Small Wonder, an amusement park, experiences seasonal attendance. It has collect
ID: 3274272 • Letter: S
Question
Small Wonder, an amusement park, experiences seasonal attendance. It has collected two years of quarterly attendance data and made a forecast of annual attendance for the coming year. Compute the seasonal indexes for the four quarters and generate quarterly forecasts for the coming year, assuming annual attendance for the coming year to be 1525.
Quarter
Park Attendance (in thousands)
Year 1
Year 2
Summer
314
352
Quarter
Average
Seasonal Index
Summer
Quarter
Forecast of
Average Seasonal Demand
Summer
(For seasonal indices: round your intermediate computations to 2 decimal places and final answers to 3 decimal places, the tolerance is +/- 0.005.)
(For forecasts: use average seasonal indices from your previous answers for computations, round your answers to 0 decimal places, the tolerance is +/- 5.)
Quarter
Park Attendance (in thousands)
Year 1
Year 2
Fall 352 391 Winter 156 212 Spring 489 518Summer
314
352
Explanation / Answer
Calculation of seasonal index calculation is given below
for calculating seasonal index we will first devide demand for fall by average demand for that year per season. Then, we will average it for each year and that would be the seasonal index value.
Now we will find trendline here
lets say trendline is y = a + bt
we will require the value of y , t2 , t and yt
the table for this value is given below
a = [(y) (t2 ) - (t) (yt)]/ [ n (t2 ) - (t)2 ]
a = [(2784 * 204 - 36 * 13056)/ (8* 204 - 362 )] = 97920/336 = 291.43
b = [ n(yt) - (t)((y)]/ [ n (t2 ) - (t)2 ]
b= [8 * 13056 - 36*2784)/ (8* 204 - 362 )] = 4224/336 = 12.57
so y = 291.4 + 12.57t
The trendline and seasonal factor is
so forecasted values are given below.
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