What is factor analysis? State with illustration the various uses of factor analysis.

Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors, plus "error" terms.Simply put, the factor loading of a variable quantifies the extent to which the variable is related with a given factor.A common rationale behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in psychometrics, personality theories, biology, marketing, product management, operations research, finance, ___ ___ ____ __________ _____ ___ ____ _______ _____ ______ _______ _______.
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