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)