The purpose of this problem is to analyze the data set ROCK included in the script file rock.asc, to illustrate the inner workings of the S-Plus implementation of the projection pursuit regression algorithm. The data consist of 48 measurements on 4 crosssections of each of 12 oil-bearing rocks. Our goal is to predict the permeability y from the other 3 measurements (the total area, the total perimeter and a measure of roundness of the pores in the rock cross section).
1. Attach the data frame rock and run the projection pursuit algorithm to perform such a prediction.
2. Assess the quality of the fit by computing the sum of square residuals.
3. Produce the plots of the first three additive terms in the projection pursuit regression formula and give the 2-D scatterplots of the response against the fitted values and the residuals respectively.