Links

F. Husson website





Book Exploratory Multivariate Analysis Using R

Outline

Introduction

Principal Component Analysis

Correspondence Analysis

Multiple Correspondence Analysis

Clustering

Multiple Factor Analysis

To conclude

Forum

PCA quiz: aids for interpretation

For each question, tick the correct answer or answers.

Q1) The individuals' representation
two individuals close together in the global space will be close together in the 1-2 plane
two individuals close together in the 1-2 plane will necessarily be close together in the global space
two individuals close together in the 1-2 plane but poorly projected are necessarily far apart in the global space
two individuals far apart in the 1-2 plane will also be far apart in the global space
the projection quality of an individual, measured by the squared cosine, can only be summed over two axes

Q2) Individuals' contributions
an individual with values close to the mean for all variables does not contribute to the construction of any axes
an individual's contribution is measured by a squared cosine value
an individual that contributes greatly to the construction of the 1st PCA axis cannot contribute much to the construction of the 2nd
an individual with a large (absolute) coordinate value on a given axis contributes strongly to construction of that axis

Q3) The variables plot
a variable is well-projected on a plane if its arrow is short and far from the correlation circle
pairs of poorly-projected variables are strongly (positively or negatively) correlated
the projection quality of a variable on an axis is equal to the correlation coefficient of the variable with the axis
the projection quality of a variable on an axis is equal to the square of the correlation coefficient of the variable with the axis

Q4) Supplementary variables
active variables are necessarily quantitative
supplementary variables cannot be qualitative
supplementary qualitative variables are represented in terms of their categories on the individuals plot
the category of a supplementary qualitative variable is located at the barycenter in the global space of the individuals who are in this category

Quiz percentage of inertia

The following variables plot was obtained from running PCA on a data table with 9 variables.
Graphe des variables

Q5.1) The percentage of inertia associated with the 1st dimension is close to
0 %
10 %
25 %
40 %
65 %

Q5.2) The percentage of inertia associated with the plane shown is close to
0 %
10 %
25 %
40 %
65 %

Score =
Correct answers: