Use the SVD in Equation 10.70 to find the first three values of the first principal component of the minimum temperature data in Table A.1.
Construct a biplot for the data in Table A.3, using the information in Exercise 12.2.
Exercise 12.2
A principal component analysis of the data in Table A.3 yields the three eigenvectors e1
T
= [.593, .552, –.587], e2
T
= [ .332, –.831, –.446], and e3
T
= [ .734, –.069, .676], where the three elements in each vector pertain to the temperature, precipitation, and pressure data, respectively. The corresponding three eigenvalues are
1
= 2.476, l ¼=0.356, and l = 0.169.
a. Was this analysis done using the covariance matrix or the correlation matrix? How can you tell?
b. How many principal components should be retained according to Kaiser’s rule, Jolliffe’s modification, and the broken stick model?
c. Reconstruct the data for 1951, using a synthesis truncated after the first two principal components.