13.28 Demand for Utilities Utility companies, which must plan the operation and expansion of electricity generation, are vitally inter- ested in predicting customer demand over both short and long periods of time. A short-term study was conducted to investigate the effect of mean monthly daily temperature .x, and cost per kilowatt-hour x2 on the mean daily consumption (in kilowatt-hours, kWh) per household. The company expected the demand for electricity to rise in cold weather (due to heating), fall when the weather was moderate, and rise again when the temperature rose and there was need for air conditioning. They expected demand to decrease as the cost per kilowatt-hour increased, reflecting greater attention to conservation. Data were available for two years, a period in which the cost per kilowatt-hour x2 increased owing to the increasing cost of fuel. The company fitted the model

to the data shown in the table. The MINITAB printout for this multiple regression problem is also provided.

a. Do the data provide sufficient evidence to indicate that the model contributes information for the prediction of mean daily kilowatt-hour consumption per household? Test at the 5% level of significance.

b. Graph the curve depicting as a function of tem- perature x, when the cost per kilowatt-hour is x2 = 8. Construct a similar graph for the case when x2 = 10 per kilowatt-hour. Are the consump- tion curves different?

c. If cost per kilowatt-hour is unimportant in predict- ing use, then you do not need the terms involving x in the model. Therefore, the null hypothesis Ho: x2 does not contribute information for the prediction of Y is equivalent to the null hypothesis Ho: 3 = 4= s 0 (if B3 B4 =s = 0, the terms involving x2 disappear from the model). The MINITAB printout, obtained by fitting the reduced model E(Y)=Bo +Br + Bi to the data, is shown here. Use the methods of Section 13.5 to determine whether price per kilowatt-hour x contributes significant information for the prediction of Y.

d. Compare the values of R2(adj) for the two models fit in this exercise. Which of the two models would you recommend?

Transcribed Image Text:

= E(Y) Bo+Bx1+ Box + Bat + Box+2