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11 FORECASTING PROBLEMS DUE TONIGHT OCTOBER 2ND AT 21:45 UTC-05:00.
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FORECASTING PROBLEMS
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Question 2 |
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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
Actual Values
January
36
February
42
March
42
April
45
May
44
3-Period Moving Average
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
(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
5-Period Moving Average
Naïve method
(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)
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
322
2
342
3
326
4
360
5
386
6
342
Forecasts using α = 0.1, MAD
Forecasts using α = 0.7, MAD
Using provides a better historical fit based on the MAD criterion.
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?
Visitors
Season
Year 1
Year 2
Fall
196
225
Winter
1,415
1,616
Spring
504
601
Summer
693
818
(Round your answers to 0 decimal place, the tolerance is +/-1.)
Season
Forecast
Fall
Winter
Spring
Summer
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
Number of customers
Week 1
Week 2
Tuesday
52
48
Wednesday
36
32
Thursday
35
30
Friday
89
97
Saturday
98
99
Sunday
65
69
Day
Forecast
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
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
(in thousands)
Training
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 linear association between sales and training hours.
b. 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)
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
Enrollment
1
220
2
245
3
256
4
289
5
310
Year 6 forecast
Year 7 forecast
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.
Month
Average
Temperature
Resort Attendance
(in thousands)
1
24
41
2
25
34
3
31
38
4
38
31
5
40
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 = thousand attendees.
b. 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.)
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
Park Attendance (in thousands)
Year 1
Year 2
Fall
352
391
Winter
156
212
Spring
489
518
Summer
314
352
Quarter
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.)
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
Actual
Forecast
1
15
17
2
18
3
14
4
16
5
13
6
16
Period
Actual
Forecast
α = 0.2
α = 0.5
1
15
17
17
2
18
3
14
4
16
5
13
6
16
MAD:
MSE:
Exponential smoothing using α = yields lower MSE.
(Round your answers to 2 decimal places, the tolerance is +/-0.05)
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 = .
(For computation use only December data.)
The approach is better.
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
Actual
Method A
Method B
Method C
1
10
10
9
8
2
8
11
10
11
3
12
12
8
10
4
11
13
12
11
5
12
14
11
12
MAD
MSE
Method A
Method B
Method C
(b) Which of these is actually the naïve method?
(Round your answers to 1 decimal place, no tolerance)
44
44.67
43.6
45
43.67
