Six diferent tests of intelligence and ability were administered to 112 people. The covariance matrix (but not the original data) of the test results is given in ability.cov in the datasets library. The six tests are called general, picture, blocks, maze, reading, vocabulary, and reading. More information is given in the R help fle. a. Perform a factor analysis on the covariance matrix with

factanal(factors = 2, covmat = ability.cov)

Use the loadings to identify those variables that group together within the frst two factors. Interpret these factors.

b. Perform a principal components analysis using the covariance matrix

pc = princomp(ability.cov$cov) summary(pc) pc$loadings

and identify the variables making the largest contributions to the frst two principal components. How do you interpret these principal components?

c. Do you think it is more appropriate to examine the covariance or the correlation (standardize) in a principal components analysis of this data?

d. The cov2cor function efciently converts covariances into correlation matrices.

ability.cor = cov2cor(ability.cov$cov)

princomp(ability.cor)

princomp(ability.cor)$loadings

This obtains the correlation and performs the principal components analysis. Examine the loadings and interpret the frst two principal components. Compare this data summary with parts a and b. How do these difer? How are thy similar?