Question

3. For the following Eigenvalues tables, how many Factors are there? Explain

Eigenvalues of the Correlation Matrix: Total = 13 Average =

1

Eigenvalue       Difference     Proportion    Cumulative

1 3.56707480 0.56943025    0.2744            0.2744

2 2.99764455 1.25956706    0.2306            0.5050

3 1.73807749 0.45085244     0.1337          0.6387

4 1.28722505 0.28198745     0.0990           0.7377

5 1.00523760 0.38662334     0.0773           0.8150

6 0.61861426 0.06718656     0.0476          0.8626

7 0.55142770 0.10443379     0.0424          0.9050

8 0.44699392 0.16625812     0.0344          0.9394

9 0.28073579 0.08002691     0.0216          0.9610

Answer 1

Given the eigenvalues, we decide the number of factors on the basis of variance explained by the eigenvalues. The components that explain the higher proportion of variance are chosen first. The components with larger eigenvalues explain more variation.

Now, to decide how much of the variance we need to be explained, for decriptive purposes 80% of the explained variance is a good number. Hence, looking at the cumulative proportion column in the table, we have 5 significant factors.