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4: CHAPTER FORECASTING
TRUE/FALSE
1. 2. A nave forecast for September sales of a product would be equal to the forecast for August. False (Time-series forecasting, moderate) The forecasting time horizon and the forecasting techniques used tend to vary over the life cycle of a product. True (What is forecasting? moderate) Demand (sales) forecasts serve as inputs to financial, marketing, and personnel planning. True (Types of forecasts, moderate) Forecasts of individual products tend to be more accurate than forecasts of product families. False (Seven steps in the forecasting system, moderate) Most forecasting techniques assume that there is some underlying stability in the system. True (Seven steps in the forecasting system, moderate) The sales force composite forecasting method relies on salespersons estimates of expected sales. True (Forecasting approaches, easy) A time-series model uses a series of past data points to make the forecast. True (Forecasting approaches, moderate) The quarterly "make meeting" of Lexus dealers is an example of a sales force composite forecast. True (Forecasting approaches, easy) Cycles and random variations are both components of time series. True (Time-series forecasting, easy) A naive forecast for September sales of a product would be equal to the sales in August. True (Time-series forecasting, easy) One advantage of exponential smoothing is the limited amount of record keeping involved. True (Time-series forecasting, moderate) The larger the number of periods in the simple moving average forecasting method, the greater the method's responsiveness to changes in demand. False (Time-series forecasting, moderate) Forecast including trend is an exponential smoothing technique that utilizes two smoothing constants: one for the average level of the forecast and one for its trend. True (Time-series forecasting, easy) Mean Squared Error and Coefficient of Correlation are two measures of the overall error of a forecasting model. False (Time-series forecasting, easy)
3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
13. 14.
15. 16. 17. 18.
In trend projection, the trend component is the slope of the regression equation. True (Time-series forecasting, easy) In trend projection, a negative regression slope is mathematically impossible. False (Time-series forecasting, moderate) Seasonal indexes adjust raw data for patterns that repeat at regular time intervals. True (Time-series forecasting, moderate) If a quarterly seasonal index has been calculated at 1.55 for the October-December quarter, then raw data for that quarter must be multiplied by 1.55 so that the quarter can be fairly compared to other quarters. False (Time-series forecasting: Seasonal variation in data, moderate) The best way to forecast a business cycle is by finding a leading variable. True (Time-series forecasting, moderate) Linear-regression analysis is a straight-line mathematical model to describe the functional relationships between independent and dependent variables. True (Associative forecasting methods: Regression and correlation analysis, The larger the standard error of the estimate, the more accurate the forecasting model. False (Associative forecasting methods: Regression and correlation analysis, A trend projection equation with a slope of 0.78 means that there is a 0.78 unit rise in Y for every unit of time that passes. True (Time-series forecasting: Trend projections, moderate) In a regression equation where Y is demand and X is advertising, a coefficient of determination (R ) of .70 means that 70% of the variance in advertising is explained by demand. False (Associative forecasting methods: Regression and correlation analysis, moderate)
2
19. 20. easy) 21. easy) 22.
23.
24. 25. 26.
Demand cycles for individual products can be driven by product life cycles. True (Time-series forecasting, moderate) If a forecast is consistently greater than (or less than) actual values, the forecast is said to be biased. True (Monitoring and controlling forecasts, moderate) Focus forecasting tries a variety of computer models and selects the best one for a particular application. True (Monitoring and controlling forecasts, moderate) Many service firms use point-of-sale computers to collect detailed records needed for accurate short-term forecasts. True (Forecasting in the service sector, moderate)
27.
MULTIPLE CHOICE
28.
What two numbers are contained in the daily report to the CEO of Walt Disney Parks & Resorts regarding the six Orlando parks? 1. a. yesterdays forecasted attendance and yesterdays actual attendance 2. b. yesterdays actual attendance and todays forecasted attendance 3. c. yesterdays forecasted attendance and todays forecasted attendance 4. d. yesterdays actual attendance and last years actual attendance 5. e. yesterdays forecasted attendance and the year-to-date average daily forecast error a (Global company profile, moderate)
29.
Using an exponential smoothing model with smoothing constant = .20, how much weight would be assigned to the 2 most recent period? 1. a. .16 2. b. .20 3. c. .04 4. d. .09 5. e. .10
nd
a (Time-series forecasting, moderate) {AACSB: Analytic Skills} 30.
1. 2. 3. 4. 5.
Forecasts a. become more accurate with longer time horizons b. are rarely perfect c. are more accurate for individual items than for groups of items d. all of the above e. none of the above b (What is forecasting? moderate)
31.
1. 2. 3. 4. 5.
One use of short-range forecasts is to determine a. production planning b. inventory budgets c. research and development plans d. facility location e. job assignments e (What is forecasting? moderate)
32.
Forecasts are usually classified by time horizon into three categories 1. a. short-range, medium-range, and long-range 2. b. finance/accounting, marketing, and operations 3. c. strategic, tactical, and operational 4. d. exponential smoothing, regression, and time series 5. e. departmental, organizational, and industrial a (What is forecasting? easy) A forecast with a time horizon of about 3 months to 3 years is typically called a 1. a. long-range forecast
33.
2. 3. 4. 5.
b. medium-range forecast c. short-range forecast d. weather forecast e. strategic forecast b (What is forecasting? moderate)
34.
Forecasts used for new product planning, capital expenditures, facility location or expansion, and R&D typically utilize a 1. a. short-range time horizon 2. b. medium-range time horizon 3. c. long-range time horizon 4. d. naive method, because there is no data history 5. e. all of the above c (What is forecasting? moderate)
35.
1. 2. 3. 4. 5.
The three major types of forecasts used by business organizations are a. strategic, tactical, and operational b. economic, technological, and demand c. exponential smoothing, Delphi, and regression d. causal, time-series, and seasonal e. departmental, organizational, and territorial b (Types of forecasts, moderate)
36.
1. 2. 3. 4. 5.
Which of the following is not a step in the forecasting process? a. Determine the use of the forecast. b. Eliminate any assumptions. c. Determine the time horizon. d. Select forecasting model. e. Validate and implement the results. b (The strategic importance of forecasting, moderate)
37.
The two general approaches to forecasting are 1. a. qualitative and quantitative 2. b. mathematical and statistical 3. c. judgmental and qualitative 4. d. historical and associative 5. e. judgmental and associative a (Forecasting approaches, easy)
38.
Which of the following uses three types of participants: decision makers, staff personnel, and respondents? 1. a. executive opinions 2. b. sales force composites
3. c. the Delphi method 4. d. consumer surveys 5. e. time series analysis
39. c (Forecasting approaches, moderate) The forecasting model that pools the opinions of a group of experts or managers is known as the 1. a. sales force composition model 2. b. multiple regression 3. c. jury of executive opinion model 4. d. consumer market survey model 5. e. management coefficients model c (Forecasting approaches, moderate) 40.
1. 2. 3. 4. 5.
Which of the following is not a type of qualitative forecasting? a. executive opinions b. sales force composites c. consumer surveys d. the Delphi method e. moving average e (Forecasting approaches, moderate)
41.
Which of the following techniques uses variables such as price and promotional expenditures, which are related to product demand, to predict demand? 1. a. associative models 2. b. exponential smoothing 3. c. weighted moving average 4. d. simple moving average 5. e. time series a (Forecasting approaches, moderate)
42.
Which of the following statements about time series forecasting is true? 1. a. It is based on the assumption that future demand will be the same as past demand. 2. b. It makes extensive use of the data collected in the qualitative approach. 3. c. The analysis of past demand helps predict future demand. 4. d. Because it accounts for trends, cycles, and seasonal patterns, it is more powerful than causal forecasting. 5. e. All of the above are true. c (Time-series forecasting, moderate)
43.
1. 2. 3. 4.
Time series data may exhibit which of the following behaviors? a. trend b. random variations c. seasonality d. cycles
5. e.
They may exhibit all of the above.
e (Time-series forecasting, moderate) 44. Gradual, long-term movement in time series data is called 1. a. seasonal variation 2. b. cycles 3. c. trends 4. d. exponential variation 5. e. random variation c (Time-series forecasting, moderate) Which of the following is not present in a time series? 1. a. seasonality 2. b. operational variations 3. c. trend 4. d. cycles 5. e. random variations b (Time-series forecasting, moderate) 46.
45.
1. 2. 3. 4. 5.
The fundamental difference between cycles and seasonality is the a. duration of the repeating patterns b. magnitude of the variation c. ability to attribute the pattern to a cause d. all of the above e. none of the above a (Time-series forecasting, moderate)
47.
1. 2. 3. 4. 5.
In time series, which of the following cannot be predicted? a. large increases in demand b. technological trends c. seasonal fluctuations d. random fluctuations e. large decreases in demand d (Time-series forecasting, moderate)
48.
What is the approximate forecast for May using a four-month moving average? Nov. Dec. Jan. Feb. Mar. April 39 36404248 46
1. 2. 3. 4. 5.
a. 38 b. 42 c. 43 d. 44 e. 47
d (Time-series forecasting, moderate) {AACSB: Analytic Skills} 49. Which time series model below assumes that demand in the next period will be equal to the most recent period's demand? 1. a. naive approach 2. b. moving average approach 3. c. weighted moving average approach 4. d. exponential smoothing approach 5. e. none of the above a (Time-series forecasting, easy) Johns House of Pancakes uses a weighted moving average method to forecast pancake sales. It assigns a weight of 5 to the previous months demand, 3 to demand two months ago, and 1 to demand three months ago. If sales amounted to 1000 pancakes in May, 2200 pancakes in June, and 3000 pancakes in July, what should be the forecast for August? 1. a. 2400 2. b. 2511 3. c. 2067 4. d. 3767 5. e. 1622 b (Time series forecasting, moderate) {AACSB: Analytic Skills} 51. A six-month moving average forecast is better than a three-month moving average forecast if demand 1. a. is rather stable 2. b. has been changing due to recent promotional efforts 3. c. follows a downward trend 4. d. follows a seasonal pattern that repeats itself twice a year 5. e. follows an upward trend a (Time-series forecasting, moderate) 52. Increasing the number of periods in a moving average will accomplish greater smoothing, but at the expense of 1. a. manager understanding 2. b. accuracy 3. c. stability 4. d. responsiveness to changes 5. e. All of the above are diminished when the number of periods increases. d (Time-series forecasting, moderate) 53. Which of the following statements comparing the weighted moving average technique and exponential smoothing is true? 1. a. Exponential smoothing is more easily used in combination with the Delphi method. 2. b. More emphasis can be placed on recent values using the weighted moving average. 3. c. Exponential smoothing is considerably more difficult to implement on a computer.
50.
4. d. 5. e.
Exponential smoothing typically requires less record keeping of past data. Exponential smoothing allows one to develop forecasts for multiple periods, whereas weighted moving averages does not.
d (Time-series forecasting, moderate) 54.
1. 2. 3. 4. 5.
55.
Which time series model uses past forecasts and past demand data to generate a new forecast? a. naive b. moving average c. weighted moving average d. exponential smoothing e. regression analysis
d (Time-series forecasting, moderate) Which is not a characteristic of exponential smoothing? 1. a. smoothes random variations in the data 2. b. easily altered weighting scheme 3. c. weights each historical value equally 4. d. has minimal data storage requirements 5. e. none of the above; they are all characteristics of exponential smoothing c (Time-series forecasting, moderate)
56.
Which of the following smoothing constants would make an exponential smoothing forecast equivalent to a naive forecast? 1. a. 0 2. b. 1 divided by the number of periods 3. c. 0.5 4. d. 1.0 5. e. cannot be determined d (Time-series forecasting, moderate)
57.
Given an actual demand of 103, a previous forecast value of 99, and an alpha of .4, the exponential smoothing forecast for the next period would be 1. a. 94.6 2. b. 97.4 3. c. 100.6 4. d. 101.6 5. e. 103.0 c (Time-series forecasting, moderate) {AACSB: Analytic Skills}
58.
A forecast based on the previous forecast plus a percentage of the forecast error is a(n) 1. a. qualitative forecast 2. b. naive forecast 3. c. moving average forecast 4. d. weighted moving average forecast
5. e. exponentially smoothed forecast
e (Time-series forecasting, moderate) 59. Given an actual demand of 61, a previous forecast of 58, and an of .3, what would the forecast for the next period be using simple exponential smoothing? 1. a. 45.5 2. b. 57.1 3. c. 58.9 4. d. 61.0 5. e. 65.5 c (Time-series forecasting, moderate) {AACSB: Analytic Skills} Which of the following values of alpha would cause exponential smoothing to respond the most slowly to forecast errors? 1. a. 0.10 2. b. 0.20 3. c. 0.40 4. d. 0.80 5. e. cannot be determined a (Time-series forecasting, moderate) 61. A forecasting method has produced the following over the past five months. What is the mean absolute deviation? Forecast 11 10 8 6 8 Error -1 -2 2 0 1 |Error| 1 2 2 0 1
60.
Actual 10 8 10 6 9
1. 2. 3. 4. 5.
a. -0.2 b. -1.0 c. 0.0 d. 1.2 e. 8.6 d (Time-series forecasting, moderate) {AACSB: Analytic Skills}
62. 1. 2. 3. 4.
The primary purpose of the mean absolute deviation (MAD) in forecasting is to a. estimate the trend line b. eliminate forecast errors c. measure forecast accuracy d. seasonally adjust the forecast
5. e. all of the above c (Time-series forecasting, moderate) 63. 1. 2. 3. 4. 5. Given forecast errors of -1, 4, 8, and -3, what is the mean absolute deviation? a. 2 b. 3 c. 4 d. 8 e. 16
c (Time-series forecasting, moderate) {AACSB: Analytic Skills} 64. The last four months of sales were 8, 10, 15, and 9 units. The last four forecasts were 5, 6, 11, and 12 units. The Mean Absolute Deviation (MAD) is 1. a. 2 2. b. -10 3. c. 3.5 4. d. 9 5. e. 10.5 c (Time-series forecasting, moderate) {AACSB: Analytic Skills} 65. 1. 2. 3. 4. 5. A time series trend equation is 25.3 + 2.1 X. What is your forecast for period 7? a. 23.2 b. 25.3 c. 27.4 d. 40.0 e. cannot be determined d (Time-series forecasting, moderate) {AACSB: Analytic Skills} 66. For a given product demand, the time series trend equation is 53 - 4 X. The negative sign on the slope of the equation 1. a. is a mathematical impossibility 2. b. is an indication that the forecast is biased, with forecast values lower than actual values 3. c. is an indication that product demand is declining 4. d. implies that the coefficient of determination will also be negative 5. e. implies that the RSFE will be negative c (Time-series forecasting, moderate) 67. Yamaha manufacturers which set of products with complementary demands to address seasonal fluctuations? 1. a. golf clubs and skis 2. b. swimming suits and winter jackets 3. c. jet skis and snowmobiles
4. d. 5. e.
pianos and guitars ice skates and water skis
c (Time-series forecasting, moderate) 68. Which of the following is true regarding the two smoothing constants of the Forecast Including Trend (FIT) model? 1. a. One constant is positive, while the other is negative. 2. b. They are called MAD and RSFE. 3. c. Alpha is always smaller than beta. 4. d. One constant smoothes the regression intercept, whereas the other smoothes the regression slope. 5. e. Their values are determined independently.
e (Time-series forecasting, moderate) 69. Demand for a certain product is forecast to be 800 units per month, averaged over all 12 months of the year. The product follows a seasonal pattern, for which the January monthly index is 1.25. What is the seasonally-adjusted sales forecast for January? 1. a. 640 units 2. b. 798.75 units 3. c. 800 units 4. d. 1000 units 5. e. cannot be calculated with the information given d (Time-series forecasting, moderate) {AACSB: Analytic Skills} 70. A seasonal index for a monthly series is about to be calculated on the basis of three years' accumulation of data. The three previous July values were 110, 150, and 130. The average over all months is 190. The approximate seasonal index for July is 1. a. 0.487 2. b. 0.684 3. c. 1.462 4. d. 2.053 5. e. cannot be calculated with the information given b (Time-series forecasting, moderate) {AACSB: Analytic Skills} 71. A fundamental distinction between trend projection and linear regression is that 1. a. trend projection uses least squares while linear regression does not 2. b. only linear regression can have a negative slope 3. c. in trend projection the independent variable is time; in linear regression the independent variable need not be time, but can be any variable with explanatory power 4. d. linear regression tends to work better on data that lack trends 5. e. trend projection uses two smoothing constants, not just one c (Associative forecasting methods: Regression and correlation analysis, moderate)
72.
The percent of variation in the dependent variable that is explained by the regression equation is measured by the 1. a. mean absolute deviation 2. b. slope 3. c. coefficient of determination 4. d. correlation coefficient 5. e. intercept c (Associative forecasting methods: Regression and correlation analysis, moderate)
73. 1. 2. 3. 4. 5. 74.
The degree or strength of a linear relationship is shown by the a. alpha b. mean c. mean absolute deviation d. correlation coefficient e. RSFE
d (Associative forecasting methods: Regression and correlation analysis, moderate) If two variables were perfectly correlated, the correlation coefficient r would equal 1. a. 0 2. b. -1 3. c. 1 4. d. b or c 5. e. none of the above d (Associative forecasting methods: Regression and correlation analysis, moderate)
75.
The last four weekly values of sales were 80, 100, 105, and 90 units. The last four forecasts were 60, 80, 95, and 75 units. These forecasts illustrate 1. a. qualitative methods 2. b. adaptive smoothing 3. c. slope 4. d. bias 5. e. trend projection d (Monitoring and controlling forecasts, easy)
76. 1. 2. 3. 4. 5.
The tracking signal is the a. standard error of the estimate b. running sum of forecast errors (RSFE) c. mean absolute deviation (MAD) d. ratio RSFE/MAD e. mean absolute percentage error (MAPE) d (Monitoring and controlling forecasts, moderate)
77.
Computer monitoring of tracking signals and self-adjustment if a signal passes a preset limit is characteristic of 1. a. exponential smoothing including trend 2. b. adaptive smoothing 3. c. trend projection 4. d. focus forecasting 5. e. multiple regression analysis b (Monitoring and controlling forecasts, moderate)
78. 1. 2. 3. 4. 5.
Many services maintain records of sales noting a. the day of the week b. unusual events c. weather d. holidays e. all of the above e (Forecasting in the service sector, moderate)
79. 1. 2. 3. 4. 5.
Taco Bell's unique employee scheduling practices are partly the result of using a. point-of-sale computers to track food sales in 15 minute intervals b. focus forecasting c. a six-week moving average forecasting technique d. multiple regression e. a and c are both correct e (Forecasting in the service sector, moderate)
FILL-IN-THE-BLANK
80. _________ forecasts are concerned with rates of technological progress, which can result in the birth of exciting new products, requiring new plants and equipment. Technological (Types of forecasts, easy) _________ forecasts address the business cycle by predicting inflation rates, money supplies, housing starts, and other planning indicators. Economic (Types of forecasts, moderate) Demand forecasts, also called _________ forecasts, are projections of demand for a company's products or services. sales (Types of forecasts, moderate) __________ forecasts employ one or more mathematical models that rely on historical data and/or causal variables to forecast demand. Quantitative (Forecasting approaches, moderate) ___________ is a forecasting technique based upon salespersons' estimates of expected sales. Sales force composite (Forecasting approaches, moderate)
81.
82.
83.
84.
85. 86.
__________ forecasts use a series of past data points to make a forecast. Time-series (Forecasting approaches, moderate) A(n) ______________ forecast uses an average of the most recent periods of data to forecast the next period. moving average (Forecasting approaches, moderate) The smoothing constant is a weighting factor used in ______________. exponential smoothing (Forecasting approaches, moderate) Linear regression is known as a(n) _____________ because it incorporates variables or factors that might influence the quantity being forecast. associative model (Forecasting approaches, easy) A measure of forecast error that does not depend on the magnitude of the item being forecast is the ___________. mean absolute percent error or MAPE (Forecasting approaches, easy) _____________ is a measure of overall forecast error for a model. MAD or Mean Absolute Deviation (Forecasting approaches, moderate) When one constant is used to smooth the forecast average and a second constant is used to smooth the trend, the forecasting method is __________________. exponential smoothing with trend adjustment or trend-adjusted smoothing or second-order smoothing or double smoothing (Forecasting approaches, moderate)
87. 88.
89.
90. 91.
92. ____________ is a time-series forecasting method that fits a trend line to a series of historical data points and then projects the line into the future for forecasts. Trend projection (Forecasting approaches, moderate) 93. The ______________________ measures the strength of the relationship between two variables. coefficient of correlation (Associative forecasting methods: Regression and correlation analysis, moderate) If a barbershop operator noted that Tuesday's business was typically twice as heavy as Wednesday's, and that Friday's business was typically the busiest of the week, business at the barbershop is subject to ____________. seasonal variations (Forecasting approaches: seasonal variations in data, moderate) __________ forecasting tries a variety of computer models and selects the best one for a particular application. Focus (Monitoring and controlling forecasts, moderate)
94.
95.
SHORT ANSWER
96. A skeptical manager asks what short-range forecasts can be used for. Give her three possible uses/purposes. Any three of: planning purchasing, job scheduling, work force levels, job assignments, production levels. (What is forecasting? moderate) A skeptical manager asks what long-range forecasts can be used for. Give her three possible uses/purposes. Any three of: planning new products, capital expenditures, facility location or expansion, research and development. (What is forecasting? moderate)
97.
98.
Describe the three forecasting time horizons and their use. Forecasting time horizons are: short rangegenerally less than three months, used for purchasing, job scheduling, work force levels, production levels; medium rangeusually from three months up to three years, used for sales planning, production planning and budgeting, cash budgeting, analyzing operating plans; long rangeusually three years or more, used for new product development, capital expenditures, facility planning, and R&D. (What is forecasting? moderate)
99.
List and briefly describe the three major types of forecasts. The three types are economic, technological, and demand; economic refers to macroeconomic, growth and financial variables; technological refers to forecasting amount of technological advance, or futurism; demand refers to product demand. (Types of forecasts, moderate) 100. Identify the seven steps involved in forecasting. 1. Determine the use of the forecast. 2. Select the items that are to be forecast. 3. Determine the time horizon of the forecast. 4. Select the forecasting model(s). 5. Gather the data needed to make the forecast. 6. Make the forecast. 7. Validate the forecasting mode and implement the results. (Seven steps in the forecasting process, moderate) 101. What are the realities of forecasting that companies face? First, forecasts are seldom perfect. Second, most forecasting techniques assume that there is some underlying stability in the system. Finally, both product family and aggregated forecasts are more accurate than individual product forecasts. (Seven steps in the forecasting system, moderate) 102. What are the differences between quantitative and qualitative forecasting methods? Quantitative methods use mathematical models to analyze historical data. Qualitative methods incorporate such factors as the decision maker's intuition, emotions, personal experiences, and value systems in determining the forecast. (Forecasting approaches, moderate) 103. Identify four quantitative forecasting methods. The list includes naive, moving averages, exponential smoothing, trend projection, and linear regression. (Forecasting approaches, moderate) 104. What is a time-series forecasting model? A time series forecasting model is any mathematical model that uses historical values of the quantity of interest to predict future values of that quantity. (Forecasting approaches, easy) 105. What is the difference between an associative model and a time-series model? A time series model uses only historical values of the quantity of interest to predict future of values that quantity. The associative model, on the other hand, attempts to identify underlying causes or factors that control the variation of the quantity of interest, predict future values of these factors, and use these predictions in a model to predict future values of the specific quantity of interest. (Forecasting approaches, moderate)
106. Name and discuss three qualitative forecasting methods. Qualitative forecasting methods include: jury of executive opinion, where high-level managers arrive at a group estimate of demand; sales force composite, where salespersons estimates are aggregated; Delphi method, where respondents provide inputs to a group of decision makers; the group of decision makers, often experts, then make the actual forecast; consumer market survey, where consumers are queried about their future purchase plans. (Forecasting approaches, moderate) 107. Identify four components of a time series. Which one of these is rarely forecast? Why is this so? Trend, seasonality, cycles, and random variation. Since random variations follow no discernible pattern, they cannot be predicted, and thus are not forecast. (Time-series forecasting, moderate) 108. Compare seasonal effects and cyclical effects. A cycle is longer (typically several years) than a season (typically days, weeks, months, or quarters). A cycle has variable duration, while a season has fixed duration and regular repetition. (Time-series forecasting, moderate) 109. Distinguish between a moving average model and an exponential smoothing model. Exponential smoothing is a weighted moving average model wherein previous values are weighted in a specific manner--in particular, all previous values are weighted with a set of weights that decline exponentially. (Time-series forecasting, moderate) 110. Describe three popular measures of forecast accuracy. Measures of forecast accuracy include: (a) MAD (mean absolute deviation). This is a sum of the absolute values of individual errors divided by the number of periods of data. (b) MSE (mean squared error). This is the average of the squared differences between the forecast and observed values. (c) MAPE (mean absolute percent error) is independent of the magnitude of the variable being forecast. (Forecasting approaches: Measuring forecast error, moderate) 111. Give an exampleother than a restaurant or other food-service firmof an organization that experiences an hourly seasonal pattern. (That is, each hour of the day has a pattern that tends to repeat day after day.) Explain. Answer will vary. However, two non-food examples would be banks and movie theaters. (Time-series forecasting, moderate) {AACSB: Reflective Thinking} 112. Explain the role of regression models (time series and otherwise) in forecasting. That is, how is trend projection able to forecast? How is regression used for causal forecasting? For trend projection, the independent variable is time. The trend projection equation has a slope that is the change in demand per period. To forecast the demand for period t, perform the calculation a + bt. For causal forecasting, the independent variables are predictors of the forecast value or dependent variable. The slope of the regression equation is the change in the Y variable per unit change in the X variable. (Time-series forecasting, difficult) 113. Identify three advantages of the moving average forecasting model. Identify three disadvantages of the moving average forecasting model. Three advantages of the model are that it uses simple calculations, it smoothes out sudden fluctuations, and it is easy for users to understand. The disadvantages are that the averages always stay within past ranges, that they require extensive record keeping of past data, and that they do not pick up on trends very well. (Time-series forecasting, moderate)
114. What does it mean to "decompose" a time series? To decompose a time series means to break past data down into components of trends, seasonality, cycles, and random blips, and to project them forward. (Time-series forecasting, easy) 115. Distinguish a dependent variable from an independent variable. The independent variable causes some behavior in the dependent variable; the dependent variable shows the effect of changes in the independent variable. (Associative forecasting methods: Regression and correlation, moderate) 116. Explain, in your own words, the meaning of the coefficient of determination. The coefficient of determination measures the amount (percent) of total variation in the data that is explained by the model. (Associative forecasting methods: Regression and correlation, moderate) 117. What is a tracking signal? How is it calculated? Explain the connection between adaptive smoothing and tracking signals. A tracking signal is a measure of how well the forecast actually predicts. Its calculation is the ratio of RSFE to MAD. The larger the absolute tracking signal, the worse the forecast is performing. Adaptive smoothing sets limits to the tracking signal, and makes changes to its forecasting models when the tracking signal goes beyond those limits. (Monitoring and controlling forecasts, moderate) 118. What is focus forecasting? It is a forecasting method that tries a variety of computer models, and selects the one that is best for a particular application. (Monitoring and controlling forecasts, easy)
PROBLEMS
119. Weekly sales of ten-grain bread at the local organic food market are in the table below. Based on this data, forecast week 9 using a five-week moving average. Week 1 2 3 4 5 6 7 8 Sales 415 389 420 382 410 432 405 421
(382+410+432+405+421)/5 = 410.0 (Time-series forecasting, easy) {AACSB: Analytic Skills} 120. Given the following data, calculate the three-year moving averages for years 4 through 10. Year Demand 1 74 2 90 3 59 4 91 5 140
6 98 7 110 8 123 9 99 Year Demand 3-Year Moving Ave. 1 74 2 90 3 59 4 91 74.33 5 140 80.00 6 98 96.67 7 110 109.67 8 123 116.00 9 99 110.33 110.67 (Time-series forecasting, moderate) {AACSB: Analytic Skills} 121. What is the forecast for May based on a weighted moving average applied to the following past demand data and using the weights: 4, 3, 2 (largest weight is for most recent data)? Nov. Dec. Jan. Feb. Mar. April 37 36404247 43 2x42 + 3x47 + 4x43 = 84+141+172 = 397; 397/9 = 44.1 (Time-series forecasting, easy) {AACSB: Analytic Skills} 122. Weekly sales of copy paper at Cubicle Suppliers are in the table below. Compute a threeperiod moving average and a four-period moving average for weeks 5, 6, and 7. Compute MAD for each forecast. Which model is more accurate? Forecast week 8 with the more accurate method. Week Sales (cases) 1 17 2 21 3 27 4 31 5 19 6 17 7 21 Week Sales (cases) 3MA |error| 4MA |error| 1 17 2 21
3 27 4 31 21.7 9.3 5 19 26.3 7.3 24.0 5.0 6 17 25.7 8.7 24.5 7.5 7 21 22.3 1.3 23.5 2.5 8 19.0 22.0 MAD = 6.7 5.0 The four-week moving average is more accurate. The forecast with the 4-movingaverage is 22.0. (Time-series forecasting,
moderate) {AACSB: Analytic Skills} 123. The last four weekly values of sales were 80, 100, 105, and 90 units. The last four forecasts (for the same four weeks) were 60, 80, 95, and 75 units. Calculate MAD, MSE, and MAPE for these four weeks. Sales 80 100 105 90 Forecast 60 80 95 75 Error 20 20 10 15 Error squared 400 400 100 225 Pct. error .25 .20 .095 .167
MAD = 65/4 = 16.25; MSE = 1125/4 = 281.25; MAPE = 0.712/4 = .178 or 17.8% (Time series forecasting: Measuring forecast error, moderate) {AACSB: Analytic Skills} 124. A management analyst is using exponential smoothing to predict merchandise returns at an upscale branch of a department store chain. Given an actual number of returns of 154 items in the most recent period completed, a forecast of 172 items for that period, and a smoothing constant of 0.3, what is the forecast for the next period? How would the forecast be changed if the smoothing constant were 0.6? Explain the difference in terms of alpha and responsiveness. 166.6; 161.2 The larger the smoothing constant in an exponentially smoothed forecast, the more responsive the forecast. (Time-series forecasting, easy) {AACSB: Analytic Skills} 125. Use exponential smoothing with = 0.2 to calculate smoothed averages and a forecast for period 7 from the data below. Assume the forecast for the initial period is 7.
Period 1 2 3 4 5 6 Period Demand 10 8 7 10 12 9 Demand Forecast
1 2 3 4 5 6
10 8 7 10 12 9
7.0 7.6 7.7 7.5 8.0 8.8
(Time-series forecasting, moderate) {AACSB: Analytic Skills} 126. The following trend projection is used to predict quarterly demand: Y = 250 - 2.5t, where t = 1 in the first quarter of 2004. Seasonal (quarterly) relatives are Quarter 1 = 1.5; Quarter 2 = 0.8; Quarter 3 = 1.1; and Quarter 4 = 0.6. What is the seasonally adjusted forecast for the four quarters of 2006? Period Projection Adjusted 9 227.5 341.25 10 225 180.00 11 222.5 244.75 12 220 132.00 (Time-series forecasting, moderate) {AACSB: Analytic Skills} 127. Jim's department at a local department store has tracked the sales of a product over the last ten weeks. Forecast demand using exponential smoothing with an alpha of 0.4, and an initial forecast of 28.0. Calculate MAD and the tracking signal. What do you recommend? Period Demand 1 24 2 23 3 26 4 36 5 26 6 30 7 32 8 26 9 25 10 28 Period Demand Forecast Error RSFE Absolute 1 24 28.00 2 23 26.40 -3.40 -3.40 3.40 3 26 25.04 0.96 -2.44 0.96 4 36 25.42 10.58 8.14 10.58 5 26 29.65 -3.65 4.48 3.65 6 30 28.19 1.81 6.29 1.81 7 32 28.92 3.08 9.37 3.08 8 26 30.15 -4.15 5.22 4.15 9 25 28.49 -3.49 1.73 3.49 10 28 27.09 0.91 2.64 0.91 Total 2.64 32.03 Average 0.29 0.74 3.56
Bias TS MAD The tracking signal is acceptable; therefore, keep using the forecasting method. (Time-series forecasting, and Monitoring and controlling forecasts, moderate) {AACSB: Analytic Skills} 128. Favors Distribution Company purchases small imported trinkets in bulk, packages them, and sells them to retail stores. They are conducting an inventory control study of all their items. The following data are for one such item, which is not seasonal. 1. a. Use trend projection to estimate the relationship between time and sales (state the equation). 2. b. Calculate forecasts for the first four months of the next year.
1 2 3 4 5 6 7 8 9 10 11 12 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Sales 51 55 54 57 50 68 66 59 67 69 75 73
The trend projection equation is Y = 48.32 + 2.105 T. The next four months are forecast to be 75.68, 77.79, 79.89, and 82.00. (Time-series forecasting, moderate) {AACSB: Analytic Skills} 129. Use exponential smoothing with trend adjustment to forecast deliveries for period 10. Let alpha = 0.4, beta = 0.2, and let the initial trend value be 4 and the initial forecast be 200. Period Actual Demand 1 200 2 212 3 214 4 222 5 236 6 221 7 240 8 244 9 250 10 266
Actual Forecast Trend FIT 1 200 200.00 4.00 2 212 202.40 3.68 206.08 3 214 208.45 4.15 212.60 4 222 213.16 4.27 217.43 5 236 219.26 4.63 223.89 6 221 228.73 5.60 234.33 7 240 229.00 4.53 233.53
8 244 236.12 5.05 241.17 9 250 242.30 5.28 247.58 10 266 248.55 5.47 254.02 (Time-series forecasting, moderate) {AACSB: Analytic Skills} 130. A small family-owned restaurant uses a seven-day moving average model to determine manpower requirements. These forecasts need to be seasonalized because each day of the week has its own demand pattern. The seasonal relatives for each day of the week are: Monday, 0.445; Tuesday, 0.791; Wednesday, 0.927; Thursday, 1.033; Friday, 1.422; Saturday, 1.478; and Sunday 0.903. Average daily demand based on the most recent moving average is 194 patrons. What is the seasonalized forecast for each day of next week? The average value multiplied by each day's seasonal index. Monday: 194 x .445 = 86; Tuesday: 194 x .791 = 153; Wednesday: 194 x .927 = 180; Thursday: 194 x 1.033 = 200; Friday: 194 x 1.422 = 276; Saturday: 194 x 1.478 = 287; and Sunday: 194 x .903 = 175. (Associative forecasting methods: Regression and correlation, moderate) {AACSB: Analytic Skills} 131. A restaurant has tracked the number of meals served at lunch over the last four weeks. The data shows little in terms of trends, but does display substantial variation by day of the week. Use the following information to determine the seasonal (daily) index for this restaurant. Week Day 1234 Sunday 40 35 39 43 Monday 54 55 51 59 Tuesday 61 60 65 64 Wednesday 72 77 78 69 Thursday 89 80 81 79 Friday 91 90 99 95 Saturday 80 82 81 83 Day Index Sunday 0.5627 Monday 0.7855 Tuesday 0.8963 Wednesday 1.0618 Thursday 1.1800 Friday 1.3444 Saturday 1.1692 (Time-series forecasting, moderate) {AACSB: Analytic Skills} 132. A firm has modeled its experience with industrial accidents and found that the number of accidents per year (Y) is related to the number of employees (X) by the regression equation Y = 3.3 + 0.049*X. R-Square is 0.68. The regression is based on 20 annual observations. The firm intends to employ 480 workers next year. How many accidents do you project? How much confidence do you have in that forecast? Y = 3.3 + 0.049 * 480 = 3.3 + 23.52 = 26.82 accidents. This is not a time series, so next year = year 21 is of no relevance. Confidence comes from the coefficient of determination; the model explains 68% of the variation in number of accidents, which seems respectable. (Associative forecasting methods: Regression and correlation, moderate) {AACSB: Analytic Skills}
133. Demand for a certain product is forecast to be 8,000 units per month, averaged over all 12 months of the year. The product follows a seasonal pattern, for which the January monthly index is 1.25. What is the seasonally-adjusted sales forecast for January? 8,000 x 1.25 = 10,000 (Time-series forecasting, easy) {AACSB: Analytic Skills} 134. A seasonal index for a monthly series is about to be calculated on the basis of three years' accumulation of data. The three previous July values were 110, 135, and 130. The average over all months is 160. The approximate seasonal index for July is (110 + 135 + 130)/3 = 125; 125/160 = 0.781 (Time-series forecasting, moderate) {AACSB: Analytic Skills} 135. Marie Bain is the production manager at a company that manufactures hot water heaters. Marie needs a demand forecast for the next few years to help decide whether to add new production capacity. The company's sales history (in thousands of units) is shown in the table below. Use exponential smoothing with trend adjustment, to forecast demand for period 6. The initial forecast for period 1 was 11 units; the initial estimate of trend was 0. The smoothing constants are = .3 and = .3 Period 1 2 3 4 5 6 Period 1 2 3 4 5 6 Actual 12 15 16 16 18 20 Actual 12 15 16 16 18 20 Forecast 11.00 11.30 12.47 13.82 14.96 16.45 Trend 0.00 0.09 0.41 0.69 0.83 1.03 FIT 11.39 12.89 14.52 15.79 17.48
(Time-series forecasting, moderate) {AACSB: Analytic Skills} 136. The quarterly sales for specific educational software over the past three years are given in the following table. Compute the four seasonal factors. YEAR 1 YEAR 2 YEAR 3 Quarter 1 1710 1820 1830 Quarter 2 960 910 1090 Quarter 3 2720 2840 2900 Quarter 4 2430 2200 2590 Avg. Sea. Fact. Quarter 1 1786.67 0.8933 Quarter 2 986.67 0.4933 Quarter 3 2820.00 1.4100 Quarter 4 2406.67 1.2033 Grand Average 2000.00 (Time-series forecasting, moderate) {AACSB: Analytic Skills} 137. An innovative restaurateur owns and operates a dozen "Ultimate Low-Carb" restaurants in northern Arkansas. His signature item is a cheese-encrusted beef medallion wrapped in lettuce. Sales (X, in millions of dollars) is related to Profits (Y, in hundreds of thousands of
dollars) by the regression equation Y = 8.21 + 0.76 X. What is your forecast of profit for a store with sales of $40 million? $50 million? Students must recognize that sales is the independent variable and profits is dependent; the problem is not a time series. A store with $40 million in sales: 40 x 0.76 = 30.4; 30.4 + 8.21 = 38.61, or $3,861,000 in profit; $50 million in sales is estimated to profit 46.21 or $4,621,000. (Associative forecasting methods: Regression and correlation, moderate) {AACSB: Analytic Skills} 138. Arnold Tofu owns and operates a chain of 12 vegetable protein "hamburger" restaurants in northern Louisiana. Sales figures and profits for the stores are in the table below. Sales are given in millions of dollars; profits are in hundreds of thousands of dollars. Calculate a regression line for the data. What is your forecast of profit for a store with sales of $24 million? $30 million?
Stor e 1 2 3 4 5 6 7 8 9 10 11 12 Profits 14 11 15 16 24 28 22 21 26 43 34 9 Sale s 6 3 5 5 15 18 17 12 15 20 14 5
Students must recognize that "sales" is the independent variable and profits is dependent. Store number is not a variable, and the problem is not a time series. The regression equation is Y = 5.936 + 1.421 X (Y = profit, X = sales). A store with $24 million in sales is estimated to profit 40.04 or $4,004,000; $30 million in sales should yield 48.566 or $4,856,600 in profit. (Associative forecasting methods: Regression and correlation, moderate) 139. The department manager using a combination of methods has forecast sales of toasters at a local department store. Calculate the MAD for the manager's forecast. Compare the manager's forecast against a naive forecast. Which is better?
Month January February March April May Unit Sales 52 61 73 79 66 Manager's Forecast
June July August September October November December Month January February March April May June July August September October November December Actua l 52 61 73 79 66 51 47 44 30 55 74 125
51 47 44 30 55 74 125 Manager's Abs. Error
50 55 52 42 60 75 Naive Abs. Error
50 55 52 42 60 75 MAD
3 11 22 13 14 50 18.83
51 47 44 30 55 74
4 3 14 25 19 51 19.33
The manager's forecast has a MAD of 18.83, while the naive is 19.33. Therefore, the manager's forecast is slightly better than the naive. (Monitoring and controlling forecasts, moderate) {AACSB: Analytic Skills}
MGT 301: Operations Management Name: Alban Mariau Fall 2008 8/50 84% Instructor: Kurt Haskell Quiz: Chapter 4 Due: Wed Oct 1, 11 PM 1. A nave forecast for September sales of a product would be equal to the forecast for August. True False 2. The forecasting time horizon and the forecasting techniques used tend to vary over the life cycle of a product. True False 3. Forecasts of individual products tend to be more accurate than forecasts of product families. True False 4. Most forecasting techniques assume that there is some underlying stability in the system. True False 5. A time-series model uses a series of past data points to make the forecast. True False 6. Cycles and random variations are both components of time series. True False
7. A naive forecast for September sales of a product would be equal to the sales in August. True False 8. Mean Squared Error and Coefficient of Correlation are two measures of the overall error of a forecasting model. True False 9. In trend projection, the trend component is the slope of the regression equation. True False 10. In trend projection, a negative regression slope is mathematically impossible. True False 11. Seasonal indexes adjust raw data for patterns that repeat at regular time intervals. True False 12. If a quarterly seasonal index has been calculated at 1.55 for the October-December quarter, then raw data for that quarter must be multiplied by 1.55 so that the quarter can be fairly compared to other quarters. True False 13. Linear-regression analysis is a straight-line mathematical model to describe the functional relationships between independent and dependent variables. True False 14. The larger the standard error of the estimate, the more accurate the forecasting model. True False 15. A trend projection equation with a slope of 0.78 means that there is a 0.78 unit rise in Y for every unit of time that passes. True False 16. Demand cycles for individual products can be driven by product life cycles. True False 17. Focus forecasting tries a variety of computer models and selects the best one for a particular application. True False 18. Many service firms use point-of-sale computers to collect detailed records needed for accurate shortterm forecasts. True False 19. Using an exponential smoothing model with smoothing constant = .20, how much weight would be assigned to the 2 most recent period? a. .16 b. .20 c. .04 d. .09 e. .10 20. One use of short-range forecasts is to determine a. production planning b. inventory budgets c. research and development plans d. facility location e. job assignments 21. Forecasts are usually classified by time horizon into three categories a. short-range, medium-range, and long-range b. finance/accounting, marketing, and operations c. strategic, tactical, and operational d. exponential smoothing, regression, and time series e. departmental, organizational, and industrial 22. A forecast with a time horizon of about 3 months to 3 years is typically called a
nd
a. long-range forecast b. medium-range forecast c. short-range forecast d. weather forecast e. strategic forecast 23. Forecasts used for new product planning, capital expenditures, facility location or expansion, and R&D typically utilize a a. short-range time horizon d. naive method, because there is no data history e. all of the above
24. The three major types of forecasts used by business organizations are a. strategic, tactical, and operational b. economic, technological, and demand c. exponential smoothing, Delphi, and regression d. causal, time-series, and seasonal e. departmental, organizational, and territorial 25. Which of the following is not a step in the forecasting process? a. Determine the use of the forecast. b. Eliminate any assumptions. c. Determine the time horizon. d. Select forecasting model. e. Validate and implement the results. 26. The two general approaches to forecasting are a. qualitative and quantitative b. mathematical and statistical c. judgmental and qualitative d. historical and associative e. judgmental and associative 27. Which of the following uses three types of participants: decision makers, staff personnel, and respondents? a. executive opinions b. sales force composites c. the Delphi method d. consumer surveys e. time series analysis 28. Which of the following is not a type of qualitative forecasting? a. executive opinions b. sales force composites c. consumer surveys d. the Delphi method e. moving average 29. Which of the following statements about time series forecasting is true? a. It is based on the assumption that future demand will be the same as past demand. b. It makes extensive use of the data collected in the qualitative approach. c. The analysis of past demand helps predict future demand. d. Because it accounts for trends, cycles, and seasonal patterns, it is more powerful than causal forecasting.
e. All of the above are true. 30. Time series data may exhibit which of the following behaviors? a. trend b. random variations c. seasonality d. cycles e. They may exhibit all of the above. 31. The forecasting model that pools the opinions of a group of experts or managers is known as the a. sales force composition model b. multiple regression c. jury of executive opinion model d. consumer market survey model e. management coefficients model 32. What is the approximate forecast for May using a four-month moving average? Nov. Dec. Jan. Feb. Mar. April 39 36404248 46 a. 38 b. 42 c. 43 d. 44 e. 47 33. The primary purpose of the mean absolute deviation (MAD) in forecasting is to a. estimate the trend line b. eliminate forecast errors c. measure forecast accuracy d. seasonally adjust the forecast e. all of the above 34. Given forecast errors of -1, 4, 8, and -3, what is the mean absolute deviation? a. 2 b. 3 c. 4 d. 8 e. 16 35. Weekly sales of ten-grain bread at the local organic food market are in the table below. Based on this data, forecast week 9 using a five-week moving average. Week Sales 1 415 2 389 3 420 4 382 5 410 6 432 7 405 8 421 Moving average= Demand in previous 8 weeks/8= 409.25 means 410 36. Which of the following techniques uses variables such as price and promotional expenditures, which are related to product demand, to predict demand? a. associative models b. exponential smoothing c. weighted moving average d. simple moving average e. time series
37. Gradual, long-term movement in time series data is called a. seasonal variation b. cycles c. trends d. exponential variation e. random variation 38. The fundamental difference between cycles and seasonality is the a. duration of the repeating patterns b. magnitude of the variation c. ability to attribute the pattern to a cause d. all of the above e. none of the above 39. Which is not a characteristic of exponential smoothing? a. smoothes random variations in the data b. easily altered weighting scheme weights each historical value equally c. d. has minimal data storage requirements e. none of the above; they are all characteristics of exponential smoothing 40. Which of the following values of alpha would cause exponential smoothing to respond the most slowly to forecast errors? a. 0.10 b. 0.20 c. 0.40 d. 0.80 e. cannot be determined 41. The degree or strength of a linear relationship is shown by the a. alpha b. mean mean absolute deviation c. d. correlation coefficient e. RSFE 42. The percent of variation in the dependent variable that is explained by the regression equation is measured by the a. mean absolute deviation b. slope c. coefficient of determination d. correlation coefficient e. intercept 43. Many services maintain records of sales noting a. the day of the week b. unusual events c. weather d. holidays e. all of the above 44. What is the forecast for May based on a weighted moving average applied to the following past demand data and using the weights: 4, 3, 2 (largest weight is for most recent data)?
Nov. 37
Dec. 36
Jan. 40
Feb. 42
Mar. 47
April 43
[(42*2)+(47*3)+(43*4)]/9= 44.111 45. Weekly sales of ten-grain bread at the local organic food market are in the table below. Based on this data, forecast week 9 using a five-week moving average. Week Sales 1 415 2 389 3 420 4 382 5 410 6 432 7 405 8 421 Moving average= Demand in previous 8 weeks/8= 409.25 means 410 46. Times series forecasts use a series of past data points to make a forecast. 47. Moving average methods forecasts employ one or more mathematical models that rely on historical data and/or causal variables to forecast demand. 48. Times series forecasts use a series of past data points to make a forecast. 49. Linear regression is known as an associative forecasting because it incorporates variables or factors that might influence the quantity being forecast. 50. A mean absolute deviation is a measure of overall forecast error for a model.

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1P L AT OPhaedo: SelectionsPlato of Athens (c. 429347 B.C.E.) stands with Aristotle as one of the two most important philosophers of Antiquity and as a major shaper of the Western intellectual history as a whole. Descended from a wealthy and aristocrat

Columbia State Community College - MATH - Math 1131

MATH 1131 3.00 A S1 Assignment 1 Question 1: Water quality ratings, which range from A+ to F- and which reect the risk of getting sick from swimming at any particular one of 36 Southern California beaches, are given in the following list: A+ A A D D A A+

Columbia State Community College - MATH - Math 1131

MATH 1131 3.00 A S1 Assignment 2 Question 1: The following two relationships together for any two events A and B are called De Morgans laws: (A B )c = Ac B c (A B )c = Ac B c . Convince yourself of the truth of these two laws by expressing in words the st

Columbia State Community College - MATH - Math 1131

MATH 1131 3.00 A S1 Assignment 3 Total marks = 55 Question 1: A contractor is required by a county planning department to submit anywhere from one to ve forms (depending on the nature of the project) in applying for a building permit. Let r.v. X = the num

Columbia State Community College - MATH - Math 1131

MATH 1131 3.00 A S1 Assignment 4 Total marks = 50 Question 1: On your shelf, you have four books that you are planning to read in the near future. Two are ctional works, containing 212 and 379 pages, respectively, and the other two are nonction, with 350

Columbia State Community College - NATURAL SC - Nats 1520

Review of Lectures 2 to 9 (slide 5):For 2009 Fall Midterm Test (Test 1) The Fall Midterm test will be based on ALL material covered inlectures 2 through 9 (up to and including slide 5) For the complete list of topics and associated material that will

Columbia State Community College - NATURAL SC - Nats 1520

Test 2 - Review of Lectures 2 to 22:For 2009 December Exam (Test 2)The December Exam will be based on ALL material covered in lectures 2 through 22 (all of the Fall Semester content) For the complete list of topics and associated material that will be c

University of Texas - PHY - 303L

harvey (zmh93) Homework 1 Homann (56745) This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. 001 10.0 points There are two identical small metal spheres with charges 2

Academy of Design Chicago - MECT - 27982

Materials ScienceandEngineering Compositionmeans thechemicalmakeupof a material. Structuremeansa descriptionofthe arrangements ofatomsorionsina material. Synthesisisthe processbywhich materialsare madefromnaturally occurringorother chemicals. Processingme

AUP - A - 0111

A 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 28 29 30 31 32 33 34 35 36 37 38BCDEGHIJKTemplate for the M/M/s Queueing Model= = s= Pr(W > t) = when t = Prob(Wq > t) = when t =0.25 0.2 Probability 0.15 0.1 0.05 0 0 1

Temple - ENGR - 2112

G. Rizzoni, Principles and Applications of Electrical EngineeringProblem solutions, Chapter 1Chapter 1 Instructor NotesChapter 1 is introductory in nature, establishing some rationale for studying electrical engineering methods, even though the student

Temple - ENGR - 2112

G. Rizzoni, Principles and Applications of Electrical EngineeringProblem solutions, Chapter 2Chapter 2 Instructor NotesChapter 2 develops the foundations for the first part of the book. Coverage of the entire Chapter would be typical in an introductory

Temple - ENGR - 2112

G. Rizzoni, Principles and Applications of Electrical EngineeringProblem solutions, Chapter 3Chapter 3 Instructor NotesChapter 3 presents the principal topics in the analysis of resistive (DC) circuits. The presentation of node voltage and mesh current