three statistics questions on forecast

1. Determine the error for each of the following forecasts. Compute 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

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).

a. Use these data to develop forecasts for the years 6 through 13 using a 5-year moving average.

b. Use these data to develop forecasts for the 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.

c. Compute the errors of the forecasts in parts (a) and (b) and then the MAD. Which forecast is better?

Year Factory Orders ($ billion)
1 2,512.7

2
2,739.2

3
2,874.9

4
2,934.1

5
2,865.7

6
2,978.5

7
3,092.4

8
3,356.8

9
3,607.6

10
3,749.3

11
3,952.0

12
3,949.0

13
4,137.0

3. The “Economic Report to the President of the United States” included data on the amounts of manufacturers’ new and unfi lled orders in millions of dollars. Shown here are the fi gures for new orders over a 21-year period. Use Excel to develop a regression model to fi t the trend effects for these data. Use a linear model and then try a quadratic model. How well does either model fi t the data?

Year Total Number of New Orders
1 55,022

2
55,921

3
64,1 82

4
76,003

5
87,327

6
85,139

7
99,513