20.24
Year
Quarter
Period t
y
y
ˆ
yy ˆ
/
2001
1
1
52
62.9
0.827
2
2
67
64.1
1.045
3
3
85
65.3
1.302
4
4
54
66.5
0.812
2002
1
5
57
67.7
0.842
2
6
75
68.8
1.090
3
7
90
70.0
1.286
4
8
61
71.2
0.857
1
9
60
72.4
0.829
2
77
73.6
1.046
3
94
74.7
1.258
2004
1
66
77.1
0.856
2
82
78.3
1.047
3
98
79.5
1.233
4
67
80.6
0.831
Quarter
1
2
3
4
Total
.827
1.045
1.302
.812
.842
1.090
1.286
.857
.829
1.046
1.258
.830
.856
1.047
1.233
.831
.838
1.057
1.270
.833
3.998
20.25a
y = 253.78x – 491595
16,500
17,000
17,500
18,000
Scatter Diagram
20.26a
20.27
-300
-200
-100
0
Scatter Diagram
y = 7.416x + 143.0
300
350
400
Scatter Diagram
Year
Quarter
Period t
y
y
ˆ
=143+7.42t
yy ˆ
/
1
1
1
184
150.42
1.223
2
2
173
157.84
1.096
3
3
160
165.26
0.968
4
4
189
172.68
1.095
2
1
5
191
180.1
1.061
2
6
185
187.52
0.987
3
7
184
194.94
0.944
4
8
200
202.36
0.988
3
1
9
205
209.78
0.977
2
10
192
217.2
0.884
3
11
200
224.62
0.890
4
12
229
232.04
0.987
4
1
13
236
239.46
0.986
2
14
219
246.88
0.887
3
15
211
254.3
0.830
4
16
272
261.72
1.039
5
1
17
280
269.14
1.040
2
18
261
276.56
0.944
3
19
275
283.98
0.968
4
20
322
291.4
1.105
6
1
21
331
298.82
1.108
2
22
301
306.24
0.983
3
23
306
313.66
0.976
4
24
351
321.08
1.093
Quarter
1
2
3
4
Total
1.223
1.096
.968
1.095
1.060
.987
.944
.988
.977
.884
.890
.987
.986
.887
.830
1.039
1.040
.944
.968
1.105
1.108
.983
.976
1.093
1.066
.964
.929
1.051
4.010
20.28 Regression line:
y
ˆ
= 145 + 1.66 t
Week
Day
Period t
y
y
ˆ
=145+1.66t
yy ˆ
/
1
1
1
240
146.66
1.636
2
2
85
148.32
0.573
3
3
93
149.98
0.620
4
4
106
151.64
0.699
5
5
125
153.3
0.815
6
6
188
154.96
1.213
7
7
314
156.62
2.005
2
1
8
221
158.28
1.396
2
9
80
159.94
0.500
3
10
75
161.6
0.464
4
11
121
163.26
0.741
5
12
110
164.92
0.667
6
13
202
166.58
1.213
7
14
386
168.24
2.294
3
1
15
235
169.9
1.383
2
16
86
171.56
0.501
3
17
74
173.22
0.427
4
18
100
174.88
0.572
5
19
117
176.54
0.663
6
20
205
178.2
1.150
7
21
402
179.86
2.235
4
1
22
219
181.52
1.206
2
23
91
183.18
0.497
3
24
102
184.84
0.552
4
25
89
186.5
0.477
5
26
105
188.16
0.558
6
27
192
189.82
1.011
7
28
377
191.48
1.969
Day
Week
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Total
1
1.636
.573
.620
.699
.815
1.213
2.005
2
1.396
.500
.464
.741
.667
1.213
2.294
3
1.383
.501
.427
.572
.663
1.150
2.235
4
1.206
.497
.552
.477
.558
1.011
1.969
1.405
.518
.516
.657
.676
1.187
2.126
7.085
Year
Quarter
t
y
y
ˆ
=90.4 + 2.02t
yy ˆ
/
1
1
1
106
92.42
1.147
2
2
92
94.44
0.974
3
3
65
96.46
0.674
4
4
121
98.48
1.229
2
1
5
115
100.5
1.144
2
6
100
0.975
3
7
73
0.698
4
8
135
1.267
3
1
9
114
1.050
2
105
110.6
0.949
3
79
0.701
4
1
121
1.037
2
111
0.935
3
82
120.7
0.679
4
163
1.328
Quarter
Year
1
2
3
4
Total
1
1.147
.974
.674
1.229
2
1.144
.975
.698
1.267
3
1.050
.949
.701
1.221
4
1.037
.935
.679
1.328
1.095
.959
.688
1.261
Index
1.094
.958
.688
1.260
20.30
1259994949
=++++=
20.31 Model 1:
Model 2:
625.
4
5.2
4
9.12.1.3.
4
5.74.91.73.77.66.63.60.6
MAD
==
+++
=
−+−+−+−
=
Model 2 is more accurate.
Model 2 is more accurate.
20.32
60707175867072606357
MAD
−+−+−+−+−
=
20.33 Technique 1:
0.2
5
10
5
31132
5
35383132292827242119
MAD
==
++++
=
−+−+−+−+−
=
Technique 3:
5
39383132252820241719
MAD
−+−+−+−+−
=
20.34
Quarter
t
ty 3150
ˆ+=
SI
Forecast
1
41
273
.7
191.1
2
42
3
43
279
418.5
4
44
282
.6
169.2
20.35
Day
t
ty 3.2120
ˆ+=
SI
Forecast
Sunday
29
186.7
1.5
280.1
Monday
30
31
191.3
Wednesday
32
193.6
116.2
Thursday
33
195.9
137.1
34
198.2
Saturday
35
200.5
1.9
381.0
20.36
5.540)65(3.16253.1625
ˆ
1
=−=−=
−t
yt
y
20.39
Day
t
ty 366.8.16
ˆ+=
SI
Forecast
1
21
24.49
.675
16.53
2
22
24.85
3
23
25.22
4
24
25.58
31.01
5
25
25.95
20.40
Quarter
t
ty 06.17.47
ˆ−=
SI
Forecast
1
21
25.44
1.207
30.71
2
22
24.38
23.38
3
23
23.32
22.67
4
24
22.26
19.21
20.41
Quarter
t
ty 18.175.61
ˆ+=
SI
Forecast
1
17
81.81
0.839
68.64
2
18
82.99
1.058
87.80
3
19
84.17
1.270
4
20
85.35
0.833
71.10
1
21
86.53
0.839
72.60
2
22
87.71
1.058
92.80
3
23
88.89
1.270
4
24
90.07
0.833
75.03
20.44
Quarter
t
ty 42.7143
ˆ+=
SI
Forecast
1
25
1.063
2
26
4
28
1.048
20.45
Day
t
ty 66.1145
ˆ+=
SI
Forecast
1
29
193.14
1.404
271.17
2
30
194.80
0.517
100.71
3
31
196.46
0.515
101.18
4
32
198.12
0.621
123.03
5
33
199.78
0.675
134.85
6
34
201.44
1.145
230.65
7
35
203.10
2.123
431.18
20.46
Day
t
ty 02.24.90
ˆ+=
SI
Forecast
1
17
124.74
1.094
136.47
2
18
126.76
0.958
121.44
3
19
128.78
0.688
88.60
4
20
130.80
1.260
164.81
20.47
20.48 There is a small upward trend and seasonality.
20.50
20.51
Quarter
t
ty 732.21.20
ˆ+=
SI
Forecast
1
21
35.58
0.646
23.00
2
22
36.31
1.045
37.95
1
2
3
A B
Seasonal Indexes
Season Index
40
50
60
20.52a
b.
Period Month
y
ˆ
= 16.34-.1008t Seasonal Index Forecasts Actual
61 January 10.19 .7192 7.33 2.2
62 February 10.09 .6729 6.79 3.6
63 March 9.99 .8936 8.93 5.3
c. MAD = 4.47
SSE = 254.32