1) The first principal component may be viewed in general as the single best summary of the correlations among the predictors. Specifically, this particular linear combination of the variables accounts for more variability than any other conceivable linear combination.

2)The second principal component, Y2, is the second-best linear combination of the variables, on the condition that it is orthogonal to the first principal component. Two vectors are orthogonal if they are mathematically independent, have no correlation, and are at right angles to each other. The second component is derived from the variability that is left over once the first component has been accounted for.

3)The third component is the third-best linear combination of the variables, on the condition that it is orthogonal to the first two components. The third component is derived from the variance remaining after the first two components have been extracted. The remaining components are defined similarly.

4)The eigenvalue criterion states that each component should explain at least one variable’s worth of the variability, and therefore the eigenvalue criterion states that only components with eigenvalues greater than 1 should be retained.

5)For the proportion of variance explained criterion, the analyst simply selects the components one by one until the desired proportion of variability explained is attained.

6)The minimum communality criterion states that enough components should be extracted so that the communalities for each of these variables exceeds a certain threshold (e.g., 50%).

7)The scree plot criterion is this: The maximum number of components that should be extracted is just prior to where the plot begins to straighten out into a horizontal line.