A local public utility would like to be able to predict a dwelling unit's average monthly electricity bill. The company statistician estimated by least squares the following regres sion model: where Ya+ B + Box + B+ YAverage monthly electricity bill, in dollars x Average bimonthly automobile gasoline bill, in dollars x Number of rooms in dwelling unit From a sample of twenty-five dwelling units, the statistician obtained the following output from the SAS program:

(a) Interpret, in the context of the problem, the least squares estimate of B

(b) Test against a two-sided alternative the null hypothesis Ho: B =0

(c) The statistician is concerned about the possibility of multicollinearity. What informa- tion is needed to assess the potential severity of this problem?

(d) It is suggested that household income is an important determinant of size of electricity bill. If this is so, what can you say about the regression estimated by the statistician?

(e) Given the fitted model, the statistician obtains the predicted electricity bills, , and the residuals,

e. He then regresses e' on , finding that the regression has a coefficient of determination of .0470. Interpret this finding.