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Table 3.1 Sales data for products A–E
Quarter
A
B
C
D
E
1
98
45
64
21
23
2
58
21
45
23
14
3
23
36
21
31
56
4
43
21
14
30
78
1
89
49
27
35
27
2
52
20
40
40
20
3
24
43
58
37
67
4
34
21
76
40
89
1
81
53
81
42
34
2
49
27
93
39
30
3
16
49
84
42
73
4
29
30
70
46
83
1
74
60
57
42
43
2
36
28
45
34
32
3
17
52
43
45
85
4
26
34
34
54
98
1
67
68
29
53
50
2
34
34
36
37
36
3
18
64
51
49
101
4
25
41
65
60
123
1
68
73
72
67
63
2
29
42
81
40
46
3
20
73
93
57
125
4
24
53
98
74
146
thousands of dollars
is based on a yearly time frame is referred to as seasonality , due to the data’s
variation with the seasons of the year.
3. The one quarter difference between A and E (phase difference) can be explained
as E leading A by a period. For example, E peaks in quarter 4 of the ﬁrst year
and A peaks in quarter 1 of the second year, thus the peak in E leads A by one
quarter. The quarterly lead appears to be exactly one period for the entire six year
horizon.
4. Product E seems to behave differently in the last three years of the series by
displaying a general tendency to increase. We call this pattern trend , and in this
case, a positive trend over time. We will, for simplicity’s sake, assume that this
is linear trend ; that is, it increases or decreases at a constant rate. For example,
a linear trend might increase at a rate of 4,000 dollars per quarter.
5. There are numerous other features of the data that can and will be identiﬁed later.
We must be careful not to extend the ﬁndings of our visual analysis too far.
Presuming we know all there is to know about the underlying behavior reﬂected
in the data without a more formal analysis can lead to serious problems. That is
precisely why we will apply more sophisticated data analysis once we have visually
inspected the data.

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