FORECASTING PROBLEMS
Question 2
Your answer is partially correct. Try again.
Hospitality Hotels forecasts monthly labor needs.
(a) Given the following monthly labor figures, make a forecast for June using a three-period
moving average and a five-period moving average. (Round answers to 2 decimal places,
e.g. 15.25.)
Month
January
February
March
April
May
Actual Values
36
42
42
45
44
3-Period Moving Average
43.67
5-Period Moving Average
(b) What would be the forecast for June using the naïve method? (Round answers to 2
decimal places, e.g. 15.25.)
Forecast for June
44
(c) If the actual labor figure for June turns out to be 45, what would be the forecast for July
using each of these models? (Round answers to 2 decimal places, e.g. 15.25.)
3-Period Moving Average
44.67
5-Period Moving Average
43.6
Naïve method
45
(d) Compare the accuracy of these models using the mean absolute deviation
(MAD). (Round answers to 2 decimal places, e.g. 15.25.)
MAD (3-period)
MAD (5-period)
MAD (naïve)
(e) Compare the accuracy of these models using the mean squared error (MSE). (Round
answers to 2 decimal places, e.g. 15.25.)
MSE (3-period)
MSE (5-period)
MSE (naïve)
FORECASTING PROBLEMS
Question 3
The manager of a small health clinic would like to use exponential smoothing to forecast
demand for laboratory services in the facility. However, she is not sure whether to use a high
or low value of. To make her decision, she would like to compare the forecast accuracy of a
high and low on historical data. She has decided to use an α=0.7 for the high value and
α=0.1 for the low value. Given the following historical data, which do you think would be
better to use?(Round answers to 2 decimal place, e.g. 15.25)
Week
Demand
(lab requirements)
1
2
3
4
5
322
342
326
360
386
342
6
Forecasts using α = 0.1, MAD
Forecasts using α = 0.7, MAD
Using
provides a better historical fit based on the MAD criterion.
FORECASTING PROBLEMS
Question 4
Demand at Nature Trails Ski Resort has a seasonal pattern. Demand is highest during the
winter, as this is the peak ski season. However, there is some ski demand in the spring and
even fall months. The summer months can also be busy as visitors often come for summer
vacation to go hiking on the mountain trails. The owner of Nature Trails would like to make a
forecast for each season of the next year. Total annual demand has been estimated at 4,020
visitors. Given the last two years of historical data, what is the forecast for each season of
the next year?
Season
Fall
Winter
Spring
Summer
Visitors
Year 1
Year 2
196
225
1,415
1,616
504
601
693
818
(Round your answers to 0 decimal place, the tolerance is +/-1.)
Season
Fall
Winter
Spring
Summer
Forecast
FORECASTING PROBLEMS
Question 5
Rosa's Italian restaurant wants to develop forecasts of daily demand for the next week. The
restaurant is closed on Mondays and experiences a seasonal pattern for the other six days of
the week. Mario, the manager, has collected information on the number of customers served
each day for the past two weeks. If Mario expects total demand for next week to be around
350, what is the forecast for each day of next week? (Round answers to 1 decimal place,
e.g. 15.2.)
Day
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Day
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Number of customers
Week 1
Week 2
52
48
36
32
35
30
89
97
98
99
65
69
Forecast
FORECASTING PROBLEMS
Question 6
The president of a company was interested in determining whether there is a correlation
between sales made by different sales teams and hours spent on employee training. These
figures are shown.
Sales
Training
(in thousands)
Hours
12
8
34
12
29
10
46
15
8
4
a.
Compute the correlation coefficient for the data. (Round your answer to 4
decimal places, the tolerance is +/-0.0001.)
The correlation coefficient is
What is your interpretation of this value? (Do not round your intermediate
computations to answer this question.)
There is
hours.
b.
linear association between sales and training
Using the data, what would you expect sales to be if training was increased to
eighteen hours? Use the linear regression model. (Round your answer to 2
decimal places, the tolerance is +/-0.01.)
Sales =
(in thousands)
FORECASTING PROBLEMS
Question 7
The number of students enrolled at Spring Valley Elementary has been steadily increasing
over the past five years. The school board would like to forecast enrollment for years 6 and 7
in order to better plan capacity. Use a linear trend line to forecast enrollment for years 6 and
7. (Round answers to 1 decimal place, e.g. 15.1.)
Year
1
2
3
4
5
Year 6 forecast
Year 7 forecast
Enrollment
220
245
256
289
310
FORECASTING PROBLEMS
Question 8
Happy Lodge Ski Resorts tries to forecast monthly attendance. The management has noticed
a direct relationship between the average monthly temperature and attendance.
Average
Month Temperature
1
24
2
25
3
31
4
38
5
40
Resort Attendance
(in thousands)
41
34
38
31
27
a.
Given five months of average monthly temperatures and corresponding monthly
attendance, compute a linear regression equation of the relationship between the
two. Round your answer to 2 decimal places, the tolerance is +/-0.01. For negative
amounts use a negative sign preceding the number eg -45.
Resort attendance =
+
(average temperature)
If next month’s average temperature is forecast to be 45 degrees, use your linear regression
equation to develop a forecast. (To achieve this answer do not round your interim
calculations. Round your answer to 1 decimal place, the tolerance is +/-0.1.)
Resort attendance =
b.
thousand attendees.
Compute a correlation coefficient for the data and determine the strength of the
linear relationship between average temperature and attendance. How good a
predictor is temperature for attendance? (Round your answer to 2 decimal
places, the tolerance is +/-0.01.)
The correlation coefficient is
It indicates that the average temperature
predictor of resort
attendance. (Do not round your intermediate computations to answer this
question.)
FORECASTING PROBLEMS
Question 9
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
Fall
Winter
Spring
Summer
Quarter
Park Attendance (in thousands)
Year 1
Year 2
352
391
156
212
489
518
314
352
Average
Seasonal Index
Fall
Winter
Spring
Summer
Quarter
Forecast of
Average Seasonal Demand
Fall
Winter
Spring
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.)
FORECASTING PROBLEMS
Question 10
Given the following data, use exponential smoothing with α = 0.2 and α = 0.5 to generate
forecasts for periods 2 through 6. Use MAD and MSE to decide which of the two models
produced a better forecast.
Period
1
2
3
4
5
6
Actual
15
18
14
16
13
16
Forecast
17
Forecast
Period
1
Actual
15
2
18
3
14
4
16
5
13
6
16
α = 0.2
17
α = 0.5
17
MAD:
MSE:
Exponential smoothing using α =
yields lower MSE.
(Round your answers to 2 decimal places, the tolerance is +/-0.05)
FORECASTING PROBLEMS
Question 11
Pumpkin Pies Galore is trying to forecast sales of pies for the month of December. Demand
for pies in September, October, and November has been 220, 315, and 396, respectively.
Edith, the company’s owner, uses a three-period weighted moving average to forecast sales.
Based on her experience, she chooses to weight September as 0.1, October as 0.3, and
November as 0.6. (Round your answers to 1 decimal place, the tolerance is +/-0.1.)
a.
What would Edith’s forecast for December be?
Forecast using a weighted moving average =
b.
What would her forecast be using the naïve method?
Forecast using the naïve approach =
c.
If actual sales for December turned out to be 439 pies, which method was
better (use MAD)?
Absolute deviation using a weighted moving average =
Absolute deviation using naïve method =
only December data.)
The
approach is better.
. (For computation use
FORECASTING PROBLEMS
Question 12
A company has used three different methods to forecast sales for the past five months.
Use MAD and MSE to evaluate the performance of the three methods.
(a) Which forecasting method performed best?
Period
1
2
3
4
5
Actual
10
8
12
11
12
Method A
10
11
12
13
14
Method B
9
10
8
12
11
MAD
Method A
Method B
Method C
(b) Which of these is actually the naïve method?
(Round your answers to 1 decimal place, no tolerance)
Method C
8
11
10
11
12
MSE