An article in the Journal of the American Ceramics Society

Chapter 12, Problem 117SE

(choose chapter or problem)

An article in the Journal of the American Ceramics Society (1992, Vol. 75, pp. 112–116) described a process for immobilizing chemical or nuclear wastes in soil by dissolving the contaminated soil into a glass block. The authors mix \(\mathrm{CaO}\) and \(\mathrm{Na}_2 \mathrm{O}\) with soil and model viscosity and electrical conductivity. The electrical conductivity model involves six regressors, and the sample consists of n=14 observations.

(a) For the six-regressor model, suppose that \(S S_T=0.50\) and \(R^2=0.94\). Find \(S S_E\) and \(S S_R\), and use this information to test for significance of regression with \(\alpha=0.05\). What are your conclusions?

(b) Suppose that one of the original regressors is deleted from the model, resulting in \(R^2=0.92\). What can you conclude about the contribution of the variable that was removed?

Answer this question by calculating an F-statistic.

(c) Does deletion of the regressor variable in part (b) result in a smaller value of \(M S_E\) for the five-variable model, in comparison to the original six-variable model? Comment on the significance of your answer.