(a) Compute four-week and five-week moving averages for the time series. If required, round your answers to two decimal places. Week Sales 4 Period Moving Average 5 period Moving Average 1 18 2 22 3 15 4 24 5 18 6 15 7 21 8 19 9 21 10 20 11 16 12 22 (b) Compute the MSE for the four-week and five-week moving average forecasts. If required, round your final answers to three 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? Consider that the MSE for the three-week moving average is 10.086.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Refer to the gasoline sales time series data in the given table.
| Week | Sales (1,000s of gallons) |
| 1 | 18 |
| 2 | 22 |
| 3 | 15 |
| 4 | 24 |
| 5 | 18 |
| 6 | 15 |
| 7 | 21 |
| 8 | 19 |
| 9 | 21 |
| 10 | 20 |
| 11 | 16 |
| 12 | 22 |
| (a) | Compute four-week and five-week moving averages for the time series. | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| If required, round your answers to two decimal places. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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| (b) | Compute the MSE for the four-week and five-week moving average forecasts. | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| If required, round your final answers to three 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? Consider that the MSE for the three-week moving average is 10.086. |
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