Decision Science
What is the correct range for R2 values?
(0 ≤ R2 ≤ 1)
Based on the following regression output, what proportion of the total variation in Y is explained by X?
0.841282
How many independent variables are there in simple regression analysis?
1
What is the latest finish time for activity D in the following diagram?
13
Exhibit 14.3 The following questions are based on the information below. An investor is considering 4 investments, A, B, C and leaving his money in the bank. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following payoff matrix has been developed for the decision problem. The investor has estimated the probability of a declining economy at 70% and an expanding economy at 30%. Refer to Exhibit 14.3. What is the expected monetary value of Investment A?
20
Exhibit 14.5 The following questions are based on the information below. An investor is considering 4 investments, A, B, C, D. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following decision tree has been developed for the problem. The investor has estimated the probability of a declining economy at 40% and an expanding economy at 60%. Refer to Exhibit 14.5. What is the expected monetary value for the investor's problem?
38
How many paths are there in the following project precedence network?
9
Exhibit 14.2 The following questions are based on the information below. An investor is considering 4 investments, A, B, C and leaving his money in the bank. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following payoff matrix has been developed for the decision problem. Refer to Exhibit 14.2. What formula should go in cell F5 of the Regret Matrix above to compute the regret value?
=MAX(B$5:B$8)-B5
Exhibit 14.2 The following questions are based on the information below. An investor is considering 4 investments, A, B, C and leaving his money in the bank. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following payoff matrix has been developed for the decision problem. Refer to Exhibit 14.2. What formula should go in cell H5 and copied to H6:H8 of the Regret Table above to implement the minimax regret decision rule?
=MAX(F5:G5)
Which activities are critical in the following diagram?
A, C, D, F
There are various similarities between the CPM and PERT methods. Which of the following is not one of those similarities?
Both techniques use the same method to calculate the time element of the activities in the project.
What are the immediate successors of activity D in this network?
E,F
What is the formula for the earliest finish time for activity i?
EFTi = ESTi + ti
Decision analysis supports all but one of the following goals. Which goal is not supported?
Help ensure selection of good outcomes.
Which of the following is a goal of decision analysis?
Help individuals make good decisions.
For an activity with duration t, slack can be calculated as
LF-EF
For an activity with duration t, slack can be calculated as
LS-ES
Slack for activity I is computed as
LSTi − ESTi
Which of the following forecasting methodologies is considered a causal forecasting technique?
Linear regression
The objective function in regression analysis is
MIN (Yi-^Yi)^2
Although modeling provides valuable insight to decision makers, decision making remains a difficult task. Which of the following is not a primary cause for this difficulty discussed in the Decision Analysis chapter?
Models provide decisions for the decision maker.
The main difference between CPM and PERT is that
PERT is probabilistic
Activity-on-Arc (AOA) networks do not allow multiple arcs with common start and finish nodes. If this must be represented, how is an AOA network modified?
Phantom (dummy) activity arcs are added.
Which of the following definitions correctly defines the acronym, PERT?
Program Evaluation and Review Technique.
R2 is calculated as
RSS/TSS
In regression terms what does "best fit" mean?
The error terms are as small as possible.
Probabilistic decision rules can be used if the states of nature in a decision problem can be assigned probabilities that represent their likelihood of occurrence. Which of the following is not true regarding the probabilities employed?
The probabilities are always obtained from historical data.
Which of the following correctly describes the focus of the Critical Path Method (CPM)?
To determine when a project should be completed and to schedule when each activity in the project must begin in order to keep the project on schedule.
Why do we create a scatter plot of the data in regression analysis?
To visually check for a relationship between X and Y.
When using the Regression tool in Excel the independent variable is entered as the
X-range
An analyst has identified 3 independent variables (X1, X2, X3) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R2 value for the X3 model the same as the R2 value for the X1 and X3 model, but the Adjusted R2 values differ?
X1 does not reduce ESS enough to compensate for its addition to the model.
An analyst has identified 3 independent variables (X1, X2, X3) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Which combination of variables provides the best regression results?
X2 and X3
The regression residuals are computed as
Y i - ^Y i
When using the Regression tool in Excel the dependent variable is entered as the
Y-range
The estimated value of Y1 is given by
^Y1=B0+b1X1
Based on the following regression output, what is the equation of the regression line?
^Yi=31.62378 + 1.131661Xh
What does regression analysis attempt to establish?
a mathematical relationship between a dependent variable, for which future values will be forecast, and one or more independent variables with known values
What is the earliest start time for activity D in the following diagram?
a. 6
In deciding which activities to crash, select
activities on the critical path(s)
An activity
activity time estimates
CPM and PERT differ because of
activity time estimates
What goodness-of-fit measure is commonly used to evaluate a multiple regression function?
adjusted R2
Slack represents the amount of time by which an activity can be delayed without delaying the entire project, assuming that
all predecessor activities start at their earliest start times.
A(n) ____ is a course of action intended to solve a problem.
alternative
The problem of finding the optimal values of b0 and b1 is
an unconstrained nonlinear optimization problem.
The regression function indicates the
average value the dependent variable assumes for a given value of the independent variable.
A project plan is established
before project activities begin and is modified as time goes on and conditions change
R2 is also referred to as
coefficient of determination.
R^2 is also referred to as
coefficient of determination.
The ____ in a decision problem represent factors that are important to the decision maker.
criteria
The longest path through a network is comprised of the ____ activities.
critical
Every nonprobabilistic method has a weakness for decision making. Which of the following is incorrect regarding a method and its weakness? a.The maximax method ignores potentially large losses. b.The maximin method ignores potentially large payoffs. c.The minimax regret method can lead to inconsistent decisions. d. All of these are correct.
d. All of these are correct.
A way to crash an activity is to a. use overtime b. spend extra money c. subcontract d. all of the above
d. all of the above
The error term ε in a regression model represents a. a random error in the data. b. unsystematic variation in the dependent variable. c. variation not explained by the independent variables. d. all of these.
d. all of these.
A square node in a decision tree is called a(n) ____ node.
decision
The purpose of the forward pass in the Critical Path Method (CPM) technique is to
determine the earliest time each activity can start and finish.
The terms b0 and b1 are referred to as
estimated population parameters.
A circular node in a decision tree is called a(n) ____ node.
event
Regression analysis is a modeling technique
for analyzing the relationship between dependent and independent variables.
One of PERT's bold assumptions is that
individual activity times are independent of each other.
An alternative
is a course of action intended to solve a problem
An activity
is an effort required to complete part of the project
In CPM, the duration of the project
is equal to the duration of the critical path
A state of nature
is observed
The critical path is the ____ path throughout the network.
longest
The critical path in PERT analysis is the path with the
longest expected completion time.
The decision rule which determines the maximum payoff for each alternative and then selects the alternative associated with the largest payoff is the
maximax decision rule.
Which decision rule optimistically assumes that nature will always be "on our side" regardless of what decision we make?
maximax decision rule.
The decision rule which determines the minimum payoff for each alternative and then selects the alternative associated with the largest minimum payoff is the
maximin decision rule.
A pattern resulting from random variation or unexplained causes is called
noise
The category of decision rules that contains the maximax decision rule is the
non-probabilistic category.
In decision-making, luck
often plays a role in determining whether good or bad outcomes occur
The terms β0 and β1 are referred to as
population parameters
Non-critical activities are distinguished by the presence of
positive slack
If we are employing Activity-On-Node (AON) network design, the arcs in the network diagram represent
precedence relationships.
In a PERT network the time required to complete a path is a(n)
random variable
The forecasting model that makes use of the least squares method is called
regression
The amount of opportunity lost in making a decision is called
regret
Estimation errors are often referred to as
residuals
A weakness of Gantt charts is that they do not explicitly
show precedence relationships.
The ____ correspond to future events that are not under the control of the decision maker.
states of nature
What is the correct formula to compute the expected duration of an activity using PERT?
t= a+4m+b/6
If we are employing Activity-On-Arc (AOA) network design, the arcs in the network diagram represent
tasks to complete.
The β1 term indicates
the average change in Y for a unit change in X.
R2 measures
the percentage of variability in the dependent variable, Y, explained by the model
Which are characteristics of decision-making under uncertainty?
the probability of possible future events is unknown
In the equation Y = β0 + β1 X1i + ε, β1 is
the slope of the regression line
The term "time zero" identifies
the start time for the project.
The total sum of squares (TSS) is best defined as
the total variation of Y around its mean.
Decision models are applicable when
there are multiple alternatives
Polynomial regression is used when
there is a non-linear relationship between the dependent and independent variables.
A persistent upward or downward movement of data is called
trend
The actual value of a dependent variable will generally differ from the regression equation estimate due to
unaccounted for random variation.
The standard prediction error is
used to construct confidence intervals for predicted values.
What is the correct formula to compute the variance of an activity using PERT?
v= (b-a)^2/36
The standard error measures the
variability in the actual data around the fitted regression function.
In project control charts, the horizontal bars are shaded to indicate
work completed
Critical activities are distinguished by the presence of
zero slack
What is the formula for total sum of squares (TSS)
Σ (Yi - "flat line in top of Y"i)^2
Error sum of squares (ESS) is computed as
Σ (Yi-^Yi)^2
