Statistics Toolbox

The Component Variances (Third Output)

The third output, variances, is a vector containing the variance explained by the corresponding column of newdata.

variances
variances =
    3.4083
    1.2140
    1.1415
    0.9209
    0.7533
    0.6306
    0.4930
    0.3180
    0.1204

You can easily calculate the percent of the total variability explained by each principal component.

percent_explained = 100*variances/sum(variances)
percent_explained =
   37.8699
   13.4886
   12.6831
   10.2324
    8.3698
    7.0062
    5.4783
    3.5338
    1.3378

A "Scree" plot is a pareto plot of the percent variability explained by each principal component.

pareto(percent_explained)
xlabel('Principal Component')
ylabel('Variance Explained (%)')

We can see that the first three principal components explain roughly two thirds of the total variability in the standardized ratings.

The Component Scores (Second Output)

Hotelling's T2 (Fourth Output)