Forecasting Methods

I have 5 forecasting problems that I need completed onto template

2

>P

1 y

>

mos moving average forecast

abs()

Error abs()

1

2

3

9

10

8

9

5, 0.10

Note: average over month 4 through 8 only. No data available to month 9

																																																																																																						Carpet City
		Month	Demand for Soft Shag Carpet (1,000 yd.)				3	Weighted	3 mos moving average forecast			Error
				10
						9
				8
		4
		5
		6				12
				7					14
		11
	Please apply weights stated in the problem	Weights: 0.55 (most recent month),	0.3
	Compute MAD on 3 mos moving average		Note: average over month 4 through 8 only. No data available to month 9
	Compute MAD on weighted 3 mos moving average
	Which is a better forecast method?

P2

Month

p Forecast

Error

5

0

0

00

Petroco Service Station
	alpha =	0.4
Gas Demand		E	x
October		77								—-
November	835
December	605
January		45
February	600
March		70
April	8		20
May	9	25
June			15
July	1200
August
8410	SUM
MAPD

P3

alpha = 0.3
Month

3 mos moving average forecast

Exp Forecast

1

—- —- —-

2

—- —-

3

—- —-

4

1/8

5

6

7

8

9

10

11

12 58
14

15

3/4

20

Please apply weights stated in the problem

Compute MAD on 3 mos moving average
Compute MAD on weighted 3 mos moving average

Which is a better forecast method?

Science and Technology Mutual Fund
Fund Price	Weighted 3 mos moving average forecast	3 mos MA error	Weighted 3 mos MA error	Exp. Smoothing error
55 3/4
54 1/4
55 1/8
	58
53 3/8
51 1/8
56 1/4
59 5/8
62 1/4
59 1/4
62 3/8
	13	58 1/8
62 3/4
64 3/4
16	66 1/8
	17		68
18	60 1/2
	19	65 7/8
72 1/4
	21
Weight 0.5 (most recent), 0.3, 0.2
Compute MAD on exponentially smoothed forecast

P4

17 9
25 14
8 10
7 12
14 15
7 9
45

19 21

20

28

Carpet City Regression
X – axis	Y – axis
Monthly Construction Permits	Monthly Carpet Sales (1,000 yd.)
24
	28
29
	Place regression output here
	Y = A + Bx
	A =
	B =
Forecast Carpet sales for 30 construction permits
	Correlation Coefficient

P5

x y
1 68

2 70

3

4

5 77

6

7

8

9 85

10

11 90 144
12

13 80 144
14

Place regression output here

Y = A + Bx

A =
B =

Correlation Coefficient

Gilley’s Ice Cream Parlor
Ave. Temp	Ice cream Sold
Week	(degrees)	(gal.)
	80
115
73	91
79	87
110
82	128
	85	164
	90	178
		144
92	179
95	197
75	123
(a)
(b)
(c’)	Coefficient of Determination
Explain the meaning of the coefficient of Determination below. What does it indicate?

MAT540Homework

Week 4

Page 1 of 5

MAT540

Week 4 Homework

Chapter 15

1. The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft

Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill,

customer will buy their carpet from one of Carpet City’s many competitors. The manager has

collected the following demand data for the past 8

months:

Month
Demand for Soft Shag

Carpet

(1,000 yd.)

1 10

2 9

3 8

4 9

5 10

6 12

7 14

8 11

a. Compute a 3-month moving average forecast for months 4 through 9.

b. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign

weights of 0.55, 0.35, and 0.10 to the months in sequence, starting with the most recent

month.

c. Compare the two forecasts by using MAD. Which forecast appears to be more accurate?

2. The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline

next month so that the proper number of gallons can be ordered from the distributor. The owner has

accumulated the following data on demand for unleaded gasoline from sales during the past 10

months:

MAT540 Homework
Week 4

Page 2 of 5

Month Gasoline Demanded

(gal.)

October 775

November 835

December 605

January 450

February 600

March 700

April 820

May 925

June

July

1500

1200

a. Compute an exponential smoothed forecast, using an α value of 0.4

b. Compute the MAD.

3. Emily Andrews has invested in a science and technology mutual fund. Now she is considering

liquidating and investing in another fund. She would like to forecast the price of the science and

technology fund for the next month before making a decision. She has collected the following data

on the average price of the fund during the past 20 months:

Month Fund Price

1 $55 ¾

2 54 ¼

3 55 1/8

4 58 1/8

5 53 3/8

6 51 1/8

7 56 ¼

8 59 5/8

9 62 ¼

10 59 ¼

11 62 3/8

12 57 1/1

MAT540 Homework
Week 4

Page 3 of 5

13 58 1/8

14 62 ¾

15 64 ¾

16 66 1/8

17 68 ¾

18 60.5

19 65.875

20 72.25

a. Using a 3-month average, forecast the fund price for

month 21.

b. Using a 3-month weighted average with the most recent month weighted 0.5, the next most

recent month weighted 0.30, and the third month weighted 0.20, forecast the fund price for

month 21.

c. Compute an exponentially smoothed forecast, using α=0.3, and forecast the fund price for

month 21.

d. Compare the forecasts in (a), (b), and (c), using MAD, and indicate the most accurate.

4. Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that

the store’s sales are directly related to the number of new housing starts in town. The manager has

gathered data from county records on monthly house construction permits and from store records

on monthly sales. These data are as follows:

Monthly Carpet Sales

(1,000 yd.)

Monthly Construction

Permits

9 17

14 25

10 8

12 7

15 14

9 7

24 45

21 19

20 28

MAT540 Homework
Week 4

Page 4 of 5

29 28

a. Develop a linear regression model for these data and forecast carpet sales if 30 construction

permits for new homes are filed.

b. Determine the strength of the causal relationship between monthly sales and new home

construction by using correlation.

5. The manager of Gilley’s Ice Cream Parlor needs an accurate forecast of the demand for ice cream.

The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses

business, and if it orders too much, the extra must be thrown away. The manager belives that a

major determinant of ice cream sales is temperature (i.e.,the hotter the weather, the more ice cream

people buy). Using an almanac, the manager has determined the average day time temperature for

14 weeks, selected at random, and from store records he has determined the ice cream consumption

for the same 14 weeks. These data are summarized as follows:

Week
Average Temperature

(Degrees)

Ice Cream Sold

(gal.)

1 68 80

2 70 115

3 73 91

4 79 87

5 77 110

6 82 128

7 85 164

8 90 178

9 85 144

10 92 179

11 90 144

12 95 197

13 80 144

14 75 123

MAT540 Homework
Week 4

Page 5 of 5

a. Develop a linear regression model for these data and forecast the ice cream consumption if the

average weekly daytime temperature is expected to be 85 degrees.

b. Determine the strength of the linear relationship between temperature and ice cream

consumption by using correlation.

c. What is the coefficient of determination? Explain its meaning.