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Suppose the Pacific SSTs are described by values at grid points: x1,
x2,
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x3, ...xN. We know that
the xi’s are probably correlated with each other.
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Now, we want to determine a new set of independent predictors zi
to
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describe the state of Pacific SST, which are linear combinations of xi:
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Mathematically, we are rotating the old set of variable (x) to a new
set
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of variable (z) using a projection matrix (e):
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