Deck 11: Forecasting Models

Question 1

In using a moving average forecasting technique,as the number of averaging period,k,increases:

A)the forecast will respond more quickly to recent changes in the data
B)the forecast will be more accurate especially if the data exhibits a trend
C)the moving average will increase in value
D)the moving average approximates the weighted moving average
E)the moving average will smooth out variations

Answer 1

E

Question 2

The value of the correlation coefficient "r" ranges between

A)- infinity and + infinity
B)+1 and + infinity
C)0 and -1
D)-1 and +1
E)0 and +1

Answer 2

D

Question 3

"Blips" in the data that follow no discernible pattern are referred to as

A)trend
B)random variations
C)seasonality
D)cycles
E)stationary variations

Answer 3

B

Question 4

A time series which has a significant upward or downward trend is referred to as:

A)stationary time series
B)non-stationary time series
C)random time series
D)cyclical time series
E)seasonal time series

Question 5

Which of the following is NOT a qualitative method of forecasting?

A)Delphi Method
B)Trend Analysis
C)Jury of Executive Opinion
D)Sales Force Composition
E)Consumer Market Survey

Question 6

Time series models usually incorporate variables or factors that are perceived to influence the variable being forecasted.

Question 7

The least squares method for linear regression:

A)minimizes the sum of the errors
B)minimizes the sum of the squared errors
C)maximizes forecasting accuracy
D)minimizes the value of the coefficient of determination R²
E)minimizes the regression equation coefficients

Question 8

Consider the following forecast errors.What is the Mean Absolute Deviation (MAD)?
$$\begin{array} { | c | c | } \hline \text { Period } & \text { Error } \\\hline 1 & - 2 \\\hline 2 & 1 \\\hline 3 & 3 \\\hline 4 & 0 \\\hline 5 & - 1 \\\hline 6 & 2 \\\hline 7 & 4 \\\hline\end{array}$$

A)1
B)1.86
C)7
D)13
E)5

Question 9

Consider the following data that was fitted using a linear trend.
$$\begin{array} { | c | c | c | } \hline \text { Period } & \begin{array} { c } \text { Actual value } \\\text { (or) Y }\end{array} & \begin{array} { c } \text { Period number } \\\text { (or) X }\end{array} \\\hline \text { Period 1 } & 10 & 1 \\\hline \text { Period 2 } & 11 & 2 \\\hline \text { Period 3 } & 9 & 3 \\\hline \text { Period 4 } & 12 & 4 \\\hline \text { Period 5 } & 13 & 5 \\\hline \text { Period 6 } & 12 & 6 \\\hline \text { Period 7 } & 15 & 7 \\\hline\end{array}$$
The intercept of the trend line is 8.714,and the slope is 0.75.What is the forecast error for period 7?

A)1.036
B)8
C)2.37
D)5.714
E)4.75

Question 10

The basic exponential smoothing formula is:

A) $F _ { t } = F _ { t } + 1 + \alpha \left( A _ { t } - F _ { t } \right)$
B) $F _ { t } + 1 = F _ { t } - 1 + \alpha \left( A _ { t } - F _ { t } \right)$
C) $\mathrm { F } _ { \mathrm { t } + 1 } = \mathrm { F } _ { \mathrm { t } - 1 } + \alpha \left( \mathrm { A } _ { \mathrm { t } } - \mathrm { F } _ { \mathrm { t } } \right)$
D) $F _ { t + 1 } = F _ { t } + \alpha \left( A _ { t } - F _ { t } \right)$
E) $\mathrm { F } _ { \mathrm { t } } = \mathrm { F } _ { \mathrm { t } } + 1 + \alpha \left( \mathrm { A } _ { \mathrm { t } } - \mathrm { F } _ { \mathrm { t } } \right)$

Question 11

Suppose that you intend to use Solver to compute the optimal weights for a weighted moving average.Changing variable cells would refer to:

A)the MAD cell
B)the MSE cell
C)the MAPE cell
D)the weights cells
E)the forecast cells

Question 12

Consider the following data that was fitted using a Linear Trend.
$$\begin{array} { | c | c | c | } \hline \text { Period } & \begin{array} { c } \text { Actual value } \\\text { (or) Y }\end{array} & \begin{array} { c } \text { Period number } \\\text { (or) X }\end{array} \\\hline \text { Period 1 } & 10 & 1 \\\hline \text { Period 2 } & 11 & 2 \\\hline \text { Period 3 } & 9 & 3 \\\hline \text { Period 4 } & 12 & 4 \\\hline \text { Period 5 } & 13 & 5 \\\hline \text { Period 6 } & 12 & 6 \\\hline \text { Period 7 } & 15 & 7 \\\hline\end{array}$$
The intercept of the trend line is 8.714,and the slope is 0.75.What is the forecast for period 8?

A)13.714
B)14.714
C)15.714
D)16.714
E)15.75

Question 13

Cycles,one of the components of time series,is a pattern that repeats itself during the exact same time period.

Question 14

Consider the following data and Excel output for a simple linear regression model.How much of the total variation in the dependent variable (Y)is explained by the independent variable (X)?
$$\begin{array} { | c | c | c | } \hline \text { Period } & \text { Y } & \text { X } \\\hline \text { Period 1 } & 10 & 1 \\\hline \text { Period 2 } & 11 & 2 \\\hline \text { Period 3 } & 9 & 3 \\\hline \text { Period 4 } & 12 & 4 \\\hline \text { Period 5 } & 13 & 5 \\\hline \text { Period 6 } & 12 & 6 \\\hline \text { Period 7 } & 15 & 7 \\\hline\end{array}$$
$$\begin{array} { | l | l | } \hline \text { Intercept } & 2.267 \\\hline \text { Slope } & 0.843 \\\hline \text { SE } & 1.810 \\\hline \text { Correlation } & 0.890 \\\hline \text { r-squared } & 0.791 \\\hline\end{array}$$

A)2.267
B)0.843
C)1.810
D)0.890
E)0.791

Question 15

Consider the following data and its associated Excel output for a simple linear regression model.How would you describe the linear relationship between Y and X?
$$\begin{array} { | c | c | c | } \hline \text { Period } & \text { Y } & \text { X } \\\hline \text { Period 1 } & 10 & 1 \\\hline \text { Period 2 } & 11 & 2 \\\hline \text { Period 3 } & 9 & 3 \\\hline \text { Period 4 } & 12 & 4 \\\hline \text { Period 5 } & 13 & 5 \\\hline \text { Period 6 } & 12 & 6 \\\hline \text { Period 7 } & 15 & 7 \\\hline\end{array}$$
$$\begin{array} { | l | l | } \hline \text { Intercept } & 2.267 \\\hline \text { Slope } & 0.843 \\\hline \text { SE } & 1.810 \\\hline \text { Correlation } & 0.890 \\\hline \text { r-squared } & 0.791 \\\hline\end{array}$$

A)no relationship
B)positive relationship
C)negative relationship
D)inverse relationship
E)not enough information is provided

Question 16

The value of the coefficient of determination R² ranges between

A)0 and -1
B)-1 and +1
C)0 and +1
D)- infinity and + infinity
E)+1 and + infinity

Question 17

Which of the following is considered to be a category of forecasting models?

A)Qualitative
B)Time-series
C)Causal models
D)both A and B
E)A,B,and C

Question 18

Which of the following is NOT considered to be a Time-Series method of forecasting?

A)Simple Linear Regression
B)Moving Average
C)Exponential Smoothing
D)Seasonality Analysis
E)Multiplicative/Additive Decomposition

Question 19

An iterative group process that allows experts,who may be located in different places,to make forecasts is referred to as ________.

A)a jury of executive opinion
B)a sales force composite
C)ca onsumer market survey
D)the Delphi method
E)trend analysis

Question 20

Consider the following time series data.Suppose that you use exponential smoothing with an alpha of 0.7 to fit a forecasting model.The forecast for period 7 is
$$\begin{array} { | c | c | c | } \hline \text { Period } & \text { Forecast } & \text { Actual value } \\\hline \text { Period 1 } & 10 & 10 \\\hline \text { Period 2 } & 10 & 11 \\\hline \text { Period 3 } & 10.7 & 9 \\\hline \text { Period 4 } & 9.51 & 12 \\\hline \text { Period 5 } & 11.253 & 13 \\\hline \text { Period 6 } & 12.476 & 11 \\\hline\end{array}$$

A)10.443
B)12
C)9)443
D)12.443
E)11.443

Question 21

The smaller the value of the standard error of the regression estimate,the better the fit of the regression model.

Question 22

Use this information to answer the following questions.
The following time series represent the total population of the United States,in thousands,over the last 12 years.

Refer to the table above.
a.Use exponential smoothing with a smoothing constant of 0.5 to forecast the population of the United States in 2003.
b.Use exponential smoothing with a smoothing constant of 0.8 to forecast the population of the United States in 2003.
c.Which of the two methods provides a more accurate forecast based on the MAD criterion?

Question 23

A moving average forecast tends to be more responsive to recent changes in the data series when more data points are included in the average.

Question 24

The time series component random variation usually shows a discernible pattern and is easy to forecast.

Question 25

Use this information to answer the following questions.
The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001.

Refer to the table above.
a.Use a 2-period moving average to forecast the number of immigrants in 2002.
b.Use a 3-period moving average to forecast the number of immigrants in 2002.
c.Which averaging period provides a better historical fit based on the MAD criterion?

Question 26

Use this information to answer the following questions.
The following time series represent the total population of the United States,in thousands,over the last 12 years.

Refer to the table above.a.What is the linear trend equation that best fits the data?
b.What is the forecast of the population of the United States in 2003 using the linear trend equation?
c.What is the MAPE for this method?

Question 27

A time series that is unseasonalized may exhibit a trend,a random component,and a seasonal pattern.

Question 28

Use this information to answer the following questions.
The following time series represent the total population of the United States,in thousands,over the last 12 years.

Refer to the table above.Using Solver to find the optimal alpha that minimizes MAD,use exponential smoothing to forecast the population of the United States in 2003.

Question 29

Moving averages are useful in forecasting stationary time series as they tend to smooth out random variations.

Question 30

In an exponential smoothing forecast,the weight associated with older data increases exponentially over time.

Question 31

Use this information to answer the following questions.
The following time series represent the total population of the United States,in thousands,over the last 12 years.

Refer to the table above.Use a 3-period weighted moving average to forecast the population of the United States in 2003.Use Solver to determine the optimal weights based on minimizing the MAD criterion.

Question 32

Use this information to answer the following questions.
The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001.

Refer to the table above.Use a 3-period weighted moving average to forecast the number of immigrants in 2002.Use Solver to determine the optimal weights based on minimizing the MAD criterion.

Question 33

Use this information to answer the following questions.
The following time series represent the total population of the United States,in thousands,over the last 12 years.

Refer to the table above.
a.Use a 2-period moving average to forecast the population of the United States in 2003.
b.Use a 3-period moving average to forecast the population of the United States in 2003.
c.Which averaging period provides a better historical fit based on the MAD criterion?

Question 34

If a time series exhibits a strong,linear upward trend,the value of the correlation coefficient,r,is expected to be positive and close to -1.

Question 35

In an exponential smoothing forecast,the value of the smoothing constant alpha can range between -1 and +1.

Question 36

In general,the higher the value of the coefficient of determination R²,the better the fit of the regression model.

Question 37

A multiple regression model may include one or more dependent variables.

Question 38

Removing the seasonal component from a data series (i.e. ,unseasonalization)can be accomplished by multiplying each data point by its appropriate seasonal index.

Question 39

A smoothing constant of .1 will cause an exponential smoothing forecast to react less quickly to a sudden change than a value of .3 will.

Question 40

A farmer develops a simple regression model to determine if there is a relationship between the amount of crop that he will harvest and the amount of rainfall.In this example,the variable "rainfall" would be the dependent variable.

Question 41

Use this information to answer the following questions.
A hot dog stand owner has collected the following time series data on the number of hot dogs sold over the last 12 quarters.

Refer to the table above.
a.Prepare a line graph of the time series data.
b.Do the data appear to be stationary or non-stationary?

Question 42

The following data were collected on the number of study hours per week,and the current GPA of 6 students at a local college.

a.Develop a regression model to predict GPA based on the number of study hours.
b.What percent of the total variation in GPA has been explained by study hours?
c.If a student studies 20 hours per week,what would you estimate the GPA to be?

Question 43

Use this information to answer the following questions.
A hot dog stand owner has collected the following time series data on the number of hot dogs sold over the last 12 quarters.

Refer to the table above.Use a linear trend equation to forecast next quarterly sales.

Question 44

A car sales manager has collected the following data on the number of cars sold per week and years of experience for 7 of his salespeople.

a.Develop a regression model to predict sales based on years of experience.
b.Use the estimated regression model to predict sales for a salesperson with 7 years of experience.

Question 45

Use this information to answer the following questions.
The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates.

Refer to the table above.Use a 4-period weighted moving average to forecast the next weekly mortgage rate.Use Solver to determine the optimal weights based on minimizing the MAD criterion.

Question 46

The following data were collected on the height (inches)and weight (pounds)of 5 students.

a.Develop a regression model to predict weight based on height.
b.What percent of the total variation in weight has been explained by height?
c.If a student is 69 inches tall,what would you estimate the weight to be?

Question 47

Use this information to answer the following questions.
A hot dog stand owner has collected the following time series data on the number of hot dogs sold over the last 12 quarters.

Refer to the table above.Forecast next quarterly sales using a 3-period weighted moving average.Use Solver to determine the optimal weights that minimize MSE.

Question 48

Use this information to answer the following questions.
The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates.

Refer to the table above.a.Use exponential smoothing with a smoothing constant of 0.5 to forecast the next weekly mortgage rate.
b.Use exponential smoothing with a smoothing constant of 0.9 to forecast the next weekly mortgage rate.
c.Which of the two methods provides a more accurate forecast based on the MAD criterion?

Question 49

Use this information to answer the following questions.
The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates.

Refer to the table above.
a.What is the linear trend equation that best fits the data?
b.What is the forecast of the next weekly mortgage rate?
c.What is the MAPE for this method?

Question 50

Use this information to answer the following questions.
Joe Smith operates an ice cream shop and works only three days a week.The number of ice cream cones that he sells is shown as follows.

Refer to the table above.
a.Use a 3-period moving average to forecast next day's sales.
b.Use a 3-period weighted moving average to forecast next day's sales.Use Solver to determine the optimal weights.
c.Which one of the above forecasting techniques provides a lower MSE?

Question 51

Use this information to answer the following questions.
The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001.

Refer to the table above.Using Solver to find the optimal alpha that minimizes MAD,use exponential smoothing to forecast the number of immigrants in 2002.

Question 52

Use this information to answer the following questions.
The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001.

Refer to the table above.
a.What is the linear trend equation that best fits the data?
b.What is the forecast of the number of immigrants in 2002 using the linear trend equation?
c.What is the MAPE for this method?

Question 53

Use this information to answer the following questions.
The following data were collected on annual revenues (millions)and the number of slot machines in a Las Vegas casino from 1995 to 2005.

Refer to the table above.
a.Develop a regression model to predict annual revenues based on the number of slot machines.
b.Use the estimated regression model to predict annual revenues with 80 slot machines.

Question 54

Use this information to answer the following questions.
The following data were collected on annual revenues (millions)and the number of slot machines in a Las Vegas casino from 1995 to 2005.

Refer to the table above.Suppose that the casino manager believes that warmer weather attracts more gamblers.The data on average yearly temperatures from 1995 to 2005 are shown as follows.

a.Develop a regression model to predict annual revenue based on the number of slot machines and average temperature.
b.What percent of the total variation in revenue is explained by the regression model?
c.Predict annual revenue if the casino has 75 slot machines and the average temperature is 74 degrees.

Question 55

Use this information to answer the following questions.
The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates.

Refer to the table above.
a.Use a 2-period moving average to forecast the next weekly mortgage rate.
b.Use a 3-period moving average to forecast the next weekly mortgage rate.
c.Use a 4-period moving average to forecast the next weekly mortgage rate.
d.Which averaging period provides a better historical fit based on the MAD criterion?

Question 56

Use this information to answer the following questions.
A hot dog stand owner has collected the following time series data on the number of hot dogs sold over the last 12 quarters.

Refer to the table above.Forecast next quarterly sales using exponential smoothing.Use Solver to find the optimal smoothing constant value that minimizes MSE.

Question 57

Use this information to answer the following questions.
A hot dog stand owner has collected the following time series data on the number of hot dogs sold over the last 12 quarters.

Refer to the table above.Using a multiplicative decomposition model,forecast the next four quarterly sales data.

Question 58

Use this information to answer the following questions.
The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001.

Refer to the table above.
a.Use exponential smoothing with a smoothing constant of 0.3 to forecast the number of immigrants in 2002.
b.Use exponential smoothing with a smoothing constant of 0.6 to forecast number of immigrants in 2002.
c.Which of the two methods provides a more accurate forecast based on the MAD criterion?

Question 59

Two different forecasting techniques (F1 and F2)were used to forecast sales.Actual sales and the two sets of forecasts are as follows:

a.Compute MAD for each forecasting technique.Which forecasting technique is more accurate based on the MAD criterion?
b.Compute the MSE for each set of forecasts.Which forecasting technique is more accurate based on the MSE criterion?

Question 60

Use this information to answer the following questions.
The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates.

Refer to the table above.Use Solver to find the optimal alpha that minimizes MAD,and use exponential smoothing to forecast the next weekly mortgage rate.

Question 61

Use this information to answer the following questions.
Joe Smith operates an ice cream shop and works only three days a week.The number of ice cream cones that he sells is shown as follows.

Refer to the table above.Use a linear trend line to forecast ice cream sales for the next three days.

Question 62

Use this information to answer the following questions.
Joe Smith operates an ice cream shop and works only three days a week.The number of ice cream cones that he sells is shown as follows.

Refer to the table above.
a.Use exponential smoothing with an alpha value of 0.5 to forecast next day's sales.
b.Use Solver to determine the optimal alpha value that minimizes MSE.Forecast next day's sales using this optimal alpha value.

Question 63

Use this information to answer the following questions.
Joe Smith operates an ice cream shop and works only three days a week.The number of ice cream cones that he sells is shown as follows.

Refer to the table above.Using a multiplicative decomposition model,forecast ice cream sales for the next three days.

Question 64

The data below represents demand,selling price,and advertising expenditures for an electronics item.
a.Develop a multiple regression model to predict monthly demand.
b.What is the R-squared on this model?
c.Based on the model developed in part a,what would be the predicted monthly demand if the price of the item is set to $49 and $100 is spent on advertising?