Canonical Roots/Variates
In the terminology of canonical correlation analysis, the weighted sums define a canonical root or variate. You can think of those canonical variates (weighted sums) as describing some underlying "latent" variables. For example, if for a set of diverse satisfaction items we were to obtain a weighted sum marked by large weights for all items having to do with work, we could conclude that the respective canonical variate measures satisfaction with work.
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