# Mathematics

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

Then, 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.

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

(\$ billion)

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 3,555.00

11 4,221.50

12 4,551.20

13 4,137.00

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 these 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

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