If we use the multiplicative decomposition method to analyze the quarterly bicyc

Question

If we use the multiplicative decomposition method to analyze the quarterly bicycle sales data given in Table 15.3 below, we find that the quarterly seasonal factors are .42, 1.19, 1.66, and .60. Furthermore, if we use a statistical software package to fit a straight line to the deseasonalized sales values, we find that the estimate of the trend is

trt = 22.61 + .59t

In addition, we find that the half-lengths of 95 percent prediction intervals for the deseasonalized sales values in the four quarters of the next year are, respectively, 2.88, 2.89, 2.96, and 3.06.

  

(a) Calculate point predictions of bicycle sales in the four quarters of the next year.

  

(b) Calculate approximate 95 percent prediction intervals for bicycle sales in the four quarters of the next year. (Round your answers to 2 decimal places.)

  

Point Predictions = sn × tr t sn tr = 22.61 + .59t sn × tr 17 .42 18 1.19 19 1.66 20 .60 TA BLE 15.3 Quarterly Sales of the TRK-50 Mountain Bike Os BikeSales Quarter 1 (Winter) 2 (Spring) 3 (Summer) 4 (Fall) Sales, yt 10 31 43 16 Year 6 45 17 13 34 48 19 10 12 13 14 15 16 15 37 51 21

Explanation / Answer

(a)

Point predictions are calculated in the below table.

(b)

95% prediction intervals are calculated in the below table.

(32.64 - 2.88, 32.64 + 2.88) = (29.76, 35.52)

t Sn tr = 22.61 + .59t Point Predictions = sn × tr 17 0.42 tr = 22.61 + .59 * 17 = 32.64 0.42 * 32.64 = 13.71 18 1.19 tr = 22.61 + .59 * 18 = 33.23 1.19 * 33.23 = 39.54 19 1.66 tr = 22.61 + .59 * 19 = 33.82 1.66 * 33.82 = 56.14 20 0.60 tr = 22.61 + .59 * 20 = 34.41 0.6 * 34.41 = 20.65

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