29) A counseling service records the number of calls to their hotline for the last year. Plot the
data and determine which forecasting technique would be best among a moving average,
weighted moving average, exponential smoothing, and trend line.
Month
Demand
January
111
February
127
March
146
April
159
May
165
June
165
July
178
August
182
September
191
October
208
November
223
December
228
22
30) The Pancake House did a brisk business on the weekend and the maître d’ was always on the
lookout for ways to improve the customer experience. He carefully tracked the number of
customers that graced their establishment over the last four weekends. He was hopeful that he
could forecast the number of customers that would come for the world’s finest pancakes the next
weekend.
Weekend 1
Weekend 2
Weekend 3
Weekend 4
Friday
131
216
286
355
Saturday
225
311
408
490
Sunday
166
249
330
415
Using the data in the table, first plot the data and comment on the appearance of the demand
pattern. Then develop a forecast for weekend #5 that fits the data.
Friday
247
Saturday
Sunday
290
31) Using the data in the table, first plot the data and comment on the appearance of the demand
pattern. Then develop a forecast for periods 51-70 that fits the data.
Output
Time
Output
Time
Output
Time
Output
12.5
14
16.4
27
-19.2
40
11.3
14.8
15
11.7
28
10.6
41
11.1
15.3
16
11.1
29
16.8
42
52.5
15
17
11.9
30
22.5
43
11.3
11.5
18
11.3
31
15.5
44
-19.3
11.6
19
13.7
32
11.7
45
12
12.8
20
16.3
33
11.9
46
15.5
51.9
21
13.1
34
13
47
20.5
11
22
10.8
35
11.9
48
16.5
-19.7
23
10.3
36
13.5
49
12.5
11.9
24
11
37
16.5
50
10.5
17.8
25
51.4
38
14
20.3
26
11.6
39
11
25
26
Learning Objective 9-6
1) Demand was low two years ago but increased sharply last year thanks to an aggressive
marketing campaign. A time series model that puts the greatest emphasis on the most recent
period is probably the best choice to predict next year’s demand.
2) Multiple regression is used when the forecaster believes that more than one independent
variable should be used to predict the variable of interest.
27
3) A well-educated lumberjack decides to use linear regression to predict the demand for
firewood based on the ambient temperature. He has collected data on firewood sales and
temperature for the last several days and has performed some preliminary calculations as shown
in the table. What is his regression equation based on the data?
Temp
Ricks
Temp Squared
Temp ∗ # Ricks
33
17
1089
561
19
32
361
608
34
20
1156
680
34
18
1156
612
20
33
400
660
24
30
576
720
17
34
289
578
30
25
900
750
38
16
1444
608
23
29
529
667
Sums
272
254
7900
6444
A) Ricks = 50.6 – 0.93 × Temp
B) Temp = 53.3 – 1.0 × Ricks
C) Ricks = 0.93 – 50.6 × Temp
D) Temp = 1.0 – 53.3 × Ricks
28
4) A poultry farmer that dabbles in statistics is interested in exploring the relationship between
two types of feed, layer pellets and scratch, water, and the output of his laying hens. For ten days
he records the number of ounces of layer pellets and scratch the hens consume and the number of
fluid ounces of water and tracks the number of eggs that are produced. What is his regression
equation based on the data?
Layer Pellets
Water
Eggs
29
36
24
27
34
22
22
31
20
21
32
20
23
34
22
28
34
23
22
37
21
28
33
22
22
31
20
29
37
24
A) Eggs = 6.56 + .38Scratch + .17Pellets + .21Water
B) Eggs = 1.25 + .18Scratch + .29Pellets + .15Water
C) Eggs = 0.93 – .88Scratch + .37Pellets + .41Water
D) Eggs = 4.22 + .37Scratch + .67Pellets + .58Water
29
5) A poultry farmer that dabbles in statistics is interested in exploring the relationship between
layer pellets and the output of his laying hens. For ten days he records the number of ounces of
layer pellets and the number of eggs that are produced. What is his regression equation based on
the data?
Layer Pellets
Eggs
29
24
27
22
22
20
21
20
23
22
28
23
22
21
28
22
22
20
29
24
A) Eggs = 11.3 + 0.42Pellets
B) Eggs = 1.25 + 0.29Pellets
C) Eggs = 10.9 + 0.23Pellets
D) Eggs = 4.22 + 0.67Pellets
30
6) A poultry farmer that dabbles in statistics is interested in exploring the relationship between
two types of feed, layer pellets and scratch, water, and the output of his laying hens. For ten days
he records the number of ounces of layer pellets and scratch the hens consume and the number of
fluid ounces of water and tracks the number of eggs that are produced. After running a multiple
regression model, he obtains the following report. What is the best interpretation of these
statistics?
Regression Statistics
Multiple R
0.993633
R Square
0.987307
Adjusted R Square
0.98096
Standard Error
0.213764
Observations
10
A) The probability that the number of eggs is correctly predicted by the amount of scratch, layer
pellets, and water consumed is 99.36%.
B) The prediction of the amount of eggs is 98.7% accurate based on the amount of scratch, layer
pellets, and water consumed.
C) 98.7% of the variability in egg production is explained by the amount of water, scratch, and
layer pellets consumed.
D) The prediction of the amount of eggs is 99.36% accurate based on the amount of scratch,
layer pellets, and water consumed.
31
7) A poultry farmer that dabbles in statistics is interested in exploring the relationship between
two types of feed, layer pellets and scratch, water, and the output of his laying hens. For ten days
he records the number of ounces of layer pellets and scratch the hens consume and the number of
fluid ounces of water and tracks the number of eggs that are produced. After running a multiple
regression model, he obtains the following report. What is the best interpretation of these
statistics?
Coefficients
Std Error
t Stat
P-value
Intercept
1.256
1.249
1.006
0.353
Scratch
0.185
0.032
5.714
0.001
Layer Pellets
0.295
0.026
11.539
0.000
Water
0.149
0.041
3.587
0.012
A) For every egg produced, about 0.185 ounces of scratch must be consumed.
B) The standard error for the model intercept is as large as the coefficient, thus the intercept is
the most important predictor of egg production.
C) Layer pellets are not good predictors of egg production because the p-value is 0.
D) For every ounce of water consumed, the chickens produce 0.15 eggs, holding all other
independent variables constant.
8) McMahon and Tate advertising company is interested in an appropriate mix of print, radio,
and television ads for their new client. Darrin Stevens performs a multiple regression on the
effects of dollars spent on each type of media on dollars of sales of product. Darrin uses data
from the most recent advertising campaigns and develops the following equation:
y = 254,215 + 6.79 × Print – 1.4 × Radio + 16.87 × Television
The r-squared statistic is 0.77. Which of the following statements is best?
A) At a minimum, the client will sell $254,215 worth of product after the new advertising
campaign.
B) At a maximum, the client will sell $254,215 worth of product after the new advertising
campaign.
C) This equation will be of no use in predicting the amount of sales based on advertising in these
media.
D) The client should spend more money on television advertising than on radio advertising.