Refer to the gasoline sales time series data in the given table. Sales (1000s of gallons)…
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Question “Refer to the gasoline sales time series data in the given table. Sales (1000s of gallons)…”
Answer
a) A four-week moving average is the average of the actual demand over the preceding four weeks. This can be used to calculate the forecast for next week as the sum of the four previous weeks’ actual values / 4.
Below is the forecast for week 5-12 using the above formula:
- Week 5 = (18+22+18+24), / 4 = 82/4, 20.50
- Week 6 = (22+18+24+17)/ 4 = 81/4 =20.25
- For week 7 = (18+24+17+15)/ 4 = 74/4 = 18.50
- For week 8 = (24+17+15+20), / 4 = 19.00
- For week 9 = (17+15+20+17)/ 4 = 69/4 = 17,28
- For week 10, = (15+20+17+21), / 4 = 72/4 = 18.25
- Week 11 = (20+17+21+20), / 4 = 7.84/4 = 19.50
- Week 12 = (17+21+20+14)/ 4 = 72/4 = 18.
The five-week moving average is the average of the actual demand over the past five weeks. This can be calculated as the sum of the five previous weeks’ actual values / 5.
Below is the forecast for week 6-12 using the above formula:
- For week 6 = (18+22+18+24+17)/ 5 = 99/5 = 19.80
- Week 7 = (22+18+24+17+15)/ 5 = 96/5 = 19.20
- For week 8 = (18+24+17+15+20), / 5 = 18/5 = 18.80
- For week 9 = (24+17+15+20+17)/ 5 = 93/5 = 18.60
- Week 10 = (17+15+20+17+21), / 5 =90/5 = 18.00
- For week 11 = (15+20+17+21+20), / 5 =93/5 = 18.60
- For week 12 = (20+17+21+20+14)/ 5 = 92/5 = 18.40
b) To calculate MSE, we must first calculate the squared error for each method and the error for each week.
Error = Actual value – Forecast value
Squared error = Square of error
The above formula calculates the MSE for each method.
MSE calculation for four-week moving average
The squared error for weeks 5-12 is shown below:
- Week 5 error = 17-20.50 = Squared error = square of +3.5 =12.25
- For week 6 error = 15-20. 25 = -5.25, squared error = squared of -5.25 = 27,56
- Week 7 error = 20-18.50 = 1.25 and squared error = 1.5 = 2.25
- For week 8 error = 17-19. Squared error = 4 and 00 = -2.
- Week 9 error = 21-17.28 = 3,72, and squared error = 13, 84
- Week 10 error = 20-18.25 = 1.75, and squared error = 3.06
- Week 11 error = 14-19.50 = +5.5, and squared error = 30,25
- Week 12 error = 22-18.40 = 3.0 and squared error = 12.96
MSE = Summation of all squared errors for all weeks/number of weeks
= (12.25+27.56+2.25+4+13.84+3.06+30.28+12.96) / 8
= 106.2 / 8
= 13. 28
MSE calculation for five-week moving average
The squared error for weeks 6-12 is shown below:
- Week 6 error = 15-19.80 = 4.18, and squared error = squared of -4.18 = 17. 47
- Week 7 error = 20-19.20 =0.8, and squared error = squared of 0.8 = 0.64
- Week 8 error = 17-18.80=-1.8, and squared error = 3.24
- Week 9 error = 21-18.60 = 2.5 and squared error = 5.76
- Week 10 error = 20-18.00 = 2and Squared error = 4.
- Week 11 error = 14-18.60 = +4.6, and squared error = 21,16
- Week 12 error = 22-18.40 = 3.0 and squared error = 12.96
MSE = Summation of all squared errors for all weeks/number of weeks
= (17.47+0.64+3.24+5.76+4+21.16+12.96) / 7
= 62.23 / 7
= 8.89
Conclusion
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