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Stat 407 Lab 7 Principal Component Analysis Fall 2001 In this lab we will use S-Plus to conduct principal component analysis. We explore the effect of restructuring variables into comparable units. 1. Determine the principal components associated with the following covariance matrix: Σ= " 5 2 2 2 # Also calculate the proportion of total variance explained by the first principal component. 2. For the women’s track data, we have examined the PCA for the variance-covariance matrix (raw data) and the correlation matrix (standardized data). Now we will examine transforming the data in another way, and re-doing PCA. (a) Convert the national track records to speeds measured in meters per second (m/s). Notice that the records for 800m, 1500m, 3000m, and marathon are given in minutes. The marathon is 26.2 miles or 42195 meters. Write down your equations for converting the measurements. (b) Now perform PCA on the covariance matrix of the speed data. Report your results (eigenvalues, eigenvectors, percentage of total variance, scree plot, plot of PCs). (c) Compare these results to those obtained in the previous PCA results (raw, standardized)? Are the rankings of countries different? (d) Which approach is most appropriate? 1