Question

Consider the following gasoline sales time series data. Click on the datafile logo to reference the data. Week Sales (1000s of gallons) 1     17    2     20    3     19    4     23    5     18    6     16    7     19    8     18    9     23    10     19    11     15    12     22    a. Using a weight of  for the most recent observation,  for the second most recent observation, and  third the most recent observation, compute a three-week weighted moving average for the time series (to 2 decimals). Enter negative values as negative numbers. Week Time-Series Value Weighted Moving Average Forecast Forecast Error (Error)2 Total b. Compute the MSE for the weighted moving average in part (a). MSE = Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is . Prefer the unweighted moving average here; it has a - Select your answer -greatersmallerItem 42 MSE. c. Suppose you are allowed to choose any weights as long as they sum to . Could you always find a set of weights that would make the MSE at least as small for a weighted moving average than for an unweighted moving average? - Select your answer -YesNoItem 43

Answer 1

a)

week	sales	forecast	error	error^2
1	17
2	20
3	19
4	23	19.00	4.00	16.00
5	18	21.17	-3.17	10.03
6	16	19.83	-3.83	14.69
7	19	17.83	1.17	1.36
8	18	17.83	0.17	0.03
9	23	18.00	5.00	25.00
10	19	20.67	-1.67	2.78
11	15	20.17	-5.17	26.69
12	22	17.67	4.33	18.78
			total	115.36

b)

MSE =12.82

it has a smaller MSE
c)

Yes