In a regression problem with 1 output variable and p input variables, we carry out a a principal components regression with p principal components constructed from the input variables. This will result in a significant level of dimensionality reduction. PCR is one of the leading methods for dimension reduction. no dimensionality reduction whatsoever. a potentially good level of dimensionality reduction depending on the quality of the principal components us making a bad choice if we care about the output variable. In that case we should have used partial least squares as a better high dimensionality reduction technique.

In a regression problem with 1 output variable and p input variables, we carry out a a principal components regression with p principal components constructed from the input variables. This will result in a significant level of dimensionality reduction. PCR is one of the leading methods for dimension reduction. no dimensionality reduction whatsoever. a potentially good level of dimensionality reduction depending on the quality of the principal components us making a bad choice if we care about the output variable. In that case we should have used partial least squares as a better high dimensionality reduction technique.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.FOM: Focus On Modeling: Fitting Lines To Data

Problem 10P

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		a significant level of dimensionality reduction. PCR is one of the leading methods for dimension reduction.
		no dimensionality reduction whatsoever.
		a potentially good level of dimensionality reduction depending on the quality of the principal components
		us making a bad choice if we care about the output variable. In that case we should have used partial least squares as a better high dimensionality reduction technique.