Gross state product (GSP) of 50 states are measured in 13 different areas of economic activity list below. In order to remove the influence of scale, the contribution of each area is measured as the proportion of the total GSP. The data can be found in file gsp.sav. Columns 2-14 in the data are the shares of GSP of the following areas:

agriculture

mining

construction

manufacturing (durable goods)

manufacturing (nondurable goods)

transportation

communications

utilities

wholesale

retail

fiduciary, insurance, and real estate

services

government

Conduct a principal component analysis of the data set.

a.Check if the correlation in the data supports PCA.

b.Extract the factors using PCA, use a scree plot to help determine the appropriate number of factors.

c.Evaluate the goodness of the factor model using the proportion of variance explained and the communalities.

d.Comment on the unrotated component loadings.

e.Perform Varimax factor rotation, comment on the loading structure.

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