12.5. Consider a larger set of stream monitoring predictors of the index of biotic integrity for macroinvertebrates considered in Example 12.4. The 21 predictors, described in more detail in the website for this book, can be grouped into four categories:

Site chemistry measures: Acid-neutralizing capacity, chloride, specific conductance, total nitrogen, pH, total phosphorus, sulfate Site habitat measures: Substrate diameter, percent fast water, canopy density above midchannel, channel slope Site geographic measures: Elevation, longitude, latitude, mean slope above site Watershed measures: Watershed area above site; human population density; percentages of agricultural, mining, forest, and urban land cover

a. Construct a regression tree to predict the IBI.

b. Compare the performance of several strategies for tree pruning. Compare the 10-fold cross-validated mean squared prediction errors for the final trees selected by each strategy.

c. The variables are categorized above into four groups. Create a regression tree using only the variables from each group in turn. Compare the 10-fold crossvalidated mean squared prediction errors for the final trees selected for each group of predictors.