What method finds the minimum number of dimensions to account for many variables?

Factor analysis is a statistical method used to identify the underlying relationships between a set of variables by reducing the data into fewer dimensions. It accomplishes this by analyzing the correlations among observed variables and grouping them into factors, which represent those variables that share common variance.

The purpose of factor analysis is to uncover the latent constructs that can explain the patterns of correlations among variables, allowing researchers to simplify complex datasets while retaining as much information as possible. By identifying these underlying factors, researchers can account for the majority of the variability in the data with a minimum number of dimensions. This is especially useful in fields like psychology, social sciences, and marketing, where multiple variables are often interrelated.

In contrast, correlation analysis primarily focuses on the strength and direction of relationships between two variables rather than reducing dimensionality. Regression analysis is aimed at predicting one variable based on the values of others, while descriptive analysis is concerned with summarizing and describing data sets without implying relationships or dimensions. Thus, factor analysis stands out as the method specifically designed for determining the minimum number of dimensions necessary to encapsulate the vast information from multiple variables.