Consider the following time series: Quarter Year 1 Year 2 Year 3 69 66 60 44 36 46 60 62 55 4 79 82 73 (a) Choose a time series plot. (1) 100 80 60 40 20 0 ++ + 1 2 3. 4 6 7 Period (t) 10 11 12 (ii) 100 80 60 40 20 4 5 6 9 10 11 12

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 67E
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Consider the following time series:
Quarter Year 1 Year 2 Year 3
1
69
66
60
2
44
36
46
3
60
62
55
4
79
82
73
(a) Choose a time series plot.
(i)
100
80
60
40
20
3.
4
6
7
Period(t)
9
10
11
12
(ii)
100
80
60
40
20
1 2
3.
4
6
7
Period (t)
10
11
12
Transcribed Image Text:Consider the following time series: Quarter Year 1 Year 2 Year 3 1 69 66 60 2 44 36 46 3 60 62 55 4 79 82 73 (a) Choose a time series plot. (i) 100 80 60 40 20 3. 4 6 7 Period(t) 9 10 11 12 (ii) 100 80 60 40 20 1 2 3. 4 6 7 Period (t) 10 11 12
Graph (ii)
What type of pattern exists in the data? Is there an indication of a seasonal pattern?
Horizontal pattern, with seasonality
(b) Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtri = 1 if quarter 1, 0 otherwise; Qtrz = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0
otherwise. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Qtri
O Otrz +
O Qtr3
(c) Compute the quarterly forecasts for next year.
Year Quarter
Ft
4
1
4
4
3
4
4
Transcribed Image Text:Graph (ii) What type of pattern exists in the data? Is there an indication of a seasonal pattern? Horizontal pattern, with seasonality (b) Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtri = 1 if quarter 1, 0 otherwise; Qtrz = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Qtri O Otrz + O Qtr3 (c) Compute the quarterly forecasts for next year. Year Quarter Ft 4 1 4 4 3 4 4
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