Bargain Department Stores, Inc., is a chain of department stores in the Midwest. Quarterly sales of the "Bargain 8(KK)-Btu Air Conditioner" over the past three years are as given in the left hand portion of Table 16.7 on the next page.
TABLE 16.7
Air Conditioner Sales

a. Plot sales versus time and discuss why the plot indicates that the model
y0 = β0 + β1t + β2t2 + βQ2Q2 + βQ3Q3 + βQ4Q4 + εt,
might appropriately describe the sales values. In this model Q2, Q3, and Q4 are appropriately defined dummy variables for quarters 2. 3, and 4.
The righthand portion of Table 16.7 is the MINITAB output of a regression analysis of the air conditioner sales data using this model.
b. Define the dummy variables Q2, Q3, and Q4. Then use the MINITAB output to find, report, and interpret the least squares point estimates of βQ2, βQ3, and βQ4.
c. At the bottom of the MINITAB output are point and prediction interval forecasts of air conditioner sales in the four quarters of year 4. Find and report these forecasts and show how the point forecasts have been calculated.

Transcribed Image Text:

Year Quarter Sales 2,915 8,032 10,411 2,427 4,381 9,138 11,386 3,382 5,105 9,894 12,300 4,013 The regression equation is Sales2625 383 T 11.4 TSq4630 Q2 6739 03 1565 04 Predictor Coef SB Coef 2624.5 100.4 26.15 0.00092.4244 Constant TSq 03 382.82 34.03 11.25 0.000 -11.354 2.541-4.47 0.004 4629.74 76.08 60.86 0.000 6738.85 77.38 87.09 0.000 1565.32 79.34 -19.73 0.000 R-Sq = 100.0% R-Sq (adj). 99.9% 04 Time Fit SE Fit 95% CI 95% PI 13 5682.4 112.6 (5406.9, 5957.9) 〔5325.9, 6038.8) 14 10388.4 142.8 (10039.0, 10737.8) 9972.2, 10804.6) 1512551.0 177.2 く12117.4, 12984.7) (12061.9, 13040.2) 16 4277.7 213.9 3754.4, 4801.1) 3707. 4847.8)