Perform a factor analysis on the U.S. crime date set (X3 - X9) posted at "Assign3" folder. (a) Obtain the estimated factor loadings, communalities, and specific variances for m = 3 common factors, after varimax rotation, by maximum likelihood method. (b) Conduct a test of H0 : S = LL0+ ? versus H1 : S 6= LL0+ ? for m = 3 at a = 0.05 level. (c) Interpret three factors. (d) Estimate the factor scores by the regression methods. Plot each pair of factor scores - indicate each region (Northeast, Midwest, South, and West) by different colors or symbols and provides labels for each states. What do these plots reveal?