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A regression model is used to forecast sales based on advertising dollars spent. The regression line is y=500+35x and the coefficient of determination is .90. Which is the best statement about this forecasting model? |
The correlation between sales and advertising is positive. |
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The best statement about this forecasting model is that the correlation between sales and advertising is positive. In this example the relationship between coefficients is expressed as a positive (+), which indicates a positive correlation between sales and advertising. The equation does not give us enough information to predict an exact relationship between dollars spent on advertising and ultimate sales. |
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A time-series trend equation is 25.3 + 2.1X. What is your forecast for period 7? |
40.0 |
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The forecast for period 7 is 40. This is determined by solving the equation 25.3 + 2.1X, where X = time period. In this case we are interested in period 7. Therefore: 25.3 + 2.1(7) =40 |
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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: |
3.5 |
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The Mean Absolute Deviation (MAD) is 3.5. The mean absolute deviation is designed to provide a measure of overall forecast error for the model. It does this by taking the sum of the absolute values of the individual forecast errors and dividing by the number of data periods. The last four months sales were 8, 10, 15, and 9 units. The forecasts for these same months were 5, 6, 11, and 12 units. Forecast errors are calculated using the equation demand – forecast. In this case, that would be 8 – 5 = 3; 10 – 6 = 4; 15 – 11 = 4; 9 – 12 = -3. Therefore: 3+4+4+3 = 14 |
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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: |
100.6 |
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The forecast for the next period would be 100.6. The simple exponential smoothing forecast model uses the following equation: Last periods forecast + α(Last periods demand – last periods forecast), where α = the smoothing constant. Therefore, in this case: Last periods forecast = 99 99 + .4 (103 – 99) = 100.6 |
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For a given product demand, the time-series trend equation is 53 – 4X. The negative sign on the slope of the equation: |
is an indication that product demand is declining |
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The negative sign on the slope of the equation is an indication that product demand is declining. A negative slope indicates a downward trend for the regression line, which would indicate that demand is declining across time periods. While the regression equation, like other quantitative methods, includes statistical error, this is not indicated in the negative slope. Furthermore, a negative slope is mathematically possible. |
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A forecast that projects a company’s sales is a(n): |
Demand forecast |
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A forecast that projects a company’s sales is a demand forecast. Demand forecasts (also called sales forecasts) are projections of demand for a company’s products or services. Demand forecasts impact a company’s production, capacity, and scheduling systems. |
Economic forecasts utilize indicators like inflation rates, money supplies, and housing starts to understand business cycles. Technological forecasts are concerned with rates of technological progress, which can result in the birth of new products and opportunities. |
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The primary purpose of the mean absolute deviation (MAD) in forecasting is to: |
Measure forecast accurarcy |
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Forecasts are usually classified into three categories including: |
short-range, medium-range, and long-range |
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Economic forecasts utilize indicators like inflation rates, money supplies, and housing starts to understand business cycles. Technological forecasts are concerned with rates of technological progress, which can result in the birth of new products and opportunities. |
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The degree or strength of a relationship between two variables is shown by the__________ |
correlation coefficient |
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Quantitative methods of forecasting include |
Exponential smoothing |
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Quantitative methods of forecasting include exponential smoothing. Consumer market surveys and sales force composites are both considered qualitative methods. |
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Which of the following statements about time-series forecasting is true? |
It is based on the assumption that the analysis of past demand helps predict future demand. |
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The statement indicating that time-series forecasts are based on the assumption that the analysis of past demand helps predict future demand is true. While time-series forecasts do utilize past demand in the predictive model, the approach does not make the assumption that future demand will be the same as past demand. Time-series forecasts include trends, seasonality, cycles, and random variation so forecasts can increase, decrease, or stay the same as past demand. |
The quantitative method known as the naïve method makes the assumption that future demand will be the same as past demand. Associative models, such as regression models, are considered more powerful than time-series models because they do not rely solely on historical values for forecasted variables. |
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Given last periods forecast of 65, and last periods demand of 62, what is the simple exponential smoothing forecast with an alpha of .4 for the next period? |
63.8 |
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The forecast for the next period would be 63.8. The simple exponential smoothing forecast model uses the following equation: Last periods forecast + α(Last periods demand – last periods forecast), where α = the smoothing constant. Therefore, in this case: Last periods forecast = 65 65 + .4 (62 – 65) = 63.8 |
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The tracking signal is the__________ |
ratio of cumulative error/MAD |
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The tracking signal is the ratio of the cumulative error/MAD. A tracking signal is a measure of how well a forecast is predicting actual demand values. The standard formula used to provide a tracking signal is dividing the cumulative error by the mean absolute deviation. This is represented as |
Tracking signal = cumulative forecast error/mean absolute deviation The mean absolute deviation (MAD) is designed to provide a measure of overall forecast error for the forecast model. It does this by taking the sum of the absolute values of the individual forecast errors and dividing by the number of data periods. The standard error of the estimate is designed to provide a measure of variability around the regression line. |
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Given an actual demand of 61, a previous forecast value of 51, and an alpha of .3, the exponential smoothing forecast for the next period would be: |
58.9 |
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The forecast for the next period would be 58.9. The simple exponential smoothing forecast model uses the following equation: Last periods forecast + α(Last periods demand – last periods forecast), where α = the smoothing constant. Therefore, in this case: Last periods forecast = 58 58 + .3(61 – 58) = 58.9 |
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Time-series patterns that repeat themselves after a period of days or weeks are called __________ |
seasonilty |
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Which of the following uses three types of participants: decision makers, staff personnel, and respondents? |
The Delphi method |
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The Delphi method uses three types of participants: decision makers, staff personnel, and respondents to make forecasts. Sales force composites are a forecasting technique based on salespersons’ estimates of expected sales. Executive opinions are a forecasting technique that uses the opinion of a small group of high-level managers to form a group estimate of demand. |
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Given the following data about monthly demand, what is the approximate forecast for May using a four month moving average? November = 39 |
44 |
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The four-month moving average is 44. The moving average is calculated by summing the relevant monthly demand reports and dividing by the months included in the model. In this case, we are calculating a four month moving average for May so we will use the months of January (40), February (42), March (48), and April (46) in our calculation. Therefore: 40+42+48+46 = 176 |
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If demand is 106 during January, 120 in February, 134 in March, and 142 in April, what is the 3-month simple moving average for May? |
132 |
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The 3-month moving average for May is 132. The moving average is calculated by summing the relevant monthly demand reports and dividing by the months included in the model. In this case, we are calculating a three month moving average for May so we will use the months of February (120), March (134), and April (142) in our calculation. Therefore: 120+134+142 = 396 |
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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? |
1000 units |
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The seasonally-adjusted sales forecast for January is 1000 units. To calculate a seasonally-adjusted sales forecast you take the product forecast (in this case 800) and multiply that by the monthly index (in this case 1.25). Thus, 800 * 1.25 = 1000. |
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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: |
0.684 |
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The approximate seasonal index for July is 0.684. The seasonal index is calculated by dividing a month’s actual average demand by the average demand over all months. Thus, in this case: Step 1 – Calculate average historical demand. To do this, we must first obtain the actual demand during July (in this case 110, 150, 130) and divide by the number of months on record (in this case 3). Thus, average July demand is calculated as 110 + 150 + 130 = 390/3 = 130 |
Step 2 – Calculate seasonal index by taking monthly average (130) and dividing by average demand over all months (190). Seasonal index for July is 130/190 = 0.684 |
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Forecasts used for new product planning, capital expenditures, facility location or expansion, and R&D typically utilize a__________ |
long-range time horizon |
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Forecasts used for new product planning, capital expenditures, facility location or expansion, and R&D typically utilize a long-range time horizon. Long-range forecasts have a time span that is longer than 3 years. Long range forecasts are used in planning for new products, capital expenditures, and facility planning. |
Short-range forecasts have a time span of up to 1 year, but are generally less than 3 months. Short-range forecasts are used to schedule jobs, determine workforce levels, and planning purchases. Medium-range forecasts have a time span that ranges from 3 months to 3 years. Medium-range forecasts are used to plan production cycles, determine budgets, and make operation level decisions. |
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Which time-series model assumes that demand in the next period will be equal to the most recent period’s demand? |
Naïve approach |
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The time-series model that assumes demand in the next period will be equal to the most recent period’s demand is the Naïve approach. The Naïve approach is the simplest forecasting method because it assumes that future demand will equal the last period’s demand. |
The moving average approach, on the other hand, uses the average demand across the most recent periods of data (e.g. quarterly, annually, etc.) to forecast future demand. The exponential smoothing approach is a complicated forecasting approach that uses statistical weights for individual data points. |
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Given forecast errors of -1, 4, 8, and -3, what is the mean absolute deviation? |
4 |
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The mean absolute deviation is 4. The mean absolute deviation is designed to provide a measure of overall forecast error for the model. It does this by taking the sum of the absolute values of the individual forecast errors and dividing by the number of data periods. In this case, 1+4+8+3 = 16 |
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Which of the following smoothing constants would make an exponential smoothing forecast equivalent to a naïve forecast? |
1.0 |
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The smoothing constant that would make an exponential smoothing forecast equivalent to a naïve forecast is 1.0. A smoothing constant value of 1.0 suggests that the forecast for the next period is exactly the same as the forecast for this period’s demand, which is the same as the naïve forecast model. |
A smoothing constant is a weighting factor applied in an exponential smoothing forecast to improve accuracy. The smoothing constant can range from 0 to 1, but most frequently the forecaster chooses a value between .1 and .5. |
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Forcasting |
The art and science of predicting future events |
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future time horiazon |
1. short-range forecast:has a time span of up to 1 year but is generally less than 3 months-planning purchasing, job scheduling, workforce levels, job assignments, and production levels 2. medium-range forecast: or intermediate, forecast generally spans from 3 months to 3 years. used in sales planning, production planning and budgeting, cash budgeting, and analysis of various operation plans 3. Long-range forecast: generally 3 years or more in time span, long-range forecasts are used in planning for new products, capital expenditures, facility location or expansion, and research and development |
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economic forecasts |
address the business cycle by predicting inflation rates, money supplies, housing starts, and other planning indicators 2. Technological forecasts are concerned with rates of technological progress |
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demand forecasts |
projections of a company’s sales for each time period in the planing horizon |
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Seven steps in forecasting system |
1. Determine the use of the forecast 2. select the items to be forecasted 3. determine the time horizon of the forecast 4. select the forecasting models 5. gather the data needed to make the forecast 6. make the forecast 7. validate and implement the results |
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quantitative forecasts |
forecasts that employ mathematical modeing to forecast demand |
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qualitative forecasts |
forecasts that incorporate such factors as the decision maker’s intuition, emotions, personal experiences, and value system |
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jury of executive opinion |
a forecasting technique that use the opinion of a small group of high-level managers to form a group estimate of demand |
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delphi method |
a forecasting technique using a group process that allows experts to make forecasts |
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sales force composite |
a forecasting technique based on salesperson’s estimates of expected sales |
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market survey |
a forecasting method that solicits input from customers or potential customers regarding future purchasing plans. |
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time series |
a forecasting technique that uses a series of past data points to make a forecast |
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naive approach |
a forecasting technique which assumes that demand in the next period is equal to projections of a company’s sales for each time period in the planing horizon in the most recent period |
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moving averages |
a forecasting method that uses an average of the N most recent periods of data to forecast the next period |
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moving average=E demand in previous N periods/N |
weighted moving average = E ((Weight for period N) (Demand in period N))/E weights |
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problems with moving averages |
1. increasing the size of N does smooth out fluctuations better, but it makes the method less sensitive to changes in the data 2. Moving averages cannot pick up trends very well. Because they are averages, they will always stay within past levels and will not predict changes to higher or lower levels they lag the actual values 3. Moving averages require extensive records of past data |
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exponential smoothing |
a weighted-moving average forecasting technique in which data points are weighted by an exponential function |
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smoothing constant |
the weighting factor used in an exponential smoothing forecast, a number greater than or equal to 0 and less than or equal to 1 |
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Mean absolute deviation (MAD) |
a measure of the overall forecast error for a model MAD= E |actual- forecast|/ N |
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Mean squared error (MSE) |
the average of the squared differences between the forecastered and observed values |
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Mean absolute percent error (MAPE) |
the average of the absolute differences between the forecast and actual value, expressed as a percent as a percent of actual values |
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trend projection |
a time-series forecasting method that fits a tend line to a series of historic data points and then projects the line into the future for forecasts |
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seasonal variation |
regular upward or downward movements in a time series that tie to recurring events |
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Cycles |
patterns in the data that occur every several years |
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Linear-regression analysis |
straight-line mathematical model to describe the functional relationships between independent and dependent variables |
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standard error of the estimate |
a measure of variability around the regression line-its standard deviation |
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coefficient of correlation |
a measure of the strength of the relationship between two variables |
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page 132 |
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