Question

# 2. (8 pt) Consider the matrix X0 in Q1, this time with px, yq " p4, 4q. As in Q1(f), modify the lefthand display

in the 2D PCA example in http://setosa.io/ev/principal-component-analysis/ to represent X0. Select all correct statements about observations related to the 2D example displaying your matrix X0: The plots show... ( ) the direction of maximal variation in the data is the diagonal pointing from the origin toward the top-right corner of the display. ( ) roughly two-thirds of the total variance of the data is explained by the first principle component. ( ) roughly half of the total variance of the data is explained by the second principle component. ( ) roughly two-thirds of the total variance of the data is explained by the second principle component. ( ) changing the final data point from p1, 1q as in Q1 to p4, 4q in Q2 did not change the principle component vectors much. ( ) changing the final data point from p1, 1q as in Q1 to p4, 4q in Q2 did not change the total variance of the data much. ( ) changing the final data point from p1, 1q as in Q1 to p4, 4q in Q2 did not change the total variance of the data much. ( ) shows that we can reduce the dimension of the data to 1, from 2, and still explain at least half of the variation in the data.

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