the design phase
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The Design Phase. What Is A Model?. - PowerPoint PPT PresentationTRANSCRIPT
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Q u a lita tiveM eth od
U n ivaria teD ata
A n a lys is
Q u an tita tiveM eth od s
In te llig en ceP h ase
U n d ers tan d in gth e R e la tion s
M od e lin g th eP rob lem
B iiva ria te o rM u ltiva ria te
D ataA n a lys is
D es ig nP h ase
C h o ice P h ase
D ec is ionS c ien ce
F ou n d ation s
The Design Phase
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What Is A Model?
• A model is a representation or abstraction of a real-world object, process, concept or “problem” which is reduced in scope or complexity relative to the problem itself but yet retains the certain “essential” aspects which we believe define or characterize the particular real-world problem.
•A good model should have a good balance between accuracy and simplicity.
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What Is A Model?
• A models may be used to:•describe
•predict, or
•optimize
• Three types of general models
• Physical/iconic: model car, model house• Analog/graphic: road map, speedometer• Symbolic: algebraic or spreadsheet model
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Why Use Models?
In support of Decision Making and help management make sound decisions
A model is valuable if you make better decisions when you use it (modeling approach) than when you don’t (intuition approach)
Models + Managerial Judgement = The best way to run business
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Advantages of Using Models
Models are generally less expensive and disruptive than experimenting with real systems
Models allow managers to ask “what-if” questions
Models force a consistent and systematic approach to the analysis of problems
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Advantages of Using Models
“By modeling various alternatives for future system design, Federal Express has, in effect, made its mistakes on paper. Computer modeling works; it allows us to examine many different alternatives and it forces the examination of the entire problem”
Fred Smith
Chairman and CEO of FedEx
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Disadvantages of Models
They may be expensive and time-consuming to develop and test
They are often misused and misunderstood because of their mathematical complexity
They may have assumptions that oversimplify the real-world system
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Model Components
Model- Relationships
Inputs Outputs
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Decision Model Components
DecisionVariables &Parameters
Relationships
Performance Measures or
Objective Functions
ConsequenceVariables
Inputs OutputsModel
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Model and Data
Useful (quantitative) models are developed based on relevant data (numbers); models without data are at best theoretical abstractions
Data are often collected according to the requirements of models– time series vs. cross-sectional– aggregated vs. disaggregated
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Numbers in Models
Data– Count– Measure– Rank
Results
Constant Variable Coefficient Precision
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Model Classification
Deterministic Models– All model components and relevant data are
known with certainty• Examples include: Ad hoc models, Forecasting,
Decision analysis, Constrained optimization
Probabilistic (Stochastic) Models– Some components or data are not known with
certainty• Examples of include: Monte Carlo simulation,
Scheduling and queueing
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General Modeling Process
Diagnose problem Organize facts Select methodology Formulate model Solve model Interpret results
Validate– Face validity
– Causal validity
– Computational validity
Sensitivity analysis
Implement solution
Monitor results
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Abstract aspect of real problem
Real World Problem
Model
Is the model valid?
Study model behavior
Make decisions
Monitor resultsModel solution
No Yes
Basic Modeling Process
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Fundamental Relationships
Accounting
Microeconomics
Logic
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Terminology and Relationships
Price Sales & Production
Volume Supply & Demand Revenue Market Share Contribution Historical &
Replacement Costs Marking to Market Allocated Costs
Sunk Costs Overhead, Fixed &
Period Costs Depreciation and
Amortization Variable or
incremental Costs Capacity Market Share
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Model Building: Influence Diagram
A graphical representation (flow chart) of
the influencing relationship among
variables in a particular problem
Constructing an influence diagram using Top-Down approach – start with output: performance measure– work downward to locate variables that affect
the output as well as other variables
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Profit
TotalCost
Revenue
Price
Demand
TVC
TFC
Unit VC
Advertising
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Spreadsheet Modeling
Inputs should be logically grouped Primary outputs should be easy to read
Input and output data should be labeled Don’t embed parameters in a formula: using
cell reference Use range name
Use fonts and color but don’t overuse them
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O utput o r H istorica lVa lid ity
R e la tionsh ip Va lid ity
Face Va lid ity
Va lida te M ode l
Bu ild M ode l
D iagnosis
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Validation
A Process of Establishing Confidence that an Inference from Model is Correct.
There is No Single Test for Validity. Series of Hurdles to Increase Model Builder
and User’s Confidence in the Model.
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Face Validity
Is Model’s Output Reasonable? When Changes Made in InputInput Variables, Is
Value of OutputOutput Variable Reasonable?– Be Aware of Counter-Intuitive Model Output!
Enhanced by Using Well-Defined Financial (or Business) Relationships within Model.
Absolute Minimum for Validation.
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Flowchart for Face Validity: Outputs Are
Change Inputs
Consistent withExpectations Establish Face Validity
Inconsistent withExpectations
Model’s LogicCorrect
Counterintuitive
Model’s LogicIncorrect
Make Changesto Model
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Historical & Relational Validity
Compare Model’s Output to Historical Data. Assess Assumptions About the Relations of the
Model Components to Each Other– Builders Must State Assumptions.
– Users Must Assess Assumptions.
– Must Examine Included and Excluded Assumptions Within the Model.
– Review List of Controllable and Uncontrollable Variables and Relevant Ranges.
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C ontro llab leVariab les
U ncontro llab leVariab les
W hat-If: Eva lua teA lte rna tives
Va lida te M ode l
Bu ild M ode l
D iagnosis
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Optimization
We wish to choose the “best” controllable input based upon the relations and constrains which we can’t control.
We may find this optimum:– Mathematically - using calculus & algebra– Arithmetically - using tables or spreadsheets– Iteratively -using optimization software
(I.e.Solver)
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Mathematical Optimization
If we have a model which lends itself to a continuous equation, we can use calculus to find a global minimum or maximum. I.e.:– Total Cost = Fixed + Variable Costs
• TC = 2000 + 10 * Demand
– Demand = 100 – 2 * Price– Profit = TR – TC = P * D – TC
Find the Profit Maximizing Price
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Arithmetical Optimization
If we don’t have a differentiable equation or a continuous relation but do have a simple equation, we may find an optimum arithmetically using one way or two way tables or spreadsheets.
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One-Way What-If Table
Order Size Total Annual Cost
6000
5000
4000
3000
2000
1000
500
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Two-Way What-If Table
Low Level, $20 High Level, $30
1500
Order Size
Order Cost
1300
1400
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Iterative Optimization
If we have several controllable variables and/or the variables can take on many different values, we may find an optimum using software which iteratively applies numerical methods such as Excel’s Solver.
Since this is numerical (and not mathematical), we cannot be assured that we have found a truly global optimum but instead may have found a local one.
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Hill Climbing
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Using Excel’s Solver for Optimization
Answers Questions Such As:– What Order Size Will Minimize Total Annual
Cost?– How Much Should I Invest in Stock 1 to
Maximize Portfolio Return?
OutputOutput (AKA TargetTarget) Cell is Cell Whose Value You Wish to Maximize or Minimize.
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Using Excel’s Solver
Input Variables or ChangingInput Variables or Changing Cells Are Those Cells Whose Values Are Adjusted Until a Solution is Found.
ConstraintConstraint – The Range of Permissible Values for the Controllable Variables.
Uses an Iterative Procedure to Found the Peak or Valley for the Target Variable.
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Optimization Using Solver
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Problem Using Excel’s Solver
Problem: Solver Sometimes Find a Local Maximum (Hill Top) and Not the Global Maximum (Mountain Top).
Solution: Try Running Solver Several Times with Different Starting Values in the Changing Cells (Base Camps).
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Q u a lita tiveM eth od
U n ivaria teD ata
A n a lys is
Q u an tita tiveM eth od s
In te llig en ceP h ase
U n d ers tan d in gth e R e la tion s
M od e lin g th eP rob lem
B ivaria teD ata
A n a lys is &R eg ress ion
D es ig nP h ase
C h o ice P h ase
D ec is ionS c ien ce
F ou n d ation s
The Design Phase
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Cross-Sectional Time-Ordered
Univariate Described by OneVariable
For One TimePeriod Over ManyPeople or Groups
Described by OneVariable
For One Group overMany Time Periods
Bivariate Described byTwo Variables(Two Columns).
For One TimePeriod OverMany People orGroups
Described byTwo Variables(Two Columns).
For One Groupover Many TimePeriods
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InterpretD ata
Sum m arizeD ata
OrganizeD ata
Overview of BivariateBivariate Data: Looking For Relationships
AnalyzingSpecific Data
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Data Base 1: Cross-SectionalData Base 1: Cross-Sectional Data Base (for One Period)
A B C D E F1 Region Adv-Last Qtr (0000) Mean Sales Exp Competitive? Rel. Price Market Share2 ATLANTA 13 3 1 1.50 203 BRMHM 28 15 0 0.60 504 CHAR 17 20 1 1.00 305 JACK 8 1 1 1.75 106 NO 16 23 1 1.30 257 ORLANDO 18 4 0 0.90 308 MIAMI 21 19 0 2.00 359 WASH 6 25 1 2.90 510 BALT 25 7 0 1.50 4511 DALLAS 32 11 0 1.10 5512 HOUSTON 11 2 1 2.50 2013 AUSTIN 16 20 1 2.25 28
DependentVariable
Potential Predictor Variables
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Does Market Share Data Exhibit Much Variation (Data Base 1)?
Compute Coefficient of Variation (CV).
If CV Greater Than 25-30%, Generate Possible Predictor Variables That Might Affect the Dependent Variable, Market Share.
%..
.551
41729
15115
x
sCV
Median
IQRCV
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Types of VariablesVariables
DependentDependent Variable is the Variable You Wish to Understand or Predict.
PredictorPredictor, or IndependentIndependent, Variables Are the Variables You Believe Affect the Dependent Variable.
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Correlation
If two variables are related to each other, then changes in one can be related to changes in the other. In other words, they rise and/or fall together.
Measured by a coefficient -1 r 1 One variable may be caused by the other
OR they both may be caused by other causes (intervening variables).
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Causal Models
Causal Models - where we have one numerical dependent variable and one or more independent variables which we say “cause” the dependent variable– Salary is “caused by” gender and months on the
job.– Wrecks are “caused by” alcohol, cell phones,
speed, etc.– Advertising “causes” sales.
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Establishing Causality
Necessary (but not sufficient) determinates of Causality:– Correlation - variables rise and/or fall together.– Temporal precedence - cause precedes effect in
time.– Logical mechanism - must have reasonable
explanation of how independent variable causes the dependent variable to vary.
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Organize Bivariate Data
S catte rD iag ram
C rossS ec tion a l
S ca tte rD iag ram
L ead in gIn d ica to rS ca tte r
D iag ram
Tim eO rd ered
M u ltiva ria teQ u an tia t ive
or M ixedD ata S e ts
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Slide 2
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Scatter Plot of Advertising Versus Share of Market, CS Data
0
10
20
30
40
50
60
0 10 20 30 40
Advertising in 000s
Mar
ket S
hare
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Scatter Plot of Mean Sales Exp. Versus Share of Market, CS Data
0
10
20
30
40
50
60
0 5 10 15 20 25
Mean Sales Experience
Mar
ket
Sh
are
50
Scatter Plot of Degree of Competitiveness Versus Market
Share, CS Data
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8 1
Competitiveness
Mark
et
Sh
are
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Scatter Plot of Relative Price Versus Market Share, CS Data
0
10
20
30
40
50
60
0.50 1.00 1.50 2.00 2.50 3.00
Relative price
Mar
ket
shar
e
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Leading Predictor Variables
Does ADV (t) Affect Sales (t)? Since the Cause proceeds the Effect in time,
if we are using time-ordered data, we may need to have the effect lag the cause in time.
If advertising causes sales, does this months advertising effect this months sales or next months sales?
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0
50
100
150
200
250
0 10 20 30 40 50
Advertising (k$)
Sal
es (
M$)
Here, we shift Adv. down 1 month
Month Adv (k$) Sales (M$)Jan 28 167Feb 23 155Mar 32 77Apr 31 179May 40 176Jun 38 228Jul 25 235
Aug 27 97Sep 29 142Oct 34 163Nov 29 167Dec 38 158
Month Lagged Adv (k$) Sales (M$)JanFeb 28 155Mar 23 77Apr 32 179May 31 176Jun 40 228Jul 38 235
Aug 25 97Sep 27 142Oct 29 163Nov 34 167Dec 29 158
0
50
100
150
200
250
0 10 20 30 40 50
Lagged Advertising (k$)
Sal
es (
M$)
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InterpretD ata
Sum m arizeD ata
OrganizeD ata
Overview of BivariateBivariate DataLooking For Relationships
AnalyzingSpecific Data
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Equation for a Line
xy
bmxy
b is the _______
m is the ______
is the _______
is the _______
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Intercept and Slope
The intercept is:
The slope is:
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Estimating The Intercept and Slope Visually
x y1 52 73 64 85 10
0
2
4
6
8
10
12
0 1 2 3 4 5 6
y
Pred y
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CoefficientsIntercept 3.9x 1.1
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InterpretD ata
Sum m arizeD ata
OrganizeD ata
Overview of Bivariate DataLooking For Relationships
AnalyzingSpecific Data
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Interpreting the Equation
x
Y
3.9
rise
run =
1.1=
1
Y Intercept = 3.9
Slope = Rise/Run = 1.1
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Multivariate AnalysisMultivariate AnalysisIs Salary Related to Months on
Job And/Or Gender?Salary Months Gender48.0 39 Male63.5 80 Male37.2 6 Male33.2 7 Male49.1 45 Male42.7 27 Male46.7 36 Male56.9 67 Male
Salary Months Gender38.5 80 Female38.8 65 Female22.5 12 Female29.7 24 Female20.4 5 Female34.0 45 Female31.2 38 Female41.1 54 Female
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Lecture FlowD raw
Scatter P lots
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Scatter Plot of Gender Vs. Salary
Conclusions:
$0.0
$10.0
$20.0
$30.0
$40.0
$50.0
$60.0
$70.0
0 0.2 0.4 0.6 0.8 1 1.2
Gender
Sal
ary
(000
's)
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Scatter Plot of Month Vs. Salary
Conclusions:
Scatter Plot of Month vs. Salary
$0.0
$10.0
$20.0
$30.0
$40.0
$50.0
$60.0
$70.0
0 10 20 30 40 50 60 70 80 90
Months on the Job
Sala
ry (0
00's
)
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Purposes of Scatter Plots
Does a relation appears to exist? If so, is the relation negative or positive? What shape is the relation?
– If linear, we can apply linear regression.– If non-linear, we may apply a linear
transformation before using regression (subjects of DSc 3120 and beyond).
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Lecture Flow
Estim ate R egressionM odel
D rawScatter P lots
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Interpreting Regression Model or Equation
. . .S M onths G ender 18 979 323 15 783
Holding Gender Constant, For Every Additional Month on Job, Salary, On Average, Increases by ________Thousands of Dollars or $______.
Holding Gender Constant, For Every Additional 1010 Months on Job, Salary, On Average, Increases by ________Thousands of Dollars or $______.
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Estimating a Regression Model or Equation
. . .S M onths G ender 18 979 323 15 783
Holding Months on Job Constant, Males (Coded as 1), On Average, Receive _________ Thousands of Dollars More than Females.
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Scatter Plot of Month vs. Salary
$0.0
$10.0
$20.0
$30.0
$40.0
$50.0
$60.0
$70.0
0 10 20 30 40 50 60 70 80 90
Months on the Job
Sal
ary
(000
's)
Of Three Lines, Which is “Best Fitting” Model or Line?
A
C
B
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A “Best-Fitting” Line:
embodies the underlying trend of the data, comes closest to all data points (I.e. misses
all the points by the least total distances), therefore it is the line which:
minimizes the sum of squared deviations or errors (this method is known as the method of “Least Squared Errors” or LSE or OLS or MLS)
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Minimizing The Sum of the Squared Deviations
..
..d1
d2
d3d4
BFL Minimizes d d d d12
22
32
42
Months on Job
Sal
ary
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How to Determine Line that Minimizes
Trial and error Special software Least Squares Equation (Developed from
Calculus)
di
2
xy
xnx
yxnyx
ii
iii
22Slope
Intercept
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Solving the Least Squares Equations
x y xy x2
1 5 5 12 7 14 43 6 18 94 8 32 165 10 50 25
15 36 119 55
= __________
= __________
y
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Generating the Best Fitting Model in Practice
Don’t Solve LSE by Hand. Use Software that Solves LSE. For Salary Study, the Best Fitting Model is:
. . .S M onths G ender 18 979 323 15 783
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Lecture Flow
If Not Significant,Seek Additional Predictor Variables
Test Overall M odelAN OVA
Estim ate R egressionM odel
D rawScatter P lots
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How Much Variation (Sum of Squares) Is There in Dependent
Variable??Salary48.063.537.233.249.142.746.756.9
Salary38.538.822.529.720.434.031.241.1
SST = ( )2 + ...+ ( )2
2003.129
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What Is SST Due To??
2003.129
Two Factors
1906.042
The Variation in the Dependent Variable is based the factors in our model plus all factors not in our model:
+ All Other Factors
97.087
SSTotal = SSRegression + SSErrors
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ANOVA for Salary Study
Determine p-Value for F StatisticIn Excel: Significance F Value
df SS MS FRegression 2 1906 953 127.61Residual 13 97.088 7.47Total 15 2003.1
R2 = SSR/SST aka: Coefficient of Determination
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The Standard Error of the Estimate Measures Impact of All Factors (Other than Months on Job and Gender) On Salary.
Equals and is $2.733 ($2,733)
for Salary Study. If Only Months on Job and Gender Affected
Salary, sY|X Would Equal
The Standard Error of the Estimate, SY|X
MSError
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Will Use Standard Error for Making Salary Predictions Using Regression Model.
Salary of Male (1) with 10 Months????
$ + MOE Size of MOE Depends, in Part, on Standard
Error of Estimate.
Why Reduce Standard Error of the Estimate
x
. . .S M onths G ender 18 979 323 15 783
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How to Reduce Standard Error?
Increase sample size.
Eliminate “weak” predictor variables through t-value screening.
dfE
SSEMSES XY |
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U se t-ValueScreening M ethod
Test Overall M odelAN OVA
Estim ate R egressionM odel
D rawScatter P lots
Lecture Flow
If OverallModel Sig,then:
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t-Value Screening Procedure to Reduce Standard Error of Estimate
1 Take the Absolute Value of the t- Values for Predictor Variables from Parameter Estimate Section.2 Delete Predictor Variable if Smallest t-Value Less Than 2.03 Use Software to Re-estimate Model.4 Repeat Steps 1 -3 As Necessary.
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Lecture Flow
U se M odel toM ake Predictions
U se t-ValueScreening M ethod
Test Overall M odelAN OVA
Estim ate R egressionM odel
D rawScatter P lots
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Interpolation vs. Extrapolation Interpolation: Predict Values of y Within Range
of Study’s Predictor Variables.– Range of Months on Job is From ____ to ______.
Extrapolation: Predict Values of y Outside Range of Study’s Predictor Variables.
Extrapolate Only When You Believe Regression Model Is Valid Outside Range of Data.
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Making Predictions using Prediction and Confidence Intervals
Confidence Intervals: Prediction on Mean Salary for Group of People.
Prediction Intervals: Prediction on
Expected Salary for a Single Person.
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Making Predictions for Persons with 50 Months on Job
For a Male with 50 Months on Job $50,912 + MOE
For a Female with 50 Months $35,129 + MOE
. . .S M onths G ender 18 979 323 15 783
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For One Male
Making Approximate Salary Predictions for Male with 50
Months on Job Average of All Males
733,22912,50
|
xystx
MoEx
n
nstx
MoEx
xy
1733,22912,50
1|
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Reducing the Width of Confidence Interval and MOE
Remove Predictor Variables from Model with |t| Values < 2 (Screening Procedure). This reduces the Standard Error.
Increase sample size - reduces the Standard Error.
Accepting lower level of confidence (I.e. smaller t) - reduces Confidence Coefficient.
90
Summary of Regression
Regression Analysis Looks for Relations between variables.
What is the business application for regression?
91
Forecasting
Time Series Models
92
Forecasting Models
Budgets Sales quotas Financial pro-formas
Time series modelsCausal modelsQualitative models
93
Causal Models vs. Time Series Models
Time as a surrogate for causal factors Relate patterns in dependent variables to the
passage of time Stationary Time Series Assumption
– Data will continue to operate in the (near) future as it has in the (recent) past.
94
Forecast Sales for
Third Year Based Upon
Last Two Years Sales
Week Sales Week Sales Week Sales Week Sales1 52 27 63 53 78 79 812 47 28 68 54 68 80 833 53 29 67 55 69 81 834 55 30 61 56 74 82 775 57 31 55 57 65 83 796 52 32 63 58 67 84 787 49 33 59 59 65 85 848 52 34 55 60 75 86 889 55 35 59 61 77 87 78
10 60 36 68 62 72 88 8411 54 37 71 63 66 89 7612 59 38 62 64 70 90 7613 56 39 71 65 78 91 8314 55 40 72 66 75 92 8315 53 41 63 67 75 93 8716 54 42 66 68 75 94 8017 58 43 62 69 68 95 7918 54 44 73 70 79 96 8819 59 45 76 71 83 97 8420 63 46 65 72 85 98 8121 55 47 65 73 76 99 8322 53 48 64 74 82 100 9323 66 49 66 75 79 101 9124 57 50 64 76 85 102 9325 61 51 63 77 80 103 9226 56 52 73 78 81 104 96
95
Time Series Scatterplot
0
20
40
60
80
100
120
0 20 40 60 80 100 120
Week
Sal
es
96
Naïve Model
Whatever happened recently will happen again this time.
The model is simple and flexible. Provides a baseline against which to
evaluate other models.
97
Exponential Smoothing Models
Advantages– Requires little data
– Quick and simple to compute
– Emphasizes the most up-to-date data
– Cheap
– Suitable for high-volume forecasts
Disadvantages– Simple ES always lags
trend in the data
– Double ES ignores seasonality
– Winter’s method is complex
98
Ft Forecast for period t
Ft-1 Most recent forecast
Yt-1 Most recent actual data point
Smoothing constant ( 0 < < 1 )
Simple Exponential Smoothing1-t1-tt F ) -1 ( Y F
99
Double Exponential Smoothing
Ft Forecast for period t
Ct Continuously updated intercept
Tt Smoothed period to period slope
Yt-1 Most recent actual observed value
Smoothing constant for intercept C Smoothing constant for trend T
1-t1-ttt
1-t1-tt
ttt
T ) -1 ( ) C - C ( TF ) - 1 ( Y C
T C F
100
Winter’s Method
Adds a third smoothing constant Adds smoothed Seasonal Indices Much more complex than exponential
smoothing
101
Bias - The arithmetic mean of the errors Mean Square Error - Similar to simple
sample variance Variance - Population variance (adjusted for
degrees of freedom) Standard Error - Standard deviation of the
sampling distribution MAD - Mean Absolute Deviation
Measuring Error
n
Forecast) - (Actual MSE
2
102
Classical Time Series Conceptual Model
Error Seasonal Cyclical Trend Y1
•Y1 - The original data representing activity in time period t
•Trend - The time pattern of the basic level of the data
•Cyclical - Long term swings above and below the trend level
•Seasonal - A cycle that has a period of exactly one year for a
complete cycle
•Error - The underlying degree of randomness or error in model
103
Trend Models
Rather than working month to month, why not fit a line through the historical data and project it into the future?
The mathematical method for calculating the best curve is called the “method of least squares.”– Minimize (Y - a - bX)2 with respect to our
choice of a and b
104
Trend Models Pros
– Can predict into the future
– Formalizes a method to minimize error term
– Can use a number of curve forms
Cons– Ignores seasonal
changes
105
Time Series Decomposition The conceptual forecasting model is:
– Y = Trend x Cyclical x Seasonal x Error
Since we cannot easily extract or predict cycles, we will assume that the trend component will capture cycles during the forecast period
Since we must live with error (we cannot predict it) our model is simplified to:– Y = Trend x Seasonal
106
Estimating Trend
Since we cannot solve for two unknowns using one equation, we must first estimate one of our values
The best estimate to work with in this case is the One Year Centered Moving Average– The advantage of CMA is that it makes no
assumptions about the underlying data and completely averages out seasonality
107
Centered Moving Average
Starting with the first datum, we average one year’s worth of observations placing the result at the center point
We continue by moving to the next datum and repeating the process until we no longer have a complete year to average
108
Centered Moving Average
The initial average lies between the middle values (quarters or months)
To get the centered moving average, we average the two values on either side to get the CMA
NOTE: In averaging one year of data, we lose the first and last six months
109
Raw Seasonal Ratios
Now that we have an estimate for trend, we can solve our general model for seasonality– Season = Y / Trend
We use this formula to calculate the Raw Seasonal Ratio
The Raw Seasonal Ratio is used to calculate the Seasonal Index
110
Seasonal Index
To calculate the Seasonal Index for each period, average the raw ratios for each similar period then center the averages about 1
Divide each season’s average by the overall (grand) average to force the average of all Seasonal Indices to equal 1
111
Deseasonalized Data
Going back to the conceptual model, solve for trend:– Trend = Y / Season
This eliminates seasonal variation and isolates the trend
Now use the Least Squares method to compute the Trend
112
Forecast
Now that we have the Seasonal Indices and Trend, we can reseasonalize the data and generate the forecast– Y = Trend x Season
113
Deciding Between Forecasting Models & Methods
Look at the errors over the backcast or for a holdout sample:– Bias near zero– MAD, MAPE, & Std Error near Zero– Coefficient of Determination (R2) near unity.
How well does it perform in repeated uses and during validation with different data.
114
Deciding Between Forecasting Models & Methods
What if several models are approximately “equally good”?– The Rule of Parsimony (or using Occam’s
Razor), we would choose the simplest, easiest, most cost effective model that meets our needs.