Q.6. A sample of n = 151 NASCAR races from the 1970s were observed and the following variables were measured for each race: X1 = # of Drivers, X2 = Race Length (miles), X3 = # of Caution Flags (crashes), and X4 = # Lead Changes. The sample correlation matrix, its eigenvalues and eigenvectors are given below. > (R R.lam R.e round (R.lam,4) [1] 2.5092 0.8919 0.4185 0.1805 > round (R.e,4) [, 1] [,2] [,3] [,4] [1, ]-0.5595 0.3367 -0.2034 0.7295 [2,]-0.5662 0.1170 -0.5160 -0.6321 [3,]-0.2903 -0.9338 -0.1106 0.1775 [4, ]-0.5311 0.0311 0.8247 -0.1917 p.6.a. For the factor analytic model, with m = 1, compute estimates of L and I' based on the principal components method