Chemical Features of Wine. Figure 4.14 shows the PCA output on data (nonnormalized) in which the attributes represent chemical characteristics of wine, and each case is a different wine.

a. The data are in the file Wine.csv. Observe the Eigenvalues table, and explain why the value for PC1 is so much greater than that of any other column.

b. Comment on the use of normalization (standardization) in part (a).

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Attribute PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 Eigenvalues Alcohol 0.002 -0.001 0.017 -0.141 -0.020 -0.194 0.923 Malic Acid -0.001 -0.002 0.122 -0.160 0.613 -0.742 -0.150 Ash 0.000 -0.005 0.052 0.010 -0.020 -0.042 0.045 Eigenvectors Ash Alcalinity -0.005 -0.026 0.939 Magnesium 0.018 -0.999 0.331 -0.064 0.024 -0.030 0.005 0.006 0.002 0.002 0.032 Total Phenols 0.001 -0.001 -0.040 0.075 -0.315 -0.279 -0.020 Cumulative Variance Flavanoids 0.002 0.000 -0.085 0.169 -0.525 -0.434 -0.039 Nonflavanoid Phenols -0.000 0.001 0.014 -0.011 0.030 0.022 -0.005 Proanthocyanins 0.001 -0.005 -0.025 0.050 -0.251 -0.242 -0.310 Annotations Color_Intensity 0.002 -0.015 0.291 -0.879 -0.332 -0.003 -0.113 Hue 0.000 00280 00315 0.001 0.003 Proline 1.000 0.018 0.005 0.003 0.001 -0.026 0.060 -0.052 0.024 0.031 -0.070 0.178 -0.261 -0.289 0.102 0.002 0.001 -0.001 Component Standard Deviation Proportion of Varian... Cumulative Variance Eigenvalues PC1 314.963 0.998 0.998 PC 2 13.135 0.002 1.000 PC3 3.072 0.000 1.000 Eigenvectors PC 4 2.234 0.000 1.000 PC 5 1.109 0.000 1.000 PC 6 0.917 0.000 1.000 Cumulative Variance PC 7 0.528 0.000 1.000 PC 8 0.389 0.000 1.000 PC 9 0.335 0.000 1.000 Annotations PC 10 0.268 0.000 1.000 PC 11 0.194 0.000 1.000 PC 12 0.145 0.000 1.000 PC 13 0.091 0.000 1.000