What method uses the correlation coefficient to reduce a set of variables to fewer factors?

Factor analysis is a statistical method employed to identify underlying relationships between a large set of variables. It does this by calculating the correlation coefficients among these variables and then grouping them into factors based on how closely related they are. The primary goal of factor analysis is to reduce the dimensionality of the data set, allowing for a simpler model that retains essential information.

By examining how variables correlate, factor analysis can determine which variables can be combined into a single factor. This facilitates a clearer understanding of the data structure and helps in identifying latent constructs that explain the relationships observed among the variables. Thus, it is specifically designed for data reduction by leveraging correlation coefficients to group variables efficiently.

In contrast, the other methods mentioned serve different purposes. Multiple regression focuses on predicting an outcome based on multiple predictors, chi-square analyzes categorical data to assess how likely it is that an observed distribution is due to chance, and the Kruskal-Wallis test is a non-parametric method for comparing more than two independent samples. None of these methods concentrate on reducing the number of variables through factor grouping based on correlation.