Question

Consider the following time series data (Insert the data in an Excel file):

Quarter Year 1 Year 2 Year 3

1 8 9 12

2 5 6 9

3 7 8 10

4 8 11 11

2.1. Construct a time series plot. What type of pattern exists in the data?

2.2. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1=1 if quarter 1, 0 otherwise; Qtr2=1 if quarter 2, 0 otherwise; Qtr3=1 if quarter 3, 0 otherwise. 2.3. Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part 2.2 to capture seasonal effects and create a variable t such that t =1 for quarter 1 in year 1, t =2 for quarter 2 in year 1, . . . t =12 for quarter 4 in year 3.

2.4. Calculate MSE for both models. Which model (2.2 or 2.3) is more accurate? Why?

2.5. Forecast the time series for Year 4, Quarters 1, 2, 3, 4.

Answer #1

**Answer:**

1. The time series plot is:

Horizontal pattern with seasonality

2. y = 10 - 0.333*Qtr 1 - 3.333*Qtr 2 - 1.667*Qtr 3

3. y = 6.5 + 0.979*Qtr 1 - 2.458*Qtr 2 - 1.229*Qtr 3 + 0.438*t

4.

2.2 | 2.3 | |

MSE | 3.5000 | 0.5000 |

2.3 is more accurate because it has a lower MSE value.

5.

Forecast |

13.167 |

10.167 |

11.833 |

13.5 |

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Consider the following time series data.
Quarter
Year 1
Year 2
Year 3
1
4
6
7
2
2
3
6
3
3
5
6
4
5
7
8
Use a multiple regression model with dummy variables as follows
to develop an equation to account for seasonal effects in the data.
Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0
otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round
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Quarter
Year 1
Year 2
Year 3
1
2
4
5
2
4
5
8
3
1
3
4
4
7
9
10
(a)
Choose the correct time series plot.
(i)
(ii)
(iii)
(iv)
- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item
1
What type of pattern exists in the data?
- Select your answer -Positive trend pattern, no
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pattern, no seasonalityPositive trend pattern, with
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Quarter
Year 1
Year 2
Year 3
1
2
5
7
2
0
2
6
3
5
8
10
4
5
8
10
(a)
Choose the correct time series plot.
(i)
(ii)
(iii)
(iv)
Plot (iii)- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot
(iv)Item 1
What type of pattern exists in the data?
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(b) Use a multiple regression model with dummy variables as
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Quarter
Year 1
Year 2
Year 3
1
71
68
62
2
48
40
50
3
59
61
54
4
78
81
72
(a) Construct a time series plot.
What type of pattern exists in the data?
a)The time series plot shows a horizontal pattern, but there is
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b)The time series plot shows a horizontal pattern with no
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Quarter
Year 1
Year 2
Year 3
1
71
68
62
2
50
42
52
3
59
61
54
4
78
81
72
(a)
Construct a time series plot.
What type of pattern exists in the data?
The time series plot shows a horizontal pattern, but there is
also a seasonal pattern in the data.
The time series plot shows a trend pattern, but there is also a
seasonal pattern in the data.
The...

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Quarter
Year 1
Year 2
Year 3
1
71
68
62
2
49
41
51
3
57
59
52
4
78
81
72
(a) Use the following dummy variables to develop an
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x1 = 1 if quarter 1, 0 otherwise;
x2 = 1 if quarter 2, 0 otherwise;
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= _____?______
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Quarter
Year 1
Year 2
Year 3
1
72
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2
49
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51
3
58
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4
77
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Year 1
Year 2
Year 3
1
923
1,112
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2
1,056
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1,301
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1,124
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992
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Year
Quarter
Sales ($000)
2015
1
$400
2015
2
2,000
2015
3
3,500
2015
4
260
2016
1
740
2016
2
2,720
2016
3
4,900
2016
4
520
2017
1
1,500
2017
2
3,100
2017
3
6,520
2017
4
960
2018
1
1,840
2018
2
4,040
2018
3
7,680
2018
4
1,640
2019
1
3,520
2019
2
5,640
2019
3
8,900
2019
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3,620
Problem
2
House Depot’s quarterly sales of a lawn, landscaping, and
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