3. Following is a correlation matrix for 6 variables used to perform factor analysis using maximum likelihood method. X X 1.000 0.505 0.569 0.602 0.621 1.000 R = X 0.422 1.000 X4 0.467 0.926 1.000 X, 0.482 0.877 0.874 1.000 X6 0.603 0.450 0.878 0.878 0.937 1.000 Factor analysis result using correlation matrix shown above gives estimates for two rotation factor loadings. X X A = X 0.484 0.411 0.319 0.717 0.855 0.375 0.603 X4 0.519 X 0.861 X6 0.744 0.499 0.594 (a) Compute estimates for communalities and specific variance for each variables. (b) Determine proportion of variance explained by each factor. (c) Estimate correlation between first variable and other variables based on two factors given. Calculate residual resulted from actual correlation and correlation based on two factors.