An article in the Journal of the American Ceramics Society (Vol. 75, 1992, pp. 112–116) describes a process for immobilizing chemical or nuclear wastes in soil by dissolving the contaminated soil into a glass block. The authors mix CaO and Na2O 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 SST = 0.50 and R2 = 0.94. Find SSE and SSR, and use this information to test for significance of regression with = 0.05. What are your conclusions?
(b) Suppose that one of the original regressors is deleted from the model, resulting in R2 = 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 MSE for the five-variable model, in comparison to the original six-variable model? Comment on the significance of your answer.