1. (80 pt) Perform a factor analysis of the psychological prole data. This data set consists of 130 observations generated by scores on a psychological test administered to Peruvian teenagers (age 15,16 and 17). For each of these teenagers the gender (male=1, female=2) and socioeconomic status (low:1, medium:2) were also recorded. The scores were accu mulated into ve subscale scores labeled X1 (independence), X2(support), X3 (benevolence), X4(conformity) and X 5 (leadership). Use the sample correlation matrix R constructed from measurements on the five variables (X 1 to X5). (a) Obtain both the principal component and maximum likelihood solutions for m = 2 and m : 3 factors. (report the factor loadings, the communalities, the specific variance, the proportion of variance explained by each factor, the residual matrix. The MLE may result in a Heywood case) (40pt)