Question

The following time series shows the sales of a particular product over the past 12 months.

Month	Sales
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

(a)

Construct a time series plot.

A time series plot contains a series of 12 points connected by line segments. The horizontal axis ranges from 0 to 13 and is labeled: Month. The vertical axis ranges from 0 to 160 and is labeled: Sales. The points are plotted from left to right at regular increments of 1 month starting at month 1. The points appear to vary randomly between 60 and 125 on the vertical axis. The maximum number of sales is reached at the point (6, 125).

What type of pattern exists in the data?

The data appear to follow a horizontal pattern.

The data appear to follow a cyclical pattern.  

   The data appear to follow a trend pattern.

The data appear to follow a seasonal pattern.

(b) Use α = 0.2 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)

Month t	Time Series Value Yt	Forecast Ft
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

(c) Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts. (Round your answers to two decimal places.)

Month t	Time Series Value Yt	Forecast Ft
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

Answer 1