HW3_solutions - sep_l sep_w pet_l pet_w 0.92259864...

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HW #3 Solutions 1. a. The results from the principal components analysis suggest that this problem can probably be reduced to two dimensions: the first two components have eigenvalues of 2.92 and 0.92, together accounting for more than 95 percent of the variance in the original data. The loadings suggest that the first principal component represents the average of the sepal length, the petal length and the petal width while the second component represents the sepal width, which is not reflected in the first principal component. PRINCIPAL COMPONENTS ANALYSIS OF FISHER’S IRIS DATA: Eigenvalues Eigenvalue Difference Proportion Cumulative 1 2.91849782 2.00446735 0.7296 0.7296 2 0.91403047 0.76727360 0.2285 0.9581 3 0.14675688 0.12604204 0.0367 0.9948 4 0.02071484 0.0052 1.0000 Principal Component Loadings Factor1 Factor2 sep_l 0.89017 0.36083 sep_w -0.46014 0.88272 pet_l 0.99156 0.02342 pet_w 0.96498 0.06400 Variance Accounted for by First Two Components
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Unformatted text preview: sep_l sep_w pet_l pet_w 0.92259864 0.99091932 0.98372995 0.93528037 b. Plotting the average principal component scores for each of the three species of iris shows that the second principal component does indeed serve to help differentiate among species. The first principal component clearly separates 1 ( Iris setosa ) from 2 and 3 ( Iris versicolor and Iris virginica ). While the distinction is much less clear, the second principal component separates 2 ( Iris versicolor ) from 3 ( Iris virginica ). speci es set osa versi col vi rgi ni c meanp2-0. 6-0. 5-0. 4-0. 3-0. 2-0. 1 0. 0 0. 1 0. 2 0. 3 meanp1-3 -2 -1 0 1 2 2. The condition index is essentially the square root of the ratio of the variances of the largest principal component to the smallest. In the presence of almost perfect collinearity in the data, the last principal component has almost zero variance, leading to a very large condition index....
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This note was uploaded on 07/22/2011 for the course STA 4702 taught by Professor Staff during the Spring '08 term at University of Florida.

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HW3_solutions - sep_l sep_w pet_l pet_w 0.92259864...

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