Question

The Hillsboro Aquatic Centre has an indoor pool with lanes for lap swimming and an open area for recreational swimming and various exercise and water aerobics programs. From 1 June to mid-August it operates on a summer schedule, and from mid-August to the end of May it operates according to normal weekday and weekend schedules. The centre’s policy for the pool is to have a lifeguard-to-patron ratio of 1:40. The centre director wants to develop a forecast of pool attendance for the weekday schedule in order to determine the number of lifeguards to hire. The following data for average daily attendance for each hour of the day that the pool is open to the public (i.e., there are no swim team practices):

	Year
Time	1	2	3	4	5	6
7:00 A.M	56	64	66	60	72	65
8:00	31	41	37	44	52	46
9:00	15	22	24	30	19	26
10:00	34	35	38	31	28	33
11:00	45	52	55	49	57	50
Noon	63	71	57	65	75	70
1:00 P.M	35	30	41	42	33	45
2:00	24	28	32	30	35	33
3:00	27	19	24	23	25	27
6:00	31	47	36	45	40	46
7:00	25	35	41	43	39	45
8:00	14	20	18	17	23	27
9:00	10	8	16	14	15	18

Develop a seasonally adjusted forecast model for these data for hourly pool attendance. Forecast attendance for each hour for year 7 by using a linear trend line estimate for pool attendance in year 7. Do the data appear to have a seasonal pattern?

Answer 1

We will be calculating the seasonality of each hour (ie 7am – 9pm) and use it to predict attendance for next Year (7am – 9pm)

Steps:

1. First we calculate 4 period moving Average.
2. Then we calculate Centred Average of these 4 period moving Average.
3. Then % Average ie Attendance/Centred Average
4. Then we table the % Average for each hour (ie 7am – 9pm) for the six years (Year 1- Year 6) and calculate mean for each hour. (As Shown in Table 2)
5. 1300%/The total of these 13 period mean will be the x Adjustment Factor
6. Seasonality Index for each Hour will be X Adj Factor * Hour’s Mean ie Seasonality Index for 7am = 183%*1.01 = 1.85
7. Then we calculate ∑X, ∑Y, ∑XY, ∑X² and using these values we calculate the regression equation.
8. Regression Equation will be: Y = 34.96 + 0.06*X
9. Using this equation and Seasonality Index , we calculate value for Attendance for next Year. Eg: Year 7’ 7am Attendance = (34.96 + 0.06*79)*1.85

Table 1

Table 2

Yes, the data appears to have a seasonal pattern.

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