# Question: For a set of three mental ability tests in the

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?

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?

**View Solution:**## Answer to relevant Questions

Give an example of a specific sampling strategy that would yield a random sample of 50 households from the population of 2,000 households in that particular town. You may assume that the telephone directory for the town ...Using the data in Table 16.1, the Project Talent test score data: a. What kinds of preliminary data screening would you need to run to evaluate whether assumptions for factor analysis are reasonably well met? Run these ...Three different methods were presented for the computation of scale scores: summing raw scores on the X variables, summing z scores on the X variables, and saving factor scores from a FA of a set of X variables. (Assume that ...One way to interpret a reliability coefficient (often an r value) is as the proportion of variance in X scores that is stable across occasions of measurement. Why do we interpret r (rather than r2) as the proportion of ...What is the compound symmetry assumption? What is sphericity? What information from the SPSS printout helps us to evaluate whether the sphericity assumption is violated?Post your question