This preview shows pages 1–2. Sign up to view the full content.
STA 4702/5701 Spring 2009
HW #2 solutions
1.
(a)
Problem 4.8
a.
0.8804
b.
2
c.
2 because the two components explains 88% of variation.
The first component would be roughly interpreted as the overall average of the 8
variables because the loadings are evenly distributed to all 8 variables to some
degree and The second component seems to represent the sprints rather than the
long distance races.
(d) a. 0.9852
b. 1
(i)
Yes
(ii)
For part (a), the proportion of the variation explained by the first principal
component changes from that value obtained when the correlation matrix is used.
For part (b), I choose only the first principal component for the covariance matrix
while I choose the first two principal components for the correlation matrix.
(iii)
Because the variables are standardized in the correlation matrix but they are
not standardized in the covariance matrix.
(iv)
I would recommend the correlation matrix because the correlation matrix
represents the relationships among the variables after they are standardized and
so it isn’t affected by the varying scales of the variables.
(e) The correlation matrix
x1
x2
x3
x4
x5
x6
x7
x8
Prin1
0.79067
0.35685
0.90444
0.94711
0.96372
0.94632
0.95402
0.89572
Prin2
0.38939
0.85356
0.08942
0.02680
0.06967
0.18270
0.19016
0.27521
Prin3
0.41292
0.37688
0.32195
0.11453
0.05234
0.17265
0.15636
0.25528
The first component would be roughly interpreted as the overall average of the 8
variables. The second component seems to represent the sprints rather than the long
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Staff

Click to edit the document details