Which statement best describes PCA components?

Which statement best describes PCA components?

• A. They are the same as the original variables.
• B. They are scaled versions of the original variables with no combination.
• C. They are linear components that are orthogonal and capture maximum variance.
• D. They are used to test mean differences across groups.

Answer: (C)

PCA creates new variables, called principal components, that are linear combinations of the original variables. These components are constructed to be orthogonal to each other, meaning they are uncorrelated. They are ordered so that the first component captures the largest possible variance in the data; each subsequent component captures as much of the remaining variance as possible while remaining orthogonal to the previous ones. This combination of being linear, orthogonal, and variance-maximizing is what makes PCA components distinct from the original variables or simple scaled copies, and it’s why this option best describes them. They aren’t about testing mean differences across groups—that’s a different analysis.

PCA creates new variables, called principal components, that are linear combinations of the original variables. These components are constructed to be orthogonal to each other, meaning they are uncorrelated. They are ordered so that the first component captures the largest possible variance in the data; each subsequent component captures as much of the remaining variance as possible while remaining orthogonal to the previous ones. This combination of being linear, orthogonal, and variance-maximizing is what makes PCA components distinct from the original variables or simple scaled copies, and it’s why this option best describes them. They aren’t about testing mean differences across groups—that’s a different analysis.