Unit 2: Forecasting
A human resource department is predicting the number of quarterly safety accidents based on the number of safety hours of training provided. The table below shows a partial data set. Using MS Excel, the estimated intercept and slope of a regression equation were 8 and -.02 respectively (note negative sign). Using these parameter values and problem specific variable names (e.g. not X or Y), write the straight line regression equation.
#quarterly safety accidents= 8-0.2 (training safety hours)
When using an exponential smoothing forecast, a higher alpha will adjust the forecast more quickly to an emerging trend but it does so at the risk of picking up too much noise (randomness) in the data series. True False
True
When using the exponential smoothing method Ft = Ft-1 + α (At-1 - Ft-1) an alpha value = 0 is equivalent setting the current period forecast equal to the prior period forecast. True False
True
When using the exponential smoothing method Ft = Ft-1 + α (At-1 - Ft-1), an alpha value = 1 is equivalent to the naïve method. True False
True
When using the exponential smoothing method discussed in class the alpha (α) parameter is used to adjust the prior period forecast by some fraction α of the prior period error. True False
True
Valid values for the exponential smoothing method are from 0 to 1 inclusive. True False
True
Using a linear time trend method, the absolute deviations for five periods were 2, 3, 1, 4, 2. What is the mean absolute deviation? Round answer to nearest single decimal place.
2.4
A retail store wants to use the last two years of sales revenue shown in the table below to calculate seasonal sales proportions using the method from class notes. Using both years data, what is the sales proportion for the fall season? Write answer in decimal form rounded to two decimal places. Season Year 1 Year 2 Winter 1200 1500 Spring 550 500 Summer 800 860 Fall 1200 1800
0.36
The number of daily customers arriving at a drive-up coffee shop during morning, midday and afternoon hours is shown in the table below. Using the last two weeks data, what would be the proportion of customers during the morning part of the day? Write answer in decimal form rounded to two decimal places. Season Weekday 1 Morning-150 Mid-Day-80 Afternoon-50 Weekday 2 Morning-120 Mid-day -65 Afternoon -45
0.53
A lumber company is predicting annual lumber sales revenue based on the number of new home starts in the local economy. Using the estimated equation shown below, what is the forecasted number of sales revenue if the number of new home starts is 30? sales revenue = -24,350 + 42,300 (# new home starts) (note negative sign)
1,244,650
Consider the following time series of the number of weekly tickets sold for a movie. 102 (most distant), 90, 95, 86 (most recent) Using a two period moving average method, what would be the forecast of tickets sold for the next week?
91
Using a weighted moving average, the forecasted demand for period 8 was 45 and the actual for period 8 was 32. What is the absolute deviation?
13
Consider the below time series of the weekly demand for an automobile supply part. An analyst is using an exponential smoothing method Ft = Ft-1 + α (At-1 - Ft-1) with alpha value = .30. What would be the forecasted demand for the next week (t=3)? Begin by making a forecast for period 2 using the naïve method. Day Part Demand 1 (most distant) 122 2 (most recent) 150
130
A restaurant has made a forecast of 200 meal requests for the next day (day=3) and wants to know how many of these 200 requests will be for lunch and for dinner. Using the seasonal forecasting method discussed in class and the last two days of demand data, how many of the 200 requests will be for dinner? Meal # Meals Day 1 Lunch-40 Dinner-75 # Meals Day2 Lunch-65 Dinner-140
134
A farm is predicting the number of Christmas trees sold based on year e.g. (t=2010, 2011,...). Using the estimated regression equation shown below, what is the forecasted number of trees sold for year 2017? number of trees sold = -7,900 + 4( year) (note negative sign)
168
Using an associative regression method, the absolute deviations for four periods were 22, 31, 19, 20. What is the mean absolute deviation?
23
A toy store is predicting monthly number of a train engine sold. They are using month time period as an explanatory variable (t=1,2,3...). Using the estimated equation shown below, what is the forecasted number of patrons for month 8? monthly # train engines sold = 28 + 1.2(t)
38
The average proportions of customers requesting service at a tire shop during morning, midday and afternoon hours is shown in the table below. The forecasted number of customers for the next weekday is 85. Using the seasonal forecasting method discussed in class, what would be the forecast of customers during the next weekday's mid-day hours? Season Season Proportion Morning 20% Mid-Day 60% Afternoon 20%
51
An analyst at large garden store is predicting the number of shrubs sold based on price per shrub. Using the estimated equation shown below, what is the forecasted number of shrub sold if price is $32? number of shrubs sold = 575 - 1.5 (price / shrub)
527
Compute a MAD score using the following actual and forecast values. Time Period Actual (At) Forecast (Ft) 1 1200 1290 2 1050 1027 3 1425 1370
56
Consider the below time series of a daily price ($K) of a treasury bond. An analyst is using an exponential smoothing method Ft = Ft-1 + α (At-1 - Ft-1) with alpha value = .8. what would be the forecasted bond price for the next day (t=4)? Begin by making a forecast for period 2 using the naïve method. (Be careful, you may need to use the exponential smoothing formula more than once). Round forecasts to two decimal places. Day Bond Price 1 (most distant) 7.2 2 7.4 3(most recent) 6.8
6.91
The average proportions of diners served during the first and second parts of the week are shown in the in the table below. The restaurant forecasts 920 diners for all of the next week. Using the seasonal adjustment method discussed in class, what would be the forecast of customers during the second part of next week (Thurs -Sat)? Season Season Proportion Sun -Wed 30% Thurs - Sat 70%
644
Consider the following time series of the number of weekly tickets sold to tour a farm. 28 (most distant), 40, 52, 73 (most recent). Using a two period weighted moving average method with a most recent weight of .60, what would be forecasted number of tickets sold for the next week?
65
Using a moving average method, the forecasted number of dinners served for period 15 was 85 and the actual for period 15 was 92. What is the absolute deviation?
7
Consider the following time series of a monthly bond price: 8700 ,8205, 8222, 8777. Using a four period moving average, what would be the forecasted bond price for the next month?
8476
Consider the following time series of the number of weekly tickets sold for scuba diving trips. 102 (most distant), 90, 95, 86 (most recent) Using a naïve method, what would be the forecast of tickets sold for the next week?
86
A new fitness center is predicting the number of membership sold each month based on month time period (t=1,2,3..). The estimated regression equation has an R2 of .62. Interpret the R2 using the R2 value and problem specific variable names.
Changes in month explain 62% of changes in memberships sold per month. OR 62% of changes in memberships sold per month are accounted for by changes in month. OR Variation of monthly time periods explains 62% of the variation of memberships sold per month.
A marketing department is predicting the number of cosmetic kits sold based on promotional spending and has estimated a regression equation with an R2 of .65. Interpret R2 using the R2 value and problem specific variable names.
Changes in promotional spending explain 65% of the changes in the number of cosmetic kits sold. OR 65% of the changes in the number of cosmetic kits sold is accounted for by changes in promotional spending OR Variation of promotional spending explains 65% of the variation of the number of cosmetic kits sold
A city traffic department is predicting the revenue earned from parking tickets based on the number of parking enforcement officers deployed. The estimated regression equation has an R2 of .32. Interpret R2 using the R2 value and problem specific variable names.
Changes in the number of officers deployed explain 32% of the changes in parking ticket revenue. OR 32% of parking ticket revenue is accounted for by changes in the number of officers deployed. OR Variation of the number of officers deployed explains 32% of the variation of parking ticket revenue.
A qualitative forecast is often based on historical data. True False
False
A quantitative forecast is often based on peoples' opinions. True False
False
Consider a time series that has no trend component but which has considerable random fluctuations. In this case, a weighted moving average with heavy weight on more recent periods will help create a smoother forecast (e.g.remove fluctuations from the forecast). True False
False
R2 measures the change in the dependent variable for a one unit increase in the independent variable. True False
False
Relative to a multiple period moving average, the naïve method is more likely to produce accurate demand forecasts when demand has large random fluctuations and a weak trend component. True False
False
T/F: MAD is an acronym for Maximum Accuracy Detector.
False
T/F: The MAD criterion gives greater weight to over-forecasted errors than to under-forecasted errors.
False
The quantitative forecasting methods discussed in class are more likely to be appropriate for a new product than a mature product. True False
False
An automotive dealer is predicting annual cars sales revenue (SK) based on employment wages ($M) of the local economy. The estimated regression equation is shown below. Interpret the slope using the slope value and problem specific variable names. Sales revenue $K = -12 + 22 (employments wages $M)
On average, sales revenue increase by $22k for each $1M increase in employment wages
An analyst is at large garden store is predicting the number of shrubs sold based on price per shrub. The estimated regression equation is shown below. Interpret the slope using the slope value and problem specific variable names. Number of shrubs sold = 575 - 1.2 (price / shrub)
On average, the number of shrubs sold decrease by 1.2 for each dollar increase in price per shrub
The quantitative forecasting methods discussed in class are more likely to be appropriate for a mature product than a new product True False
True
A financial analyst is predicting a monthly stock price based on the monthly time period (t=1,2,3..larger t is most recent). The estimated regression equation is shown below. Interpret the slope using the slope value and problem specific variable names. monthly stock price = 40 - .75 (month #)
The monthly stock price is decreasing by $0.75 per month on average
The exponential smoothing methods may be interpreted as a method which adjusts the prior period forecast by some fraction of the prior period error. True False
True
The qualitative forecasting methods discussed in class are more likely to be appropriate for a new product than a mature product. True False
True
A qualitative forecast is often based on peoples' opinions. True False
True
A quantitative forecast is usually based on historical data. True False
True
In practice, the exponential smoothing method requires that an initial forecast for some earlier time period to be made using some other method such as the naïve method. This avoids the problem of an endless chain of making prior period forecasts True False
True
Informally, least squares regression fits a straight line to a series of data. True False
True
R2 is a measure of goodness of fit or of how well the independent (or explanatory) variable(s) account for changes in the dependent (or predicted) variable. True False
True
R2 is the proportion of the variance in the dependent variable explained by the variance of the independent variable(s). True False
True
Relative to a multiple period moving average, the naïve method is more likely to produce accurate demand forecasts when the time series has a strong trend component and small random fluctuations. True False
True
T/F: A deviation is computed as actual (At) - forecast (Ft) for a given period t.
True
T/F: An absolute deviation drops the sign of the deviation.
True
T/F: Proportional values must fall in the range from 0% to 100% inclusive.
True
T/F: The MAD criterion averages the absolute deviations across time periods.
True
T/F: The values of a correlation coefficient must be between -1 and 1 inclusive.
True
T/F: A synonym for deviation is error.
True
T/F: A synonym for mean is average.
True
T/F: All else being equal, lower MAD scores are preferred
True
T/F: MAD is an acronym for Mean Absolute Deviation.
True
T/F: Proportional values must fall in the range from 0 to 1 inclusive.
True
T/F: The MAD criterion gives equal weight to over-forecasted errors and under-forecasted errors.
True
The MAD criterion is a summary measure of forecasting error.
True
The exponential smoothing method may be interpreted as a weighted average of the prior period actual and the prior period forecast. True False
True
Consider the generic form of a linear regression equation: y = a + b x. In this example, x is the _________. a. independent variable b. intercept parameter c. dependent variable d. slope parameter
a. independent variable
A demand forecast is a prediction of ____________ a. sales in dollars or units b. number of employees c. inventory d. costs e. customer complaints
a. sales in dollars or units
Consider the generic form of a linear regression equation: y = a + b x. In this example, b is the _________. a. slope parameter b. intercept parameter c. independent variable d. dependent variable
a. slope parameter
A police department is predicting the average speed on a highway based on the number of patrol cars deployed. Using MS Excel, the estimated intercept and slope of a regression equation were: 75 and - 3.1 (note negative sign). Using these parameter values and problem specific variable names (e.g. do not use X or Y), write the straight line regression equation.
average highway speed= 75-3.1(number of patrol cars deployed)
The MAD score of five forecasting methods are given below. Which MAD score is the best, assuming all else is the same. a. 6777 b. 2987 c. 3003 d. 4200 e. 5345
b. 2987
A forecasting technique that uses a facilitator to iteratively collect opinions form experts in order to build consensus is called a ____________. a. a multigroup method b. a delphi technique c. a market survey d. a regression analysis e. a sales force composite
b. a delphi technique
Consider a time series where values in 95% of time periods showed a decrease from prior periods. Based on class notes this would be an example of _____________. a. a known b. a trend c. random variations d. seasonality e. cycles
b. a trend
Consider the generic form of a linear regression equation: y = a + b x. In this example, a is the _________. a. dependent variable b. intercept parameter c. independent variable d. slope parameter
b. intercept parameter
The central purpose of a forecast is to ______________. a. reduce costs b. provide an estimate about some future state c. analyze data d. obtain opinions e. increase sales
b. provide an estimate about some future state
Consider an aircraft maintenance shop where demand for some spare parts is sporadic and unpredictable. Based on class notes, this would be an example of _________. a. the knowns b. random variations c. cycles d. seasonality e. a trend
b. random variations
Demand refers to ______________ . a. inventory requirements b. requests for a product or service c. the maturity of an industry d. workforce levels e. technological change
b. requests for a product or service
Forecasting provides the basis for ____________ . a. planning inventory levels b. resource allocation decisions c. all of the above d. determining needed employees e. making finance decisions
c. all of the above
A correlation coefficient with a value ________ indicates imperfect negative correlation. a. between 0 and 1 b. equal to 1 c. between -1 and 0 d. equal to 0 e. equal to -1
c. between -1 and 0
Consider the generic form of a linear regression equation: y = a + b x. In this example, y is the _________. a. independent variable b. slope parameter c. dependent variable d. intercept parameter
c. dependent variable
A forecast used to evaluate locations of new restaurants would most likely have a ___________ time horizon and would be made at a ___________ level of analysis a. short-term, an aggregate b. short-term, a detailed c. long-term, an aggregate d. long-term, a detailed
c. long-term, an aggregate
Consider an accounting firm's that is forecasting the number of tax returns that it will need complete during the upcoming busy annual tax season. If its sets this forecast, equal to the prior seasons actual returns completed, which of the following techniques were used? a. associative regression model b. linear trend c. naïve method d. weighted moving average e. moving average
c. naïve method
Based on class notes, blips in a data series that cannot be predicted are referred to as ____________. a. seasonality b. a trend c. random variations d. cycles e. the knowns
c. random variations
Based on class notes, a data pattern that repeats itself after a period of hours, days, months, or quarters is referred to as ______________. a. random variations b. a trend c. seasonality d. cycles e. the forecast
c. seasonality
A forecast used to determine the number of salads to prepare at a restaurant would most likely have a ___________ time horizon and would be made at a ___________ level of analysis. a. long-term, an aggregate b. long-term, a detailed c. short-term, a detailed d. short-term, an aggregate
c. short-term, a detailed
Consider a process where each sales manager is asked to make an estimate of sales in their region and then these estimates are summed to form an overall forecast. Based on class notes, you would be using ______________. a. a market survey b. a regression analysis c. a delphi technique d. a sales force composite e. multigroup method
d. a sales force composite
Based on class notes, two major types of forecasts which are distinguished based on the kind of input of used to make the forecast are ______________. a. forward and backward b. positive and negative c. revenue and cost d. qualitative and quantitative e. basic and advanced
d. qualitative and quantitative
Based on class notes, a time series can be decomposed into all of the following components except ______. a. random variations b. cycles c. seasonality d. uncertainties e. trend
d. uncertainties
If a linear equation is used to make a forecast of sales based on time periods then which of the following techniques discussed in class has been used? a. associative regression model b. naïve method c. weighted moving average d. exponential smoothing e. linear time trend
e. linear time trend
An aquarium is predicting weekly visits to a new attraction based on week time period (t=1,2,3...). Using MS Excel, the estimated intercept and slope of a regression equation were 16 and 5 respectively. Using these parameter values and problem specific variable names (e.g. do not use X or Y), write the straight line regression equation.
number of aquarium visitors per week= 16+5(week#)
A new fitness center is predicting the number of membership sold each month based on time period (t=1,2,3...larger t is most recent). The estimated regression equation is shown below. Interpret the slope using the slope value and problem specific variable names. number of memberships sold = 16 + 4(month #)
the number of memberships sold is increasing by 4 per month, on average