

(b) Center and scale the variables and do a singular value decomposition on Z. Does the SVD indicate the presence of a collinearity problem? Would you have obtained the same results if the variables had not been centered and the intercept included? Explain.