Consider the following time series data.

Week	1	2	3	4	5	6	7
Value	25	14	22	13	20	23	16

(a)

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

The data appear to follow a cyclical pattern.The data appear to be stationary. The data appear to follow a trend pattern.The data appear to follow a seasonal pattern.

(b)

Develop 3-week moving average forecasts for this time series. (Round your answers to two decimal places.)

Week	Time Series Value	Forecast
1	25
2	14
3	22
4	13
5	20
6	23
7	16

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 8? (Round your answer to two decimal places.)

(c)

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

Week	Time Series Value	Forecast
1	25
2	14
3	22
4	13
5	20
6	23
7	16

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 8? (Round your answer to two decimal places.)

(d)

Compare the three-week moving average forecast with the exponential smoothing forecast using

= 0.2.

Which appears to provide the better forecast based on MSE?

The exponential smoothing using = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average.The three-week moving average provides a better forecast since it has a smaller MSE than the exponential smoothing using = 0.2. The three-week moving average provides a better forecast since it has a larger MSE than the exponential smoothing using = 0.2.The exponential smoothing using = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average.

(e)

Use trial and error (try different values of alpha) to find a value of the exponential smoothing coefficient (with 2 decimal places) that results in a smaller MSE than what you calculated for = 0.2.

=