Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	23	13	20	12	18	21	16

(a)	Choose the correct time series plot.
(i)
(ii)
(iii)
(iv)

- Select your answer -Graph (i)Graph (ii)Graph (iii)Graph (iv)Item 1

What type of pattern exists in the data?

- Select your answer -Positive trend patternHorizontal patternVertical patternNegative trend patternItem 2

(b)

Develop a three-month moving average for this time series. Compute MSE and a forecast for month 8.

If required, round your answers to two decimal places. Do not round intermediate calculation.

MSE:

The forecast for month 8:

(c)

Use= 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8.

If required, round your answers to two decimal places. Do not round intermediate calculation.

MSE:

The forecast for month 8:

(d)

Compare the three-month moving average forecast with the exponential smoothing forecast using= 0.2. Which appears to provide the better forecast based on MSE?

- Select your answer -3-month moving averageexponential smoothingItem 7

(e)

Use trial and error to find a value of the exponential smoothing coefficientthat results in the smallest MSE.

If required, round your answer to two decimal places.

=