Question 1 - Determine the error for each of the following forecasts. Then, calculate MAD and MSE.

Period                          Value                           Forecast                                   Error

1                                  202                              -                                            -

2                                  191                              202

3                                  173                              192

4                                  169                              181

5                                  171                              174

6                                  175                              172

7                                  182                              174

8                                  196                              179

9                                  204                              189

10                                219                              198

11                                227                              211

Question 2 - The U.S. Census Bureau publishes data on factory orders for all manufacturing, durable goods, and nondurable goods industries. Shown here are factory orders in the United States over a 13-year period ($ billion). First, use the data to develop forecasts for years 6 through 13 using a 5-year moving average.

Then, use the data to develop forecasts for years 6 through 13 using a 5-year weighted moving average. Weight the most recent year by 6, the previous year by 4, the year before that by 2, and the other years by 1.

Answer the following questions:

a) What is the forecast for year 13 based on the 5-year moving average?

b) What is the forecast for year 13 based on the 5-year weighted moving average?

c) What is the MAD for the moving average forecast?

d) What is the MAD for the weighted moving average forecast?

e) Which forecasting model is better?

Year                            Factory

Orders

1                                  2,512.70

2                                  2,739.20

3                                  2,874.90

4                                  2,934.10

5                                  2,865.70

6                                  2,978.50

7                                  3,092.40

8                                  3,111.10

9                                  3,222.20

10                                3,341.00

11                                3,689.00

12                                3,654.00

13

Question 3 - The "Economic Report to the President of the United States" included data on the amounts of manufacturers' new and unfilled orders in millions of dollars. Shown here are the figures for new orders over a 21-year period.

Use the charting tool in Excel to develop a regression model to fit the trend effects for the data. Use a linear model and then try a polynomial (order 2) model. Make sure the charts show the line formula and the r-squared value. Include both charts in your report. Then, answer the following question:

?How well does either model fit the data? Which model should be used for forecasting? Explain using the relevant metrics.

Year                            Total Number of New Orders

1                                  55,022

2                                  55,921

3                                  64,182

4                                  76,003

5                                  87,327

6                                  85,139

7                                  99,513

8                                  115,109

9                                  116,251

10                                121,547

11                                123,321

12                                141,200

13                                162,140

14                                168,420

15                                171,250

16                                176,355

17                                195,204

18                                209,389

19                                237,025

20                                272,544

21                                293,475