Question 1

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-In the linear trend equation, Ft+k = at + btk, at is known as the .
A) level
B) trend
C) slope
D) forecast

Accepted Answer

Level is the initial value of the time series.

Question 2

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-In the linear trend equation Ft+k = at + btk, identify the term that signifies the trend.
A) bt
B) k
C) at
D) Ft + k

Accepted Answer

The term "bt" in the linear trend equation Ft+k = at + btk represents the trend component, where "b" is the slope of the trend line, and "t" is the time period.

Question 3

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-Which of the following is the value of the root mean square error for the given data?
A) 11.56
B) 21.77
C) 13.87
D) 20.13

Accepted Answer

B

Question 4

What is a stream of historical data known as?
A) a time series
B) an index
C) a complex number
D) an orthopole

Accepted Answer

A stream of historical data is commonly known as a time series.

Question 5

Before launching a new line of toys, Toys Inc. used the method of historical analogy to obtain a forecast. In this scenario, Toys Inc.:
A) noted the behavior of its current customers while they use their products.
B) used a panel of experts, whose identities were kept confidential from one another, to respond to a sequence of questionnaires.
C) noted the consumer response to similar previous products to marketing campaigns and used the responses as a basis to predict how the new marketing campaign might fare.
D) used a brainstorming session among a group of experts to draw new ideas.

Accepted Answer

Historical analogy involves looking at past events or situations to predict how a new situation will play out. In this case, Toys Inc. is using the reaction of consumers to previous similar products to predict how the new line of toys will fare in the market.

Question 6

If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values is . 
A) $ \mathrm{MAD}=\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n} $

B) $ \mathrm{MAD}=\frac{\sum_{t=1}^{n}\left(A_{t}-F_{t} \mid\right)^{2}}{n} $

C) $ \mathrm{MAD}=\frac{\sum_{t=1}^{n} \sqrt{\left|A_{t}-F\right|}}{n} $

D) $ \mathrm{MAD}=\frac{\sum_{t=1}^{n}\left|\frac{A_{t}-F_{t}}{2}\right|}{n} $

Accepted Answer

The formula for mean absolute deviation (MAD) is the average of absolute forecast errors over a given range. Absolute forecast error is the absolute difference between the forecast value and the actual value at a given time. Therefore, formula A $ \mathrm{MAD}=\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n} $ is the correct formula for calculating MAD.

Question 7

Use the data given below to answer the following question(s).
The details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-If the smoothing constant is assumed to be 0.7, and setting F1 and F2 = A1, the exponential smoothing sales forecast for week 7 is approximately .
A) 50 clocks
B) 80 clocks
C) 60 clocks
D) 70 clocks

Accepted Answer

The answer of Use the data given below to answer...

Question 8

Time-series models may exhibit seasonal effects or cyclical effects. A seasonal effect differs from a cyclical effect in that a seasonal effect:
A) has no trend, is relatively constant, and only exhibits random behavior.
B) describes ups and downs over a time frame such as several years.
C) is one that repeats at fixed intervals of time, typically a year, month, week, or day.
D) is based on analysis of historical time-series data and are predicated on the assumption that the future is an extrapolation of the past.

Accepted Answer

A seasonal effect is one that repeats at fixed intervals of time, typically a year, month, week, or day. This is different from a cyclical effect which describes ups and downs over a time frame such as several years. Option A is incorrect because seasonal effects can exhibit a trend and are not necessarily constant. Option B is incorrect because it describes a cyclical effect, not a seasonal effect. Option D is incorrect because it describes time-series models in general, not specifically seasonal effects.

Question 9

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-What is the forecasted value for the 7th week?
A) 53 phones
B) 82 phones
C) 71 phones
D) 49 phones

Accepted Answer

The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. So, we can use a simple exponential smoothing method to forecast the value for the 7th week. The formula for simple exponential smoothing is:Ft+1 = αYt + (1-α)Ftwhere:Ft+1 is the forecast for the next periodYt is the actual value for the current periodFt is the forecast for the current periodα is the smoothing constantWe can optimize the value of α by minimizing the mean absolute error (MAE) of the forecast. The MAE is calculated as:MAE = 1/n Σ|Ft+1 - Yt+1|where:n is the number of periodsFt+1 is the forecast for the next periodYt+1 is the actual value for the next periodWe can use a trial-and-error approach to find the value of α that minimizes the MAE. In this case, we find that α = 0.1 minimizes the MAE.Using α = 0.1, we can forecast the value for the 7th week as follows:Ft+1 = αYt + (1-α)FtFt+1 = 0.1(85) + (1-0.1)(71)Ft+1 = 82Therefore, the forecasted value for the 7th week is 82 phones.

Question 10

Use the data given below to answer the following question(s).
The details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-For the given data, what is the value of the simple moving average mean square error?
A) 0.21
B) 20.12
C) 14.25
D) 207.13

Accepted Answer

The simple moving average with k=2 is calculated for weeks 3 to 6. The errors are squared and averaged to find the mean square error, which is 207.13.

Question 11

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-What is the difference between the forecasted and the actual value for the 3rd week?
A) 1 phones
B) 6 phones
C) 4 phones
D) 3 phones

Accepted Answer

The answer of Use the data given below to answer...

Question 12

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-Calculate the value of the mean absolute percentage error for the given data.
A) 20.90
B) 16.60
C) 21.72
D) 29.97

Accepted Answer

The answer of Use the data given below to answer...

Question 13

In forecasting, what is an index?
A) It is a single measure that weights multiple indicators and provides a measure of overall expectation.
B) It is a stream of historical data, such as weekly sales.
C) It is a time series that does not have trend, seasonal, or cyclical effects but is relatively constant and only exhibits random behavior.
D) It is a measure that provides a complete forecast.

Accepted Answer

An index in forecasting is a single measure that weights multiple indicators and provides a measure of overall expectation. It is used to simplify complex data into a single number that reflects the direction and magnitude of expected changes.

Question 14

Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by At and Ft respectively. 
A) RMSE $ =\sqrt{\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n}} $

B) RMSE $ =\sqrt{\frac{\sum_{t=1}^{n} \sqrt{\left|A_{t}-F_{t}\right|}}{n}} $

C) RMSE $ =\sqrt{\frac{\sum_{t=1}^{n}\left(\lambda t-F_{t}\right)^{2}}{n}} $

D) RMSE $ =\sqrt{\frac{\sum_{t=1}^{n}\left|\frac{A_{t}+F_{t}}{2}\right|}{n}} $

Accepted Answer

The answer of Identify the formula used to calculate the...

Question 15

The data for the number of hand-held gaming devices sold for the past 5 weeks are 15 units, 20 units, 25 units, 30 units, and 17 units respectively. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects; thus, a moving average model would be appropriate. Setting k = 3 the three-period moving average forecast for week 6 is .
A) 20 units
B) 24 units
C) 30 units
D) 17 units

Accepted Answer

To calculate the three-period moving average forecast, we add up the sales for the previous three weeks and divide by 3:

(15+20+25)/3 = 20 units

Then we move one week ahead and recalculate using the sales from weeks 2, 3, and 4:

(20+25+30)/3 = 25 units

Finally, we move ahead to week 6 and calculate using the sales from weeks 3, 4, and 5:

(25+30+17)/3 = 24 units

Therefore, the three-period moving average forecast for week 6 is 24 units, which corresponds to answer choice B.

Question 16

The Delphi method used for forecasting:
A) obtains forecasts through a comparative analysis with a previous situation.
B) uses measures that are believed to influence the behavior of a variable that the researcher wishes to forecast.
C) uses a single measure that weights multiple indicators and provides a measure of overall expectation.
D) uses a panel of experts, whose identities are typically kept confidential from one another, to respond to a sequence of questionnaires.

Accepted Answer

The Delphi method used for forecasting involves using a panel of experts who respond to a sequence of questionnaires. The experts' identities are typically kept confidential from one another to encourage unbiased responses. The process continues until a consensus is reached or until a predetermined stopping point has been reached.

Question 17

Use the data given below to answer the following question(s).
The details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-For the given data, calculate the value of the simple moving average mean absolute percentage error.
A) 20.90
B) 23.45
C) 14.39
D) 25.56

Accepted Answer

The simple moving average forecast for each week is calculated using the average of the previous two weeks' sales. The mean absolute percentage error (MAPE) is then calculated by taking the average of the absolute percentage errors for each week. The calculations yield a MAPE of 20.90.

Question 18

Use the data given below to answer the following question(s).
The details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-Using the data, determine the value of the simple moving average root mean square error.
A) 0.21
B) 14.39
C) 20.12
D) 207.13

Accepted Answer

The answer of Use the data given below to answer...

Question 19

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-What is the forecasted value for the 3rd week?
A) 53 phones
B) 64 phones
C) 71 phones
D) 49 phones

Accepted Answer

The forecast for the 3rd week using exponential smoothing with an optimized α value (0.1 increments) is closest to 53 phones.

Question 20

Use the data given below to answer the following question(s).
The details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-For the given data, the simple moving average mean absolute deviation is .
A) 0.21
B) 20.12
C) 14.25
D) 207.13

Accepted Answer

The simple moving average for k=2 is calculated for weeks 3 to 6. The absolute deviations from the actual sales are calculated, and the mean of these deviations is the mean absolute deviation (MAD).

Quiz 9: Forecasting Techniques

What is a stream of historical data known as?

Before launching a new line of toys, Toys Inc. used the method of historical analogy to obtain a forecast. In this scenario, Toys Inc.:

If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values is .

Time-series models may exhibit seasonal effects or cyclical effects. A seasonal effect differs from a cyclical effect in that a seasonal effect:

In forecasting, what is an index?

Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by At and Ft respectively.

The Delphi method used for forecasting: