A data scientist is performing exploratory data analysis on a high-dimensional financial dataset containing 50 macroeconomic and firm-specific features to be used in a regression model. An initial analysis of the correlation matrix reveals significant multicollinearity among many of the predictor variables. To address this, the scientist decides to create a new, smaller set of features that are linear combinations of the original features. The primary goals of this transformation are to ensure the new features are mutually uncorrelated and to retain the maximum possible variance from the original dataset. Which of the following multivariate analysis techniques is the most appropriate for this specific task?
The correct answer is Principal Component Analysis (PCA). The scenario describes a classic use case for PCA. The key objectives stated are to handle multicollinearity by creating a set of uncorrelated features and to maximize the explained variance, which are the primary goals of PCA. The new, uncorrelated features generated by PCA are called principal components.
Factor Analysis (FA) is incorrect because its primary goal is to identify underlying unobservable, latent factors that explain the covariance among observed variables, not to maximize the variance for a subsequent predictive model. The scenario's objective is explicitly about variance retention, making PCA more suitable.
Linear Discriminant Analysis (LDA) is a supervised dimensionality reduction technique used for classification. It aims to find feature combinations that maximize the separability between classes. The scenario describes an unsupervised preprocessing step for a regression model, so LDA is not applicable.
Canonical Correlation Analysis (CCA) is used to analyze the relationship between two distinct sets of variables. The scenario involves transforming a single set of predictor variables, not correlating two different sets.
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