The program issues the following statistics:

- Ranked listed of eigenvalues of
**X**^{T}**X**for all the principal components - Factor coordinates of the variable points
- Contribution of variable to the variance (inertia) of each
factorial axis
- Contribution of the variables to the eccentricity of the
factorial axis.
- Quality of representation of the variable in the subspace by the
set of principal axes.

Relative contribution of an element *j* (variable or individual) to the
inertia of the a - axis is given by

where *F**a *_{j}
is the coordinate of the *j *^{th} variable on a -axis.

Relative contribution of an element *j *(variable or individual) to the
eccentricity of the a - axis is given
by

Cor _{a}
(j) =G_{a} ^{2}

*Rules for Selecting Significant Axes*

In practice, the data set is usually so large that it is impossible to process the results of factor analysis, coordinate by coordinate, contribution by contribution or factor by factor. The following rules are suggested for the selection of significant elements that will help in the interpretation of data. Here, the word ‘significant’ should be understood in terms of relevance, not in terms of statistical significance.

*First order significant axes*

Let *N *be number of axes to be retained.

*Rule* 1: *N* is the number of factorial axes such that

*Rule* 2: *N* is the number of factorial axes such that, where t _{a }is the percentage of variance
explained by the a ^{th}
factor, and *p* is the percentage of variance explained (usually 80%).

*Second order significant axes:*

*Rule* 3: Let *N* be the rank of the a -axis to be retained. *N* is chosen so that at least one
variable or one individual exists such that Cor_{N}( * j *)
or Cor

This rule allows us to retain as significant those axes, which highlight local effects.

*Rules for Selecting Significant Elements of Factorial Axes*

Significant elements are selected on the basis of their contribution to the
inertia (** CTR**) or the eccentricity of a factorial axis.

*Contribution to inertia***:**Significant elements of a cloud of column or row points are those, which explain the dispersion of factorial axes l a . The explicative points are those which have the greatest value of*CTR**a**i*), for each l a .- A subset of points
*i*can be selected whose contributions in terms of*CTR**a**( i*) are greater than the average of the contributions for the whole set. - Rank order CTRa
*( i*) in the decreasing order and select the subset t for which - å CTRa
*i*) ³ r

·
*Contribution to eccentricity: *An element *j*
is selected as significant when its contribution to eccentricity of a factorial
axis, COR_{a.³ }*k*.. .

The selection procedure for interpretation is based
on two given values fixed by the user: r
is often taken equal to 80% and *k*
is taken equal to 0.5.

*Quality of Representation of the Factor space.*

The quality of representation of the factor space is given by:

where *s* is the number
of factors in the factor space

*Quality of representation of points in the s-dimensional factor space*.

The quality of representation of a point ( *i* or *j *) in the factor space generated
by the principal components analysis can be measured as follows: