Data Transformation takes many correlated variables and replaces them with a smaller number of new variables that capture most of the information.

Data Transformation takes many correlated variables and replaces them with a smaller number of new variables that capture most of the information.

• A. PCA
• B. Data Clustering
• C. Data Transformation
• D. Orthogonality

Answer: (C)

When you have many correlated variables, you can summarize the information with a smaller set of new variables that still capture most of what the data convey. This is what principal component analysis does: it creates principal components, which are linear combinations of the original variables. These components are arranged in order of the variance they explain, and each component is orthogonal to the others, meaning they are uncorrelated. By keeping just the first few components, you retain most of the overall information while reducing dimensionality. Data transformation is a broad idea, but the specific method that replaces correlated variables with a smaller, uncorrelated set that preserves information is principal component analysis. Clustering is about grouping observations, and orthogonality is a property, not a method.

When you have many correlated variables, you can summarize the information with a smaller set of new variables that still capture most of what the data convey. This is what principal component analysis does: it creates principal components, which are linear combinations of the original variables. These components are arranged in order of the variance they explain, and each component is orthogonal to the others, meaning they are uncorrelated. By keeping just the first few components, you retain most of the overall information while reducing dimensionality. Data transformation is a broad idea, but the specific method that replaces correlated variables with a smaller, uncorrelated set that preserves information is principal component analysis. Clustering is about grouping observations, and orthogonality is a property, not a method.