For each question, tick the correct answer or answers.

Q1) Suppose that we run an MFA with 5 groups of variables. In the graph representation of the groups,
a group can have coordinate values very close to 1 on both the 1st and 2nd axes
a group can have coordinate values very close to 0 on both the 1st and 2nd axes
if a group has a coordinate value of 1 on the 1st axis, then the first axis of this group coincides with the 1st axis of the MFA
if two groups have coordinate values close to 0 on the 1st and 2nd axes, then they necessarily induce the same structure on the individuals
if two groups have identical coordinate values on all the axes, then they necessarily induce the same structure on the individuals

Q2) Suppose we run an MFA on a table containing 3 groups of variables. The following matrices show the Lg coefficients, the VR between between groups, and the coefficients between each group and the MFA’s structure.

group A is a group of one-dimensional variables (correlations between variables from this group are equal to either 1 or -1)
variables from group A have very small correlations with variables from group C
group B is the most multidimensional group
group B induces a structure on the individuals which is closest to the structure given by the MFA

Q3) Partial points (we denote i^j the partial point of individual i as seen by variables from the group j)
if all of the partial points of individual i are located at the same point in the 1-2 plane of the MFA, then they are also on top of the mean point of individual i
if a certain individual has all of its partial points located at the same point, then the standardized values for that individual are the same from one group to the next
if the values taken by individuals i and k are exactly the same for variables in group 1, then the partial points i^1 and k^1 are at the same place
if the partial points of an individual are quite spread out, then this individual is characterized in a similar way by all of the groups

Q4) Suppose we run an MFA on a data table containing two groups of variables. The graph for the groups, the individuals plot, and the partial individuals plots, are shown below.

Which set of three labeled groups corresponds to the same actual group across the three graphs?
Gr.Z - Gr.A - Gr.1
Gr.Z - Gr.A - Gr.2
Gr.Z - Gr.B - Gr.1
Gr.Z - Gr.B - Gr.2

Q5) Partial axes. Suppose we run MFA on a table with four groups of variables. We then construct the partial axes plot showing the two principal axes of the PCAs for each group.

in the PCA for only the variables in group A, the coordinate values of the individuals in the 1st dimension are highly correlated with the coordinate values of the individuals in the 1st dimension of the MFA
in the PCA for only the variables in group A, the coordinate values of the individuals in the 1st dimension are highly correlated with the coordinate values of the individuals in the 2nd dimension of the MFA
the 1-2 plane of the PCA for the variables of group B gives a similar configuration of individuals to that of the 1-2 plane of the MFA (in the sense that close together - resp. far apart - individuals in the PCA plane are also so in the MFA plane)
in the PCA for only the variables in group C, the coordinate values of the individuals in the 1st dimension are highly correlated with the coordinate values of the individuals in the 1st dimension of the MFA
the coordinate values of the individuals in the 1st dimension of the PCA for group C are highly correlated with the coordinate values of the individuals in the 1st dimension of the PCA for group D

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