# Partial Least Squares Regression

TQ5: Partial Least Squares Regression
Investigate PLS models to predict the prize winnings (\$1000s) given a variety of information about performance and success statistics for LPGA golfers in 2009. The table attached (see excel file) contains data related to performance and success statistics for LPGA golfers in 2009. The matrix X contains 11 predictor variables:
1. Average drive (yards)
2. Percent of fairways hit
3. Percent of greens reached in regulation
4. Average putts per round
5. Percent of sand saves (2 shots to hole)
6. Tournaments played in
7. Green in regulation putts per hole
8. Completed tournaments
9. Average percentile in tournaments (high is good)
10. Rounds completed
11. Average strokes per round
The column vector y contains the output variable, prize winnings (\$1000s). For each variable in x and y. This assignment will look at the predictive ability of partial least squares regression (PLS) and compare it to the methods we've investigated previously in TQ3 and TQ4

1. Divide the data into training, test, and validation data sets. Use the same training, test, and validation data sets that you used in TQ3 and TQ4.
2. Use cross-validation to determine the appropriate number of latent variables for your PLS model. Be sure to describe the cross-validation method used
3. Analyze the loadings of the first few LVs. What do these tell you about the relationships between the inputs and between the inputs and the output?
4. Compare the LV loadings to the PC loadings from TQ4. What similarities and differences are there in the LVs and PCs? Explain any similarities or differences in the context of PLS and PCA (the correlation of PCs to the output may be helpful here!).
5. Compare the validation performance of your PLS model with that of your best PCR and regression models. Comment on the results.
6. Is there evidence that a nonlinear PLS model would outperform the linear PLS? Explain your reasoning (but you don't need to develop the nonlinear PLS model).

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