AMS 225 Multivariate Statistical Methods Homework 4 Feb 13 2014

نویسنده

  • Cheng-Han Yu
چکیده

(a) Perform a principal components analysis of this dataset on both the covariance and correlation matrices, reporting both estimated variances and loadings. Why are the results different? Why does PCA on the correlation matrix make more sense for this data? The remaining parts assume that you use PCA on the correlation matrix. Solution: The results are different because PCA is not scale invariant. The PCA result depends on whether the data is standardized (centering and scaling) or not. So the results of PCA using covariance and correlation may be very different. The PCA on the correlation matrix makes more sense because the variables in this data use different units, i.e., time events in seconds and distance events in meters. It does not make sense to compare variables or examine their relationships in seconds and meters. Hence using correlation matrix to avoid unit impact is a better choice.

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تاریخ انتشار 2014