I am not able to follow the explanation in the book 'Applied multivariate statistical analysis':
First, they nicely explain:
Suppose variables can be grouped by their correlations. That is, suppose all variables within a particular group are highly correlated among themselves, but have relatively small correlations with variables in a different group.Then it is conceivable that each group of variables represents a single underlying construct, or factor, that is responsible for the observed correlations. For example, correlations from the group of test scores in classics, French, English, mathematics, and music collected by Spearman suggested an underlying “intelligence” factor.
The paragraph nicely explains the basics, and it clarifies that each group represents a SINGLE factor.
But then it contradicts in the formula:
(The formula specifies more than one factor, why?)
Following the previous analogy, in the formula... $X_1$ would be 'classics', $X_2$'french', $X_3$'english', $X_4$'math' and so on... then $F_1$ would be 'intelligence'.
Why in the introduction they say 'single' factor, and then the formula has multiple?
(this would mean that the expected intelligence is '0'?!)