Mathematics, 27.04.2021 15:30 cornpops1749
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
12β4 a. m. β 19,291 31,219 27,330
4β8 a. m. β 33,195 37,014 32,715
8β12 noon β 99,526 119,968 152,475
12β4 p. m. 124,309 123,676 156,043
4β8 p. m. 113,545 111,727 128,899
8β12
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 12β4 A. M.; 0 otherwise
Time2 = 1 for time period 4β8 A. M; 0 otherwise
Time3 = 1 for time period 8β12 noon; 0 otherwise
Time4 = 1 for time period 12β4 P. M; 0 otherwise
c. Use the estimated regression equation developed in part (b) to estimate Timkoβs normal usage over the period of interrupted service.
d. Let Period = 1 to refer to the observation for Monday in the time period 12β4 P. M.; Period = 2 to refer to the observation for Monday in the time period 4β8 P. M; . . . and Period =18 to refer to the observation for Thursday in the time period 8β12 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 Timkoβs normal usage over the period of interrupted service.
Answers: 3
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