Statistics HW
nataliejag
lesson_9-_hw.docxInstructions:
1. Using annual data on GDP from the U.S. Census Bureau complete the following:
a. Use a simple trend projection and discuss the meaning of the estimated coefficient for the trend variable.
b. Assume that you only have data up through 1999 and conduct a 3-period moving average for GDP through 2007. Find the in-sample and out of sample MAE, MAPE, and RMSE using the forecast errors.
c. Conduct a simple exponential smoothing model using α = 0.3 and α = 0.7 using the GDP data set. Again assume that we only have data through 1999.
annual data on GDP from the U.S. Census Bureau
|
DATE |
GDP |
|
1980-01-01 |
2789.5 |
|
1981-01-01 |
3128.4 |
|
1982-01-01 |
3255.0 |
|
1983-01-01 |
3536.7 |
|
1984-01-01 |
3933.2 |
|
1985-01-01 |
4220.3 |
|
1986-01-01 |
4462.8 |
|
1987-01-01 |
4739.5 |
|
1988-01-01 |
5103.8 |
|
1989-01-01 |
5484.4 |
|
1990-01-01 |
5803.1 |
|
1991-01-01 |
5995.9 |
|
1992-01-01 |
6337.7 |
|
1993-01-01 |
6657.4 |
|
1994-01-01 |
7072.2 |
|
1995-01-01 |
7397.7 |
|
1996-01-01 |
7816.9 |
|
1997-01-01 |
8304.3 |
|
1998-01-01 |
8747.0 |
|
1999-01-01 |
9268.4 |
|
2000-01-01 |
9817.0 |
|
2001-01-01 |
10128.0 |
|
2002-01-01 |
10469.6 |
|
2003-01-01 |
10960.8 |
|
2004-01-01 |
11685.9 |
|
2005-01-01 |
12433.9 |
|
2006-01-01 |
13194.7 |
|
2007-01-01 |
13843.8 |
2. Complete the Forecasting for Tracway for mowers using the Tracway data . For this exercise, forecast industry sales as well as market share. Compare the moving average (3 month) method against Winter's method. Since we are forecasting mowers, think about which model you would expect to be more accurate.
After working through the problems, go to Lesson 9: Individual Exercises 9 and answer the associated multiple choice questions.
An important input to planning manufacturing capacity is a good forecast of sales. In reviewing the Tracway database, Henry Hudson is interested in forecasting sales for mowers and tractors in each marketing region. Although Henry has obtained expert opinions on sales forecasting using the Delphi process, he would like to generate time series forecasts for the next year for each product by region. Henry plans to then compare and incorporate the judgmental forecasts from the Delphi process to the quantitative forecasts developed via the Delphi process.
See attached worksheet labeled (Tracway data)
Questions:
Using annual data on GDP from the U.S. Census Bureau answer questions 1-6.
1.
The trend analysis reveals
A) no evidence of any clear trend either upward or downward.
B) an upward trend.
C) an downward trend.
D) a positive but insignificant coefficient for the trend variable.
2.
According to the F-statistic we cannot reject the null hypothesis that R2 = 0 when using trend analysis.
A) True
B) False
3.
When conducting a 3-period moving average for GDP through 2007 the out of sample Mean Absolute Error (MAE) is found to be approximately
A) $682
B) $696
C) $1,043
D) none of the above
4.
The moving average analysis shows forecasts that consistently underestimate actual GDP.
A) True
B) False
5.
When using an exponential smoothing model for α = 0.3, the out of sample MAPE is ____________ and the within sample MAPE is ____________.
A) 21.85%, 11.45%
B) 20.62%, 8.35%
C) 27.83%, 16.29%
D) none of the above
6.
The exponential smoothing forecast is more accurate at α = 0.7 than at α = 0.3.
A) True
B) False
Complete the Forecasting for Tracway for mowers and answer questions 7-12.
7.
Using the 3 month moving average for industry sales, which region is found to have the smallest MAE?
A) North America
B) South America
C) Europe
D) Pacific
8.
Using Winter’s method for industry sales, which region is found to have the smallest RMSE?
A) North America
B) South America
C) Europe
D) Pacific
9.
The MAPE reveals that the average forecast misses the target by 3.00% using Winter’s method in South America for industry sales.
A) True
B) False
10.
Which statement most accurately reflects the meaning of the optimal smoothing constants found for industry sales in South America and Europe?
A) The model misses the target by 1.00% using Winter’s method.
B) The model reacts slowly to changes in level, but quickly to trend and season for Winter's method.
C) The model reacts right away to changes in level, but almost never reacts to trend for Winter's method.
D) none of the above
11.
Market share forecast errors are all smaller in comparison to sales which makes sense because one would not expect any region to have significant gains or losses in market share over the course of the 12 months forecasted in the models.
A) True
B) False
12.
The regional sectors forecast for industry sales and market share are better using Winter's method which can be seen by the results for MAE and MAPE.
A) True
B) False
