1 Consider the correlations among children's test scores shown in Table 6.1. An approximate solution to the factor analysis equations gives 0.95 0.89 A = 0.83 0.77 0.71 0.65 (Note that this approximate solution was obtained by following Spearman's beliefs. The elements in this factor loading matrix are equally spaced between 0.95 and 0.65.) a For the loading matrix given, what is the matrix of reproduced correla- tions? b What is the matrix of residual differences between the original correla- tion matrix and those reproduced by this one-factor solution? c Determine the communalities of each of the original variables. d What are the specific variances for each of the original variables? e Use a statistical computing package on the sample correlation matrix to find a one-factor solution to the factor analysis equations using the principal factor method. Use prior communality estimates equal to the squared multiple correlation of each variable with all of the remaining variables. How do the factor loadings in your solution compare to the ones given above