THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The table below shows the quarterly sales of Dragon Ball Z action figures in a toy store.The forecaster uses the double exponential smoothing model to determine the forecast for future periods.
Given: α = 0.7 and β = 0.3

-The sales forecast for the 2^nd quarter of year 9 is approximately ________ in 000's.

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The table below shows the quarterly sales of Dragon Ball Z action figures in a toy store.The forecaster uses the double exponential smoothing model to determine the forecast for future periods.
Given: α = 0.7 and β = 0.3

-The sales forecast for the 2^nd quarter of year 9 is approximately ________ in 000's.

Quizplus · Accepted Answer

Using the double exponential smoothing model with α = 0.7 and β = 0.3, we can calculate the forecast for future periods:

F_t+1 = α * Y_t + (1 - α)(F_t + T_t)
T_t+1 = β(F_t+1 - F_t) + (1 - β)T_t

where:
Y_t = actual sales in the current period (t)
F_t = forecast for the current period (t)
T_t = trend for the current period (t)

For the first quarter of year 9, we have:
Y_28 = 160 (from the table)
F_28 = 161 (from the table)
T_28 = 0 (by assumption, since it is the first quarter)

Plugging these values into the formulas, we find:
F_29 = 0.7 * 160 + 0.3 * (161 + 0) = 160.3 (in thousands)

Therefore, the sales forecast for the first quarter of year 9 is approximately 160,300 (in thousands), which is closest to choice (C) 174 units.