214 CHAPTER 9. SIMPLE LINEAR REGRESSION
a: is coefcient. Often the 1 subscript in 51 is replaced by the name of the
explanatory variable or some abbreviation of it.
So the structural model says that for each value of as the population mean of Y
(over all
9.1. THE MODEL BEHIND LINEAR REGRESSION 215
we need to be sure that the size of the error in measuring a: is small compared to
the variability of Y at any given :10 value. For more on this topic, see the section
on robustness, below.
The error model under
220 CHAPTER 9. SIMPLE LINEAR REGRESSION
xed-x. In some cases, we can actually perform repeated measurements of a: on
the same case to see the spread of ac and then do the same thing for y at each of
a few values, then reject the xed-x assumption if the ra
218 CHAPTER 9. SIMPLE LINEAR REGRESSION
9.2 Statistical hypotheses
For simple linear regression, the chief null hypothesis is H0 : B1 = 0, and the
corresponding alternative hypothesis is H1 : 51 7E 0. If this null hypothesis is true,
then, from E (Y) = o
9.3. SIMPLE LINEAR REGRESSION EXAMPLE 219
Final Weight (gm)
300 400 500 600
200
100
O 20 40 60 80 1 00
Soil Nitrogen (mg/pot)
Figure 9.2: Scatterplot of corn data.
mg.
EDA, in the form of a scatterplot is shown in gure 9.2.
We want to use EDA to check t
Chapter 9
Simple Linear Regression
An analysis appropriate for a quantitative outcome and a single quantitative ex-
planatory variable.
9.1 The model behind linear regression
When we are examining the relationship between a quantitative outcome and a
sing
222 CHAPTER 9. SIMPLE LINEAR REGRESSION
By plugging different values for 33 into this equation we can nd the corre-
sponding y values that are on the line drawn. For any given b0 and b1 we get a
potential best-t line, and the vertical distances of the poi
216 CHAPTER 9. SIMPLE LINEAR REGRESSION
variable each time, serial correlation is extremely likely. Breaking the assumption
of independent errors does not indicate that no analysis is possible, only that linear
regression is an inappropriate analysis. Oth
9.1. THE MODEL BEHIND LINEAR REGRESSION 217
15
10
Figure 9.1: Mnemonic for the simple regression model.
than ANOVA. If the truth is non-linearity, regression will make inappropriate
predictions, but at least regression will have a chance to detect the non
CD S Ch 6-1
SUPPLEMENT TO CHAPTER 6
MINIMUM SPANNING-TREE PROBLEMS
Chapter 6 focuses on network optimization problems. These are problems that can be described in
terms of a complete network that has both nodes and links (or arcs) and the objective is to
Chapter 5
What-if Analysis for Linear Programming
1
If the optimal solution will remain the same over only a small range of values for
a particular coefficient in the objective function, then management will want to
take special care to narrow this estima
S 12-1
SUPPLEMENT TO CHAPTER 12
THE INVERSE TRANSFORMATION METHOD FOR
GENERATING RANDOM OBSERVATIONS
Section 12.1 mentioned that a general mathematical procedure is available for generating random
observations from either discrete or continuous distributi
CD Chapter 19
Inventory Management with Uncertain Demand
1
The objective of inventory management is to minimize inventory levels.
F
2
The overall objective of inventory management is to balance customer service and
inventory costs.
T
3
The perishable prod
CHAPTER 20
COMPUTER SIMULATION WITH CRYSTAL BALL
SOLUTION TO SOLVED PROBLEMS
20.S1 Saving for Retirement
Patrick Gordon is ten years away from retirement. He has accumulated a $100,000 nest egg that
he would like to invest for his golden years. Furthermor
CD Chapter 16
PERT/CPM Models for Project Management
1
In an Activity-On-Arc project network, the nodes are used to separate an activity
from each of its immediate predecessors.
T
2
If two paths are tied for the longest duration, the one with the most act
Chapter 9
Decision Analysis
1
Prior probabilities refer to the relative likelihood of past events.
F
2
Bayes' decision rule says to choose the alternative with the largest possible payoff.
F
3
The EVPI indicates how much the payoff will be with perfect in
CD 18-1
CHAPTER 18
INVENTORY MANAGEMENT WITH KNOWN DEMAND
Learning Objectives
After completing this chapter, you should be able to
1. Identify the cost components of inventory models.
2. Describe the basic economic order quantity (EOQ) model.
3. Draw a gr
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1 Capital Budgeting with Contingency Constraints
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Project Project Project Project Project Project Project Project
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Total
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Cash Outflow Required ($million)
Outflow
7
Year
CHAPTER 8
NONLINEAR PROGRAMMING
SOLUTION TO SOLVED PROBLEMS
8.S1 Airline Ticket Pricing Model
Business travelers tend to be less price sensitive than leisure travelers. Knowing this, airlines
have discovered that extra profit can be
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Supply/Demand
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0
-200
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-200
M
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O
Range Name
Capacity
Flow
From
NetFlow
Nodes
SupplyDemand
To
TotalCost
UnitCost
Cells
F4
D4:D11
B4:B11
J4:J11
I4:I11
L4:L11
C4:C11
D13
CHAPTER 6
NETWORK OPTIMIZATION PROBLEMS
SOLUTION TO SOLVED PROBLEMS
6.S1 Distribution at Heart Beats
Heart Beats is a manufacturer of medical equipment. The companys primary product is a
device used to monitor the heart during medica
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Forecast
ForecastingError
MAD
MSE
TrueValue
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H5
H8
C5:C34
Template for Last-Value Forecasting Method
Time
Chapter 13
Computer Simulation with Risk Solver Platform
1
To use RSPE, the results cell must be a linear function.
F
2
The standard error gives an indication of how accurate the estimated mean is.
T
3
The Likelihood box in RSPE indicates how certain it i
CHAPTER 1
INTRODUCTION
SOLUTION TO SOLVED PROBLEMS
1.S1 Make or Buy
Power Notebooks, Inc. plans to manufacture a new line of notebook computers. Management is
trying to decide whether to purchase the LCD screens for the computers from an outside supplier
CD Chapter 17
Goal Programming
1
The overall objective for a goal programming problem is to determine the most
important objective in the problem.
F
2
Goal programming provides two alternative ways of formulating problems with
multiple goals: preemptive a
Chapter 4
The Art of Modeling with Spreadsheets
1
There is only one correct way to set up a spreadsheet model.
F
2
In the Everglade Golden Years Company problem, the long-term loan had a lower
interest rate than the short-term loan.
T
3
When sketching out