Question

A statistical program is recommended.

Consider the following time series.

Quarter	Year 1	Year 2	Year 3
1	72	69	63
2	49	41	51
3	58	60	53
4	77	80	71

(a)

Construct a time series plot.

• A time series plot contains a series of 12 points connected by line segments.
• The horizontal axis is labeled: Year/Quarter. There are 12 tick marks on the horizontal axis which have been divided up into 3 groups of 4 tick marks. The groups are labeled, from left to right: Year 1, Year 2, Year 3. For each year, the individual tick marks are labeled, from left to right: 1, 2, 3, 4.
• The vertical axis ranges from 0 to 90 and is labeled: Time Series Value.
• The points are plotted from left to right in increments of 1 starting at the tick mark labeled 1 in the group Year 1 and appear to vary randomly between approximately 40 to 80 on the vertical axis. For each year, the highest point occurs above the tick mark labeled 1, and the lowest occurs above the tick mark labeled 3.

(b)

Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data:

x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x₃ = 1 if quarter 3, 0 otherwise.

=

(c)

Compute the quarterly forecasts for next year.

quarter 1 forecast

quarter 2 forecast

quarter 3 forecast

quarter 4 forecast

Answer 1

a)

b)

regress y on Q1,Q2 and Q3

y^ = 76 - 8 Q1 - 29 Q2 - 19 Q3

c)

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