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 regression model:
yt = β0 + β1x1t + β2x2t + εt
yt = average monthly electricity bill, in dollars
x1t = average bimonthly automobile gasoline bill, in dollars
x2t = number of rooms in dwelling unit
From a sample of 25 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 β2.
b. Test, against a two-sided alternative, the null hypothesis
H0: β1 = 0
c. The statistician is concerned about the possibility of multicollinearity. What information 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, y`t, and the residuals, et.He then regresses e2t on y`t, finding that the regression has a coefficient of determination of 0.0470.Interpret this finding.