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40. Electricity Consumption Using Deseasonalization. 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. Timko Products cut back con- sumption at 12:00 noon Thursday. To assess the savings, the utility must estimate Timko'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. 1 19,281 31,209 27,330 4-8 A.M. 33,195 37,014 32,715 8-12 noon 99,516 119,968 152,465 12-4 P.M. 124,299 123,666 156,033 4-8 P.M. 113,545 111,717 128,889 8-12 midnight 41,300 48,112 73,923 a. Is there a seasonal effect over the 24-hour period? b. Compute seasonal indexes for the six 4-hour periods. c. Use trend adjusted for seasonal indexes to estimate Timko's normal usage over the period of interrupted service.b. Day Time Period Power Centered Moving Seasonal Irregular Average Values Monday 12-4 PM 124.299 Monday 4 8 PM 113,545 Monday 8-12 midnight 41,300 Tuesday 12-4 AM 19.281 71,803.3 0.2685 Tuesday 4 8 AM 33.195 71,598.2 0.4636 Tuesday 8-12 noon 99,516 72.013.5 1.3819 Tuesday 12-4 PM 123.666 73.575.2 1.6808 Tuesday 4 8 PM 111,717 74.887.4 1.4918 Tuesday 8-12 midnight 48,112 76,910.0 0.6256 Wednesday 12-4 AM 31,209 81.311.6 0.3838 Wednesday 4 8 AM 37.014 85.439.8 0.4332 Wednesday 8 12 noon 119,968 89.021.8 1.3476 Wednesday 12-4 PM 156.033 90.849.4 1.7175 Wednesday 4 8 PM 128.889 90.167.9 1.4294 Wednesday 8-12 midnight 73,923 92.517.8 0.7990 Thursday 12-4 AM 27,330Thursday 4 8 AM 32.715 Thursday 8-12 noon 152.465 Time Period Seasonal Irregular Values Seasonal Index Adjusted Seasonal Index 12-4 AM 0.3838 0.2685 0.3262 0.3256 4 8 AM 0.4332 0.4636 0.4484 0.4476 8-12 noon 1.3476 1.3819 1.3648 1.3622 12-4 PM 1.6808 1.7175 1.6992 1.6959 4 8 PM 1.4918 1.4294 1.4606 1.4578 8-12 midnight 0.6256 0.7990 0.7123 0.7109 Total 6.0114 C. Day Time Period Power Adjusted Seasonal Deseasonalized Index Power Monday 12-4 PM 124,299 1.6959 73,292.80 Monday 4 8 PM 113,545 1.4578 77.885.67 Monday 8-12 midnight 41,300 0.7109 58,092.48 Tuesday 12-4 AM 19,281 0.3256 59.225.36Tuesday 4 8 AM 33,195 0.4476 74,166.93 Tuesday 8-12 noon 99,516 1.3622 73,056.72 Tuesday 12-4 PM 123,666 1.6959 72,919.55 Tuesday 4 8 PM 111,717 1.4578 76.631.76 Tuesday 8-12 midnight 48,112 0.7109 67,674.22 Wednesday 12-4 AM 31,209 0.3256 95.864.54 Wednesday 4 8 AM 37,014 0.4476 82,699.65 Wednesday 8-12 noon 119,968 1.3622 88.070.95 Wednesday 12-4 PM 156,033 1.6959 92.004.73 Wednesday 4 8 PM 128,889 1.4578 88.410.82 Wednesday 8 12 midnight 73,923 0.7109 103,979.91 Thursday 12-4 AM 27,330 0.3256 83,949.43 Thursday 4 8 AM 32,715 0.4476 73,094.48 Thursday 8-12 noon 152,465 1.3622 111,927.66 The following output shows the results of fitting a linear trend equation to the deseasonalized time series. Coefficients Term Coel SE Coef T-Value p-Value VIF Constant 63108 5185 12 .17 0 . 000E 1854 479 3. 87 0 . 001 1.00 Regression Equation Deseasonalized Power - 63108 + 1854 t Using the deseasonalized linear trend equation and the seasonal indexes computed in part b. we can forecast power consumption for the 12-4 PM and 4-8 PM time periods. 12-4 PM (corresponds to / = 19) Deseasonalized power = 63,108 + 1,854(19) = 98,334. Seasonal index for this period = 1.6959. Forecast for 12-4 PM = 1.6959(98,334) = 166,764.63 or approximately 166,765 kWh. 4 8 PM (corresponds to ( = 20) Deseasonalized power = 63, 108 + 1,854(20) = 100,188. Seasonal index for this period = 1.4578. Forecast for 4 8 PM = 1.4578(100,188) = 146,054.07 or approximately 146,054 kWh. Thus, the forecast of power consumption from noon to 8 PM is 166,765 + 146,054- 312,819 kWh