Exercise 1.

For each question, select the correct answer or answers.

Q1) On the subject of inertia:.
if the 1st CA dimension has inertia of 1, then there is an exclusive association between a set of (one or several) rows and a set of (one or several) columns
the number of CA dimensions corresponds to the sum of the number of rows and the number of columns
the inertia of the 2nd dimension of a CA is strictly less than 1
the inertia of the cloud of row points is equal to the inertia of the cloud of column points

Q2) On the subject of row and column representations:
if a row is constant for all columns, it cannot be used in the analysis
if a row is constant for all columns, it will necessarily be close to the center of gravity, and therefore close to the origin of the axes
a row which is close to the average profile will necessarily be close to the center of gravity, and therefore close to the origin of the axes

Exercise 2.

A contingency table shows the distribution of 1000 people who have answered two questions. The first question has 5 categories, and the second question has 4 categories.

A chi² test applied to this table gives that the chi² statistic equals 135.6 (and the associated p-value is 4.62e-23).

Q3) Calculate the strength of the association (Phi²)
0.2520
0.1356
135.6
0.1759

Q4) Calculate the sum of the eigenvalues
9
0.1356
4
5
1000

Q5) How many non-zero eigenvalues are there at most?
1
2
3
997
1000

Exercise 3.

To answer this question, it is not necessary to run a CA. You only need to have an understanding of the main properties of CA.

We apply CA to the following table (a careful look at the table will show you that the Handball row is double the Volleyball row)

The factor coordinates on the 1st axis are the following:

Q6) What is the coordinate value of the Volleyball category on the 1st axis? (use the Handball coordinate value to help you)
0
0.06
-0.1946
0.9817

Score =
Correct answers: