Refer to the gasoline sales time series data in the given table. a. Compute four
ID: 368954 • Letter: R
Question
Refer to the gasoline sales time series data in the given table.
a. Compute four-week and five-week moving averages for the time series. Round your answers to two decimal places.
b. Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations and final answers to two decimal places.
MSE for four-week moving average = ____?______
MSE for five-week moving average = ____?______
c. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 7.5.
Answer: three/ four/ five?
Week Sales (1000s of gallons) 1 17 2 22 3 19 4 22 5 19 6 16 7 22 8 19 9 21 10 19 11 16 12 22Explanation / Answer
First, let us compute the 4 and 5 period moving averages:
A sample calculation: For example, the 1st 4 week moving average, which is 20, is given by adding up the previous four sales figures and dividing by 4
That is, (17+22+22+19)/4 = 20
Similarly, the next value is given by taking the average of the previous 4 entries.
For the 5 period average, we simply take the sum of the previous 5 entries and divide by 5.
Now, let us get to the MSE (Mean Squared Error)
The column I have added as MSE4 and MSE5 calculate the Squared Errors for the 4 and 5 week period.
The way to calculate squared error is simple: (Actual Sales - Moving Average)2
To calculate the MSE, simply take the average of all the squared errors.
We thus get:
MSE (4 week moving average) = 7.96
MSE (5 week moving average) = 5.86
Note that the one with the lower MSE is the better method as this has lower error.
Hence, the 5 week moving average is the best method. We should take 5 weeks to calculate the moving average as it has the least MSE.
Week Sales 4-Week 5-Week Moving Average Moving Average MSE4 MSE5 1 17 2 22 3 19 4 22 5 19 20 1 6 16 20.5 19.8 20.25 14.44 7 22 19 19.6 9 5.76 8 19 19.75 19.6 0.5625 0.36 9 21 19 19.6 4 1.96 10 19 19.5 19.4 0.25 0.16 11 16 20.25 19.4 18.0625 11.56 12 22 18.75 19.4 10.5625 6.76Related Questions
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