1. Mathematics of PCR and CCA Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015

2. 2 Seasonal Forecasting Using the Climate Predictability Tool Principal Components Regression Instead of using the original data as predictors, we can use the principal components as predictors in the same simple linear regression (SLR) model. The PCR option contains the information in many of the original predictors, and so a complex MLR model can be simplified considerably:

3. 3 Seasonal Forecasting Using the Climate Predictability Tool

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7. 7 Canonical Correlation Analysis (CCA) The weights V X and V Y are defined so that Z X and Z Y have maximum correlation. R is diagonal matrix of correlations. The current SSTs are represented by x. In CPT, the CCA is performed using principal components of X and Y to avoid over-fitting. Suitable for multiple predictors, and multiple predictands. Predictions are spatially consistent.