Chapter 13.4, Problem 47E

Efficient design of certain types of municipal waste incinerators requires that information about energy content of the waste be available. The authors of the article “Modeling the Energy Content of Municipal Solid Waste Using Multiple Regression Analysis” (J. of the Air and Waste Mgmnt. Assoc., 1996: 650–656) kindly provided us with the accompanying data on y = energy content (kcal/kg), the three physical composition variables x₁ = % plastics by weight, x₂ = % paper by weight, and x₃ = % garbage by weight, and the proximate analysis variable x₄ = % moisture by weight for waste specimens obtained from a certain region.

Using Minitab to fit a multiple regression model with the four aforementioned variables as predictors of energy content resulted in the following output:

a.    Interpret the values of the estimated regression coefficients ${\hat{\beta }}_1$ and ${\hat{\beta }}_4$.

b.    State and test the appropriate hypotheses to decide whether the model fit to the data specifies a useful linear relationship between energy content and at least one of the four predictors.

c.    Given that % plastics, % paper, and % water remain in the model, does % garbage provide useful information about energy content? State and test the appropriate hypotheses using a significance level of .05.

d.    Use the fact that $s_{\hat{Y}}=\mathrm{.7.46}$ when x₁ = 20, x₂ = 25, x₃ = 40, and x₄ = 45 to calculate a 95% confidence interval for true average energy content under these circumstances. Does the resulting interval suggest that mean energy content has been precisely estimated?

e.    Use the information given in part (d) to predict energy content for a waste sample having the specified characteristics, in a way that conveys information about precision and reliability.