Abstract: Principal component regression has been perceived as a remedy for multicollinearity. Cook (2007) suggested that principal components and related methodology actually play a broader role than previously thought. Recently, Artemiou and Li (2009) provided a probabilistic explanation of the phenomenon that the response is often highly correlated with the leading principal components of the predictors. This article reinforces the previous results and offers an alternative perspective.
Key words and phrases: Dimension reduction, principal components, regression, spherically symmetric distribution.