A principal component analysis of the data in Table A.3 yields the three eigenvectors e 1 T = [.593, .552, –.587], e 2 T = [ .332, –.831, –.446], and e 3 T = [ .734, –.069, .676], where the three...

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.