What is the solution I am stuck :/ (b) The principal components of C in equation
ID: 3238551 • Letter: W
Question
What is the solution I am stuck :/
(b) The principal components of C in equations (i) and (2) are defined by the eigenvector equation: (3) where e are the principal components, are the associated eigenvalues, and the subscript khas the value 1, 2, 3, 4 or 5. It is conventional to order the principal components in terms of descending size of the eigenvalues so that Using this convention, Table 1 shows the elements of each principal component e, and the comesponding eigenvalues. City Sydney 0.37 0.01 0.18 0.74 0.53 0.43 0.77 -0.45 -0.13 -0.01 Perth Alice Springs 0.67 -0.60 -0.31 -0.30 -0.07 Darwin 0.20 -0.08 -0.11 0.51 0.82 Egenvalue 2-1.37 -0.51 0.23 0.15 -0.10 Table 1: The values of the elements of each of the principal components ofthe covariance matrix (2) are listed along with the comesponding cities where the temperature observations were collected. Also shown are the eigenvalues that corespond to each principal component.Explanation / Answer
Sum of all eigen values = 1.37 + 0.51 + 0.23 + 0.15 + 0.1 = 2.36
Total variance explained by first 3 primcipal components = 89.4%
Rotated component matrix is
The first principal component is strongly correlated with temperature in Alice Springs. The first principal component increases with increasing with temperature in Alice Springs. In fact, we could state that based on the correlation of 0.67 that this principal component is primarily a measure of the temperature in Alice Springs.
The second principal component is strongly correlated with temperature in Perth and Alice Springs. The second principal component increases with increasing temperature in Perth and decreases with increasing temperature in Alice Springs. This suggests that increase in temeprature in Perth imply low temperature in Alice Springs and viceversa.
The third principal component is strongly correlated with temperature in Melbourne. The third principal component increases with increasing with temperature in Melbourne. In fact, we could state that based on the correlation of 0.81 that this principal component is primarily a measure of the temperature in Melbourne.
Similarly, the fourth and fifth principal component is strongly correlated with temperature in Sydney and Darwin respectively.
Components Eigen Value % of variance Cumulative % 1 1.37 58.1% 58.1% 2 0.51 21.6% 79.7% 3 0.23 9.7% 89.4% 4 0.15 6.4% 95.8% 5 0.1 4.2% 100%Related Questions
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