Which of the following techniques is used for dimension reduction?

The technique that is utilized for dimension reduction in the context of statistics and data analysis is Principal Component Analysis (PCA). PCA is specifically designed to reduce the dimensionality of datasets while preserving as much variance as possible. This is achieved through the orthogonal transformation of the original variables into a new set of variables called principal components, which are linear combinations of the original variables, sorted by the amount of variance they capture. By retaining only the first few principal components, analysts can effectively reduce the complexity of the data without losing significant information.

Lasso Regression, while it does include a regularization technique that can result in some parameters being set to zero, is primarily used for feature selection rather than direct dimension reduction. Partial Least Squares (PLS) is more focused on finding a linear regression relationship between two matrices and can handle multicollinearity, but again, it does not primarily serve the purpose of dimension reduction in the same way as PCA. Ridge Regression, similar to Lasso, focuses on regularization and allows for the inclusion of all predictors but modifies the magnitude of coefficients rather than reducing the number of dimensions.

In summary, while Lasso, PLS, and Ridge Regression have their own valuable uses in data analysis, none serve the primary purpose of