Applied
Regression Analysis for Business Decision Making
Seminar
Description:
This
course aims to familiarize the student with
statistical prediction. It covers simple and multiple
regression methods as well as time series and
forecasting models in business. Instead of theoretical
development, the course emphasizes the application of
these methods in business systems analysis and
improvement.
Prerequisites:
Participants
in this seminar must have achieved Six Sigma Yellow
Belt
certification.
Six
Sigma Certification:
Applied Regression Analysis for Business Decision
Making is required to sit for the Six Sigma Black Belt
examination.
Textbook:
Montgomery, D.C., Peck, E. A., Vining, G. G., Introduction
to Linear Regression Analysis, 3^{rd}
Edition, Wiley and Sons.
Statistical
Software:
Minitab 14
Seminar
Outline:
Chapter
1: Introduction
Regression
and Model Building
Data
Collection
Uses of
Regression
Chapter
2: Simple Linear Regression:
Simple
Linear Regression Model
Least
Squares Estimation of Parameters
Hypothesis
testing on the Slope and Intercept
Interval
Estimation in Simple Linear Regression
Prediction
of New Observations
Coefficient
of Determination
Considerations
Regression
Through the Origin
Estimation
by Maximum Likelihood
Cases
Were the Regressor is Random
Chapter
3: Multiple Linear Regression
Multiple
Regression Models
Estimation
of Model parameters
Hypothesis
testing in Multiple Linear Regression
Confidence
in Multiple Regression
Prediction
of New Observations
Hidden
Extrapolation in Multiple Regression
Standardized
Regression Coefficients
Multicollinearity
Why Do
Regression Coefficients Have the Wrong Sign?
Chapter
4: Model Adequacy Checking
Residual
Analysis
PRESS
Statistic
Detection
and treatment of Outliers
Lack of
Fit of the Regression Model
Chapter
5: Transformations and Weighting to Correct
Inaccuracies
Variance
Stabilizing Transformations
Transformations
to Linearize the Model
Analytical
Methods for Selecting a Transformation
Generalized
and Weighted least Squares
Chapter
6: Diagnostics for Leverage and Influence
Importance
of Detecting Influential Observations
Leverage
Measures
of Influence (Cook’s D)
Measures
of Influence (DFFITS and DFBETAS)
Measure
of Model performance
Detecting
Groups of Influential Observations
Treatment
of Influential Observations
Chapter
7: Polynomial Regression
Polynomial
Models in One variable
Nonparametric
Regression
Polynomial
Models in Two or More variable
Orthogonal
Polynomials
Chapter
8: Indicator Variables
General
Concept of an Indicator Variable
Comments
on the Use of Indicator Variables
Regression
Approach to Analysis of Variance
Chapter
9: Variable Selection and Model Building
Model
Building
Computational
Techniques for Variable Selection
Chapter
10: Multicollinearity
Sources
Effects
Diagnostics
Methods
Chapter
11: Robust Regression
Need
for Robust Regression
MEstimators
Properties
of Robust Estimators
Other
Robust Estimators
Chapter
12: NonLinear Regression
Linear
and NonLinear Models
NonLinear
Least Squares
Transformation
to a Linear Model
Parameter
Estimation
Statistical
Inference
Chapter
13: Generalized Least Squares
Logistics
Regression Models
Poisson
Regression Models
Generalized
Linear Model
Chapter
14: Other Topics in Regression Analysis
Regression
Models with Autocorrelation Errors
Effect
of Measurement Errors in the Regressors
Inverse
Estimation
Bootstrapping
Classification
and Regression Trees
Neural
Networks
Designed
Experiments for Regression
Chapter
15:
Validation of Regression Models
Validation
Techniques
Data
from Planned Experiments
Design
of Experiments for Business Decision Making
Seminar
Description:
This course will present tools and methodology useful
in conducting experiments that provide valid answers
to questions of interest to the experimenter.
The course will discuss an overall approach to
obtaining and analyzing experimental data, the
advantages of using structured multifactor experiments
to screen for important factors, ways of minimizing
the amount of data points needed to obtain desired
information, and how to identify values of
experimental factors that optimize the value of
measured responses.
Factorial designs, fractional factorial
designs, and response surface designs will be
presented. Emphasis
will be on the knowledge required for proper
application of these methods through many examples in
business and quality management.
Prerequisites:
Participants in this
seminar must have achieved Six Sigma Yellow Belt
certification.
Six
Sigma Certification:
Design of Experiments for Business Decision Making is
required to sit for the Six Sigma Black Belt
examination.
Text:
Paul Mathews, “Design of Experiments with
Minitab,” American Society for Quality, ASQ
Quality Press, WI: Milwaukee, 2005. The book
comes with a supplementary CD containing Minitab
files.
Statistical
Software:
Minitab 14
Seminar
Outline:
Chapter
1: Graphical Presentation of Data
Types
of Data
Histograms
Dot
Plots
Scatter
Plots
Multivari
Charts
Chapter
2: Descriptive Statistics
Selection
of Samples
Measures
of Location
Measures
of Variation
The
Normal Distribution
Chapter
3: Inferential Statistics
Distribution
of Sample Means (Sigma Known)
Confidence
for the Population Mean (Sigma Known)
Hypothesis
Test for One Sample Mean (Sigma Known)
Distribution
of Sample Means (Sigma Unknown)
Hypothesis
tests fro Two means (sigma Known and Unknown)
Inferences
About One Variance
Hypothesis
Tests for Two Sample Variances
Testing
for Normality
Sample
Size Calculation
Chapter
4: DOE Language and Concepts
Definition,
Scope, and Motivation
Experiment
Defined
Identification
of Variables and Responses
Types
of Variables
Types
of Responses
Interactions
Types
of Experiments
Types
of Models
Selection
of Variable level
Nested
Variables
Covariates
Definition
of Design in
Design of Experiments
Types
of Designs
Randomization
Replication
and Repetition
Blocking
Confounding
Data
Integrity and Ethics
Experiment
Documentation
Why
Experiments Go Bad
Chapter
5: Experiments for OneWay Classifications
Analysis
by Comparison of All Possible Pairs Means
Graphical
Approach to ANOVE
Introduction
to ANOVA
Sum of
Squares Approach to ANOVA Calculations
Calculating
Forms for Sum of Squares
ANOVA
for Unbalanced Experiments
After
ANOVA: Comparing treatment Means
Completely
Randomized Designs
Analysis
of Means
Response
Transformations
Sample
Size for OneWay ANOVA
Design
Considerations for One Way Classification Experiments
Chapter
6: Experiments for MultiWay Classifications
Rationale
for TwoWay ANOVA
Sum of
Squares Approach to Two Way ANOVA (One Replicate)
Interactions
Interpretation
of Two Way Experiments
Factorial
Designs
MultiWay
Classification Designs
Chapter
9: TwoLevel (2^{k}
) Factorial Designs
2^{2}
Factorial Design
2^{3}
Factorial Design
Addition
of Center Cells to the 2^{k} Factorial Design
General
procedures for the Analysis of 2^{k} Factorial
Design
Extra
and Missing Values
Propagation
of Error
Sample
Size and Power
Chapter
10: Fractional Factorial Designs
2^{51}
Half Fractional Factorial Design
Other
Fractional Factorial Designs
Design
Resolution
Consequences
of Confounding
Interpretation
of Fractional Factorial Designs
PlackettBurman
Designs
Sample
Size Calculations
Design
Considerations
Chapter
11: Response Surface Designs
Terms
in Quadratic Models
2^{k
}Designs with Centers
3^{k
}Factorial Designs
BoxBehnken
Designs
Central
Composite Designs
Comparison
of Response Surface Designs
Sample
Size Calculations
