Electric power consumption is measured in kilowatt-hours (kWh). The local utility company offers an interrupt program whereby commercial customers that participate receive favorable rates but must agree to cut back consumption if the utility requests them to do so. A certain company cuts back consumption at 12:00 noon Thursday. To assess the savings, the utility must estimate the company's usage without the interrupt. The period of interrupted service was from noon to 8:00 p. m. Data on electric power consumption for the previous 72 hours are available. Time Period Monday Tuesday Wednesday Thursday
12–4 a. m. — 19,291 31,219 27,330
4–8 a. m. — 33,195 37,014 32,715
8–12 noon — 99,526 119,968 152,475
12–4 p. m. 124,309 123,676 156,043
4–8 p. m. 113,545 111,727 128,899
8–12
midnight 41,310 48,122 73,923
a. Construct a time series plot. What type of pattern exists in the data?
b. Use the following dummy variables to develop an estimated regression equation to account
for any seasonal effects in the data. Time1 = 1 for time period 12–4 A. M.; 0 otherwise
Time2 = 1 for time period 4–8 A. M; 0 otherwise
Time3 = 1 for time period 8–12 noon; 0 otherwise
Time4 = 1 for time period 12–4 P. M; 0 otherwise
c. Use the estimated regression equation developed in part (b) to estimate Timko’s normal usage over the period of interrupted service.
d. Let Period = 1 to refer to the observation for Monday in the time period 12–4 P. M.; Period = 2 to refer to the observation for Monday in the time period 4–8 P. M; . . . and Period =18 to refer to the observation for Thursday in the time period 8–12 noon. Using the dummy variables defined in part (b) and Period, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series.
e. Using the estimated regression equation developed in part (d), estimate Timko’s normal usage over the period of interrupted service.