For a set of three mental ability tests in the Project Talent Dataset that was used in Chapter 16, a principal components analysis was obtained and all three components were retained. Selected results from this analysis appear below:
a. Show that you can reconstruct the communality for the variable mechanic from the loadings of mechanic on all three components in the component matrix above.
b. Show that you can reconstruct the eigenvalue or SSLs for the first component by using the loadings on Component 1 in the component matrix above.
c. If you had allowed SPSS to use the default method (retain only components with eigenvalues >1), how many components would have been retained?