Chapter 8, Problem 17SE

The article “Groundwater Electromagnetic Imaging in Complex Geological and Topographical Regions: A Case Study of a Tectonic Boundary in the French Alps” (S. Houtot, P. Tarits. ct al., Geophysics. 2002:1048–1060) presents measurements of concentrations of several chemicals (in mmol/L) and electrical conductivity (in 10^–2 S/m) for several water samples in various locations near Gittaz Lake in the French Alps. The results for magnesium and calcium are presented in the following table. Two outliers have been deleted.

1. a. To predict conductivity (y) from the concentrations of magnesium (x₁) and calcium (x₂). fit the full quadratic model $y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_1^2+{\beta }_4{x}_2^2+{\beta }_5{x}_1{x}_2+\epsilon$. Compute the analysis of variance table.
2. b. Use the F test to investigate some submodels of the full quadratic model. State which model you prefer and why.
3. c. Use a best subsets routine to find the submodels with the maximum adjusted R² and the minimum Mallows C_p. Are they the same model? Comment on the appropriateness of this (these) model(s).