QM 622 Exam II

User Generated

Puevfdjreglhvbc

Mathematics

Description

QM 662 Exam II

  • The table below features three forecasting models used on the same set of data.

HI,BRO, i will put some homework template later, you can refer to it.

QM 622 Exam II is this homework.

Unformatted Attachment Preview

QM 662 Exam II 1. The table below features three forecasting models used on the same set of data. Model 1 Model 2 Model 3 Type Exponential Smoothing Regression Seasonal & Trend MSE 8755.3 4876.2 5945.8 Based solely on the information in this output, which of the following is the best answer? (5) a. b. c. d. e. The data set contains no trend or seasonality. The data set contains trend but no seasonality. The data set contains seasonality but no trend. The data set probably contains cyclicality. The data set contains both trend and seasonality. 2. In a forecasting application for 20 time periods, there are 10 negative errors and 10 positive errors. This indicates the model is performing well. (2) a. True b. False 3. Refer to the following graph: Quarterly Sales (in $) 70000 60000 50000 40000 30000 20000 10000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Which of the following apply? (8) a. b. c. d. The data contain a trend component. The data contain a seasonal component. The data ,contain a cyclical component. The data contain an irregular (random) component. 4. In #3, which method (if any) is most appropriate? (4) a. b. c. d. Exponential smoothing. Regression. Regression with seasonal indices. None of the above. 5. In #3, which of the following is most appropriate regarding sales? (4) a. b. c. d. e. We should use all of the data in our model. We should use only periods 5-16 in our model. We should use only periods 9-16 in our model. We should use only periods 13-16 in our model. We should use only periods 1-12 in our model. 6. Refer to the Excel output on the final pages. Here, we are tracking the number of orders placed by week for a 20-week period. The first set of output is for an exponential smoothing model with α = 0.25. The second set of output is for a regression. Which of the following is most appropriate? (3) a. The exponential smoothing model is most appropriate. b. The regression is most appropriate. c. Another model would be more appropriate. 7. The model with the lower MSE is always the most appropriate model. (2) a. True b. False 8. In a given application, we are using regression with seasonal indices. The regression model is y = 42 + 2.5t. The seasonal indices for quarters 1-4 are 0.85, 0.92, 0.98, and 1.25, respectively. The predicted value for period 20 is ___________. (5) 9. If our data contains seasonality but no trend, exponential smoothing is appropriate. (2) a. True b. False 10. Annual data can exhibit seasonality. (2) a. True b. False 11. We can assess quarterly seasonality with one year of data. (2) a. True b. False Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Orders 45 56 65 63 54 60 54 60 56 57 50 61 47 56 55 Forecast #N/A 45 47.75 52.0625 54.79688 54.59766 55.94824 55.46118 56.59589 56.44691 56.58519 54.93889 56.45417 54.09063 54.56797 Error #N/A 11 17.25 10.9375 -0.79688 5.402344 -1.94824 4.538818 -0.59589 0.553085 -6.58519 6.06111 -9.45417 1.909375 0.432031 Error^2 121 297.5625 119.6289 0.63501 29.18532 3.795648 20.60087 0.35508 0.305903 43.36467 36.73706 89.38128 3.645712 0.186651 16 17 18 19 20 52 57 58 61 47 54.67598 54.00698 54.75524 55.56643 56.92482 -2.67598 2.993017 3.244763 5.433572 -9.92482 7.160852 8.958153 10.52849 29.52371 98.50207 MSE = 48.47673 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.139263 0.019394 -0.03508 5.524367 20 ANOVA df 1 18 19 SS 10.86466 549.3353 560.2 Coefficients 57.04211 -0.12782 Standard Error 2.566242 0.214226 Regression Residual Total Intercept Week MS 10.86466 30.51863 F 0.356001 t Stat 22.22787 -0.59666 P-value 1.54E-14 0.558166 Exponential Smoothing 70 60 Orders 50 40 30 Actual 20 Forecast 10 0 1 3 5 7 9 11 13 15 17 19 Week Significance F 0.558166112 Data for Samantha's Super Sectional Sofas Quarter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 %Defective 7,31 6,19 7,44 6,61 7,33 7,43 6,74 7,35 6,86 11,40 6,08 6,65 8,24 7,33 6,27 7,03 7,52 7,80 7,21 7,23 7,27 6,92 7,55 7,75 Note: These data represent her percentage of defective units produced for each quarter. Data for Colleen's Cajun Cannery Week 1 2 3 4 5 6 7 8 9 10 11 12 13 # OT Hours 13 16 18 17 19 21 23 22 25 29 34 42 55 Note: These data represent her weekly number of overtime hours used. Simpson's Inc. Quarter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 # of rolls ordered 56 48 58 67 59 51 64 71 73 67 78 84 77 70 82 89 83 74 84 93 86 78 85 93 Note: Simpson's produces nonwoven fabric rolls. Sally's Sensational Stationery Sales Data Quarter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Sales 6455 8779 13897 18920 24225 26190 27440 37562 29895 29120 28540 39985 33255 32110 30875 41234 36476 34860 32197 43940 39723 37890 35230 46115 41432 39243 36922 Note: The sales figures are in dollars. Data for Upper Flutzland Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 GDP 62,6 66,7 68,8 64,5 63,2 55,6 54,5 63,8 65,3 67,4 65,9 78,9 80,8 81,3 82,5 Note: These data are the real GDP (in $000,000,000) indexed to Year 1 dollars. Forecasting Homework 1. For each of the five worksheets on here, answer the following: a. What forecasting method is most appropriate? Explain. b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data). c. What is your recommendation regarding future forecasts? 2. Discuss at least two potential application of forecasting in your job or field. es it fit the data). Forecasting Homework 1. For each of the five worksheets on here, answer the following: a. What forecasting method is most appropriate? Explain. b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data). c. What is your recommendation regarding future forecasts? 2. Discuss at least two potential applications of forecasting in your job or field. 1. Forecasting monthly registrations in the Commercial Vehicle Training Program and other program areas that have regularly s 2. Forecasting quarterly registrations in all program areas (our Continuing Ed catalogs and "terms" are set up quarterly) 3. Forecasting expense budgets of consumable supplies in large program areas with significant consumable material costs (for (comments are also made on some of the five worksheets) r program areas that have regularly scheduled monthly classes icant consumable material costs (for "instructional/student supplies) Data for Samantha's Super Sectional Sofas 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 %Defective 7.31 6.19 7.44 6.61 7.33 7.43 6.74 7.35 6.86 11.40 6.08 6.65 8.24 7.33 6.27 7.03 7.52 7.80 7.21 7.23 7.27 6.92 7.55 7.75 % Defective Scatterplot % Defective Quarter y = 0.0129x + 7.1518 R² = 0.008 12.00 10.00 8.00 6.00 4.00 2.00 0.00 Series1 Linear (Series1) 0 5 10 15 20 25 30 Quarter Note: These data represent her percentage of defective units produced for each quarter. Excel Single Parameter Exponential Smoothing - EXAMPLE FOR COMPARISON WITH…… a = 0.10 Period=Quarter Excel Damping Factor = 1 - α (1 - .10 = .90) Period Percent % Forecast Defective, Yt Sales, Ft t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 7.31 6.19 7.44 6.61 7.33 7.43 6.74 7.35 6.86 11.40 6.08 6.65 8.24 7.33 6.27 7.31 7.20 7.22 7.16 7.18 7.20 7.16 7.18 7.14 7.57 7.42 7.34 7.43 7.42 Management Scientist FORECASTING WITH EXPONENTIAL SMOOTHING ************************************** THE SMOOTHING CONSTANT IS 0.1 Forecast Error -1.12 0.24 -0.61 0.17 0.25 -0.46 0.19 -0.32 4.26 -1.49 -0.77 0.90 -0.10 -1.16 TIME PERIOD ======= Instead of a smoothing constant, Excel uses a Dampin g Factor, which is shown above. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 TIME SERIES VALUE ======= 7.31 6.19 7.44 6.61 7.33 7.43 6.74 7.35 6.86 11.40 6.08 6.65 8.24 7.33 6.27 FORECAST ======== 7.31 7.20 7.22 7.16 7.18 7.20 7.16 7.18 7.14 7.57 7.42 7.34 7.43 7.42 FORECAST ERROR ======== -1.12 0.24 -0.61 0.17 0.25 -0.46 0.19 -0.32 4.26 -1.49 -0.77 0.90 -0.10 -1.15 16 17 18 19 20 21 22 23 24 25 7.03 7.52 7.80 7.21 7.23 7.27 6.92 7.55 7.75 7.31 7.28 7.30 7.35 7.34 7.33 7.32 7.28 7.31 7.35 -0.28 0.24 0.50 -0.14 -0.11 -0.06 -0.40 0.27 0.44 0.43 Sum of Forecast Errors 16 17 18 19 20 21 22 23 24 7.03 7.52 7.80 7.21 7.23 7.27 6.92 7.55 7.75 7.31 7.28 7.30 7.35 7.34 7.33 7.32 7.28 7.31 0.00 Sum of Forecast Errors THE MEAN SQUARE ERROR MSE = -0.28 0.24 0.50 -0.14 -0.11 -0.06 -0.40 0.27 0.44 1.13 1.13 THE FORECAST FOR PERIOD 25 7.35 Model Comparison Table - Exponential Smoothing - (See worksheets) ES - α .10 ES - α .20 ES - α .30 MSE Forecast for Period 25 1.13 7.35 1.24 7.39 1.35 7.43 a. What forecasting method is most appropriate? Explain. No linear (pos or neg) trend based on scatterplot. Would use exponential smoothing based on appearance of the scatterplot. Based on Model Comparions the Exponential Smoothing using smoothing constant of .10 (in Excel damping factor .90 ((1 - .10)) is the best model. b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data). Fits well as there are no large differences between forecast and actuals except for the outlier in period 10. Residuals are both negative and positive with no obvious patterns Forecast errors (residuals) sum to zero. c. What is your recommendation regarding future forecasts? Use exponential smoothing based on previous 12 periods (3 yrs - qtrly data), unless series of unusual spikes occur. In this case, using the most current data can produce even lower MSE (minimum data needed is at least 2 yrs. to test for presence of repeated seasonal trend) 3. Discuss at least two potential applications of forecasting in your job or field. Forecasting monthly utility and fuel consumption in CDL program and forecasting monthly equipment maintenance and repair expenses FORECASTING WITH EXPONENTIAL SMOOTHING ************************************** THE SMOOTHING CONSTANT IS 0.1 TIME PERIOD TIME SERIES VALUE =========== 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 FORECAST ================= 7.31 6.19 7.44 6.61 7.33 7.43 6.74 7.35 6.86 11.40 6.08 6.65 8.24 7.33 6.27 7.03 7.52 7.80 7.21 7.23 7.27 6.92 7.55 7.75 7.31 7.20 7.22 7.16 7.18 7.20 7.16 7.18 7.14 7.57 7.42 7.34 7.43 7.42 7.31 7.28 7.30 7.35 7.34 7.33 7.32 7.28 7.31 THE MEAN SQUARE ERROR THE FORECAST FOR PERIOD 25 FORECAST ERROR ======== -1.12 0.24 -0.61 0.17 0.25 -0.46 0.19 -0.32 4.26 -1.49 -0.77 0.90 -0.10 -1.15 -0.28 0.24 0.50 -0.14 -0.11 -0.06 -0.40 0.27 0.44 1.13 7.35 FORECASTING WITH EXPONENTIAL SMOOTHING ************************************** THE SMOOTHING CONSTANT IS 0.2 TIME PERIOD =========== 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 TIME SERIES VALUE ================= 7.31 6.19 7.44 6.61 7.33 7.43 6.74 7.35 6.86 11.40 6.08 6.65 8.24 7.33 6.27 7.03 7.52 7.80 7.21 7.23 7.27 6.92 7.55 7.75 7.31 7.09 7.16 7.05 7.10 7.17 7.08 7.14 7.08 7.95 7.57 7.39 7.56 7.51 7.26 7.22 7.28 7.38 7.35 7.32 7.31 7.23 7.30 THE MEAN SQUARE ERROR THE FORECAST FOR PERIOD 25 FORECAST FORECAST ERROR ======== ============== -1.12 0.35 -0.55 0.28 0.33 -0.43 0.27 -0.28 4.32 -1.87 -0.92 0.85 -0.23 -1.24 -0.23 0.30 0.52 -0.17 -0.12 -0.05 -0.39 0.32 0.45 1.24 7.39 FORECASTING WITH EXPONENTIAL SMOOTHING ************************************** THE SMOOTHING CONSTANT IS 0.3 TIME PERIOD =========== 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 TIME SERIES VALUE ================= 7.31 6.19 7.44 6.61 7.33 7.43 6.74 7.35 6.86 11.40 6.08 6.65 8.24 7.33 6.27 7.03 7.52 7.80 7.21 7.23 7.27 6.92 7.55 7.75 7.31 6.97 7.11 6.96 7.07 7.18 7.05 7.14 7.06 8.36 7.67 7.37 7.63 7.54 7.16 7.12 7.24 7.41 7.35 7.31 7.30 7.19 7.30 THE MEAN SQUARE ERROR THE FORECAST FOR PERIOD 25 FORECAST FORECAST ERROR ======== ============== -1.12 0.47 -0.50 0.37 0.36 -0.44 0.30 -0.28 4.34 -2.28 -1.02 0.87 -0.30 -1.27 -0.13 0.40 0.56 -0.20 -0.12 -0.04 -0.38 0.36 0.45 1.35 7.43 Data for Colleen's Cajun Cannery Week 1 2 3 4 5 6 7 8 9 10 11 12 13 # OT Hours 13 16 18 17 19 21 23 22 25 29 34 42 55 60 # 50 O 40 T 30 20 H 10 16 o 13 u 0 0 r s Note: These data represent her weekly number of overtime hours used. Forecasting Thumbnail Notes - Page 1 1. Determine if the response variable tends to vary over time in some repeatable pattern. If not, consider other statistical m QM 670 Class Notes - Page 2 Scatterplot Examples ➢ ➢ Positive Nonlinear Refer to Section 2.3 of QM 670 Class Notes (Other Model Types) a. What forecasting method is most appropriate? Explain. Because Colleen's data scatterplot shows an upward curve in the data, the data is non-linear and therefore out-of-scope for the models we are using in this class. It is very important to choose the most appropriate model based on the characteristics displa Refer to Section 2.3 and 3.0 of QM 670 Class Notes and the Forecasting Thumbnail Notes located in the Forecasting M Colleen's y = 2.7198x + 6.6538 R² = 0.8 55 42 13 25 21 23 22 19 16 18 17 5 29 # OT Hours Linear (# OT Hours) 10 Week 34 15 Quarter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 # of rolls ordered 56 48 58 67 59 51 64 71 73 67 78 84 77 70 82 89 83 74 84 93 86 78 85 93 Note: Simpson's produces nonwoven fabric rolls. # of rolls ordered (scatterplot) 100 90 80 # of Rolls Ordered Simpson's Inc. y = 1.5843x + 53.946 R² = 0.7536 70 60 50 # of rolls ordered 40 Linear (# of rolls ordered) 30 20 10 0 0 5 10 15 20 25 30 Quarter Time Series Components (From Forecasting Thumbnail Notes) 1. Trend – a gradual increase or decrease over time 2. Seasonal – a pattern over a period of a year or less. The recurrence of the pattern will be seen over periods of more than a year. 3. Cyclical – a pattern over a period of more than a year (generally many years) 4. Irregular (random) – departures from a “perfect” recurring pattern The irregular component will be present in any set of “real” data. In most cases, you will not encounter cyclical data unless your data covers a large time horizon. When cyclical patterns exist, we often use the most recent data to develop our forecasts. a. What forecasting method is most appropriate? Explain. Because the scatterplot displays irregularity, trend and seasonality, the "Trend with Seasonal" forecasting (Classical Time Series) model is most appropriate. b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data). Some large forecasting errors and obvious patterns in negative and positive forecast values during first and and last two years. Model does not fit as well as it could with adjustment . Refer to "answer c" and "Trend w Season - 4 years" worksheet c. What is your recommendation regarding future forecasts? Examine the scatterplot chart and notice that the seasonal pattern begins to stabilize in quarter 9. Drop the oldest data that occurs before the seasonal pattern stabilizes (in this case, the first 8 quarters); Run the analysis again using the last 4 years of data. The MSE drops and the forecasting errors stabilize. There are an equal number of positive and negative errors, no large errors, no obvious forecast error patterns and errors sum to 0. In the future I would examine the scatterplot data closely and be sure to adjust the input data according to the latest trend and seasonality patterns, eliminating older data when these patterns change (To insure the recurrence of quarterly seaonality you need at least 2 years of data).. FORECASTING WITH TREND AND SEASONAL COMPONENTS ********************************************** SEASON SEASONAL INDEX ------------------1 2 3 4 TIME PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1.005 0.886 1.013 1.097 TIME SERIES VALUE 56 48 58 67 59 51 64 71 73 67 78 84 77 70 82 89 83 74 84 93 86 78 85 93 FORECAST FORECAST ERROR 56.50 51.15 60.00 66.65 62.60 56.53 66.15 73.31 68.71 61.92 72.30 79.98 74.81 67.30 78.45 86.64 80.91 72.68 84.60 93.30 87.02 78.06 90.75 99.96 THE MEAN SQUARE ERROR THE FORECAST FOR PERIOD 25 THE FORECAST FOR PERIOD 26 THE FORECAST FOR PERIOD 27 THE FORECAST FOR PERIOD 28 -0.50 -3.15 -2.00 0.35 -3.60 -5.53 -2.15 -2.31 4.29 5.08 5.70 4.02 2.19 2.70 3.55 2.36 2.09 1.32 -0.60 -0.30 -1.02 -0.06 -5.75 -6.96 11.68 93.12 83.44 96.90 106.62 FORECASTING WITH TREND AND SEASONAL COMPONENTS ********************************************** SEASON SEASONAL INDEX ------------------1 2 3 4 TIME PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1.000 0.895 1.014 1.091 TIME SERIES VALUE 73 67 78 84 77 70 82 89 83 74 84 93 86 78 85 93 FORECAST FORECAST ERROR 74.54 67.48 77.33 84.16 77.96 70.54 80.80 87.89 81.37 73.60 84.27 91.62 84.79 76.66 87.73 95.35 THE MEAN SQUARE ERROR THE FORECAST FOR PERIOD 17 THE FORECAST FOR PERIOD 18 THE FORECAST FOR PERIOD 19 THE FORECAST FOR PERIOD 20 -1.54 -0.48 0.67 -0.16 -0.96 -0.54 1.20 1.11 1.63 0.40 -0.27 1.38 1.21 1.34 -2.73 -2.35 1.75 88.21 79.72 91.20 99.08
Purchase answer to see full attachment
Tags: qm
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Here you go. In case o...


Anonymous
Really great stuff, couldn't ask for more.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags