The following table contains the past 20 weeks package data.

Week	Packages
1	525
2	565
3	625
4	630
5	755
6	795
7	805
8	795
9	825
10	900
11	875
12	995
13	1055
14	1185
15	1175
16	1215
17	1305
18	1385
19	1405
20	1475

Part 1:

First, use a 3-week simple moving average to forecast the number of packages for weeks 4 to 21. Compute the Mean Absolute Deviation (MAD) and the Mean Square Error (MSE) of the forecasts for weeks 4 to 20.

Recent data, you believe, have more useful information than earlier data. Use a 3-week weighted average method for weeks 4 to 21 with weights of 0.7, 0.2, and 0.1 (most recent to least recent). Using the weighted moving average approach, calculate the MAD and MSE of the forecast for weeks 4 to 20.

Using MAD as the measure, compare the performance of the two forecasting methods (moving average and weighted moving average). Which forecasting method is better? (ii) Using MSE as the measure to compare the performance of the two forecasting methods (moving average and weighted moving average), which forecasting method is better?

Part 2:

Using simple exponential smoothing, compute three sets of forecasts for the number of packages for weeks 2 to 21, with values of 0.1, 0.4 and 0.9. Assume the forecast for week 1 is equal to the actual number of packages in week 1.

To visually see the difference between forecasts and actual number of packages, plot the actual number of packages as well as the three simple exponential smoothing forecasts computed in a for weeks 1 to 20 on the same graph. Which value of produces the most responsive forecast? Explain why.

Calculate the MAD and Mean Absolute Percentage Error (MAPE) using the forecast errors for weeks 2-20 for each of the three sets of forecasts created in part (a). Which value seems to be the most appropriate?

Part 3:

Use the double exponential smoothing method to forecast number of packages for weeks 2 to 21, assuming S1 = 525 and T1 = 20. Set = 0.9 and = 0.1.

Create a plot showing the actual number of packages, the double exponential smoothing forecast, and the forecast obtained using simple exponential smoothing in Problem 2 with = 0.9 for weeks 2 to 20 on the same graph.

Compute MAD and MAPE for weeks 2 to 20 for the double exponential smoothing forecast and compare them with MAD and MAPE of the most accurate simple exponential smoothing forecast you identified in problem 2(c). Based on your calculations, is single or double exponential smoothing a better approach in this specific case? Why?

Develop a simple linear regression model using week as the independent variable to forecast the part demand for week 21. Compare this forecast to the forecast obtained in part (a) for number of packages for weeks 2 to 20 using MAD and MAPE. Based on this, explain the difference between the two methods (regression, double exponential smoothing).