Question 1

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 ________.

Accepted Answer

B

Question 2

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

Accepted Answer

Seasonal effects are patterns that repeat at fixed intervals of time, such as a year, month, week, or day. This is different from a cyclical effect, which may describe ups and downs over a longer time frame, such as several years. Option A refers to random behavior, which is not necessarily present in a seasonal effect, and Option D refers to extrapolation of the past which is not specific to seasonal effects.

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.The value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-Which of the following is the value of the root mean square error for the given data?

Accepted Answer

B

Question 4

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 ________.

Accepted Answer

To calculate the simple moving average mean absolute deviation, we first need to calculate the simple moving average. Using k = 2, we get:

Week 1: SMA = (88 + 44) / 2 = 66
Week 2: SMA = (44 + 54) / 2 = 49
Week 3: SMA = (54 + 65) / 2 = 59.5
Week 4: SMA = (65 + 72) / 2 = 68.5
Week 5: SMA = (72 + 85) / 2 = 78.5
Week 6: SMA = (85 + 85) / 2 = 85

Now we calculate the mean absolute deviation for each week:

Week 1: |88 - 66| = 22
Week 2: |44 - 49| = 5
Week 3: |54 - 59.5| = 5.5
Week 4: |65 - 68.5| = 3.5
Week 5: |72 - 78.5| = 6.5
Week 6: |85 - 85| = 0

Taking the average of these mean absolute deviations, we get:

(22 + 5 + 5.5 + 3.5 + 6.5 + 0) / 6 = 14.25

Therefore, the simple moving average mean absolute deviation is 14.25. The best choice is (C).

Question 5

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.

Accepted Answer

To calculate the simple moving average root mean square error, we need to first calculate the simple moving average values for each week.

SMA for week 3 = (88 + 44 + 54)/3 = 62
SMA for week 4 = (44 + 54 + 65)/3 = 54
SMA for week 5 = (54 + 65 + 72)/3 = 63.67
SMA for week 6 = (65 + 72 + 85)/3 = 74

Next, we need to calculate the errors, which is the difference between the actual units sold and the SMA for that week.

Error for week 3 = 54 - 62 = -8
Error for week 4 = 65 - 54 = 11
Error for week 5 = 72 - 63.67 = 8.33
Error for week 6 = 85 - 74 = 11

Then, we square the errors, add them up, divide by the number of weeks, and take the square root to get the simple moving average root mean square error.

SMARMS = sqrt[(8^2 + 11^2 + 8.33^2 + 11^2)/4] = 14.39

Therefore, the answer is B.

Question 6

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.The value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-In the linear trend equation, Ft₊k = at + btk, at is known as the ________.

Accepted Answer

Since the time series appears to be relatively stable, without trend, seasonal, or cyclical effects, there is no trend component in the linear trend equation. Therefore, at only represents the level of the time series.

Question 7

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 ________.

Accepted Answer

To calculate the three-period moving average forecast for week 6, we take the average of the past three weeks, which are weeks 3, 4, and 5, which had sales of 25, 30, and 17 units respectively. The calculation is as follows:
(25 + 30 + 17)/3 = 24
Therefore, the three-period moving average forecast for week 6 is 24 units, which corresponds to choice B.

Question 8

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.The value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-What is the forecasted value for the 3ʳᵈ week?

Accepted Answer

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

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.The value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-What is the difference between the forecasted and the actual value for the 3ʳᵈ week?

Accepted Answer

The forecasted value for the 3rd week is 54. The actual value is 54. The difference between the forecasted and the actual value is 54 - 54 = 0.

Question 10

In forecasting, what is an index?

Accepted Answer

An index is a single measure that weights multiple indicators and provides a measure of overall expectation. It is often used in forecasting to give a summary picture of the overall trend, rather than relying on individual data points.

Question 11

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.

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.The value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-Calculate the value of the mean absolute percentage error for the given data.

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

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 ________.

Accepted Answer

The formula for mean absolute deviation (MAD) is the sum of the absolute differences between the actual and forecast values, divided by the number of forecasts, so option A is the correct formula. Option B is the formula for mean squared error, not MAD. Option C is not a valid formula for MAD as it uses a square root and does not compute the absolute difference. Option D divides by 2 instead of taking the absolute value of the difference.

Question 15

What is a stream of historical data known as?

Accepted Answer

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

Question 16

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

Accepted Answer

Historical analogy involves looking at past experiences or occurrences to make predictions about future outcomes. In this scenario, Toys Inc. used the response of consumers to similar previous products and marketing campaigns to predict how the new line of toys might fare. This method relies on the assumption that similar situations will have similar outcomes, and thus can be a helpful tool in forecasting. Choice A involves observing current customer behavior, which is not the same as historical analogy. Choice B involves a panel of experts, which is a different forecasting method. Choice D involves brainstorming among a group of experts, which is not related to historical analogy.

Question 17

The Delphi method used for forecasting:

Accepted Answer

The Delphi method involves using a panel of experts who are kept confidential from each other and respond to a series of questionnaires, with the goal of achieving a consensus forecast. This method is useful when there is uncertainty or lack of data about a specific variable, and allows for a range of perspectives and expertise to be considered in the forecasting process.

Question 18

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.

Accepted Answer

The formula for calculating root mean square error (RMSE) is given by option C. It involves taking the square root of the average of the squared difference between the actual and forecasted values. This formula is commonly used to measure the accuracy of a forecasting model. Option A is incorrect as it involves taking the absolute value of the difference between the actual and forecasted values; this means that negative errors will be treated the same as positive errors. Option B involves taking the square root of the absolute difference which is not the correct formula. Option D is also incorrect as it involves taking the absolute value of the average difference between the actual and forecasted values.

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.The value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-What is the forecasted value for the 7th week?

Accepted Answer

We can use simple exponential smoothing with alpha value to forecast the 7th week value. First, we need to calculate the initial forecast( F1) which is the actual value of the first week (88 in this case).

F1 = 88
F2 = α(88) + (1- α)F1  (where α = 0.4)
F2 = 0.4(88) + 0.6(88)
F2 = 88
Similarly, we can calculate F3, F4, F5, and F6 to get the final forecast for the 7th week.

F3 = 56.8
F4 = 59.48
F5 = 64.79
F6 = 73.92
F7 = α(85) + (1-α)F6
To get the forecasted value for the 7th week, we use the formula and substitute the values,

F7 = 0.4(85) + 0.6(73.92)
F7 = 84.15

Therefore, the forecasted value for the 7th week is 84 phones.

Question 20

The actual value of the time series at time t and the forecast value for time t is denoted by At and Ft respectively.What is the formula used for calculating the mean absolute percentage error over a range of forecasted values?

Accepted Answer

The Mean Absolute Percentage Error (MAPE) is calculated using the formula: MAPE = $\frac { \sum _ { t = 1 } ^ { n } \left| \frac { A _ { t } - F _ { t } } { A _ { t } } \right| } { n }$ × 100. This measures the accuracy of a forecasting method by expressing errors as a percentage of the actual values.

Quiz 10: Forecasting Techniques

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?

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 ________.

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.:

The Delphi method used for forecasting:

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 actual value of the time series at time t and the forecast value for time t is denoted by At and Ft respectively.What is the formula used for calculating the mean absolute percentage error over a range of forecasted values?