Business Statistics Ii
Business Statistics II
ECO 362
Regression Analysis:
Model Building
General Linear Model
Determining When to Add or Delete
Variables
Variable Selection Procedures
Residual Analysis
Multiple Regression Approach to Analysis of Variance and Experimental Design
Chapter 16
Regression Analysis:
Model Building
School of Business and Economics
SUNY Plattsburgh
Dr. Kameliia Petrova
Slide 1
Dr. Kameliia Petrova
Linear models: models in which all parameters
(β 0, β 1, . . . , β p ) have exponents of one.
General linear model with p independent variables: The simplest case is when z1 = x1. We want to estimate y by using a straight-line relationship. Simple first-order model with one predictor
(independent) variable.
y = β 0 + β1 z1 + β 2 z2 + L + β p zp + ε
Each of the independent variables z is a function of x1, x2,..., xk (the variables for which data have been collected).
School of Business and Economics
SUNY Plattsburgh
Slide 2
General Linear Model
General Linear Model
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
y = β 0 + β 1 x1 + ε
0
Slide 3
Modeling Curvilinear
Relationships
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
Slide 4
Interaction
To account for a curvilinear relationship we set z1 = x1 and z2 = x12
Second-order model with two predictor variables. 2
2
y = β0 +β1x1 +β2x2 +β3x1 + β4x2 +β5x1x2 + ε
Second-order model with one predictor variable: Variable z5 = x1x2 is added to account for the potential effects of the two variables acting together. 2 y = β 0 + β 1x1 + β 2 x1 + ε
This type of effect is called interaction.
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
Slide 5
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
Slide 6
1
Nonlinear Models That Are
Intrinsically Linear
Transformations Involving the
Dependent
ECO 362
Regression Analysis:
Model Building
General Linear Model
Determining When to Add or Delete
Variables
Variable Selection Procedures
Residual Analysis
Multiple Regression Approach to Analysis of Variance and Experimental Design
Chapter 16
Regression Analysis:
Model Building
School of Business and Economics
SUNY Plattsburgh
Dr. Kameliia Petrova
Slide 1
Dr. Kameliia Petrova
Linear models: models in which all parameters
(β 0, β 1, . . . , β p ) have exponents of one.
General linear model with p independent variables: The simplest case is when z1 = x1. We want to estimate y by using a straight-line relationship. Simple first-order model with one predictor
(independent) variable.
y = β 0 + β1 z1 + β 2 z2 + L + β p zp + ε
Each of the independent variables z is a function of x1, x2,..., xk (the variables for which data have been collected).
School of Business and Economics
SUNY Plattsburgh
Slide 2
General Linear Model
General Linear Model
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
y = β 0 + β 1 x1 + ε
0
Slide 3
Modeling Curvilinear
Relationships
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
Slide 4
Interaction
To account for a curvilinear relationship we set z1 = x1 and z2 = x12
Second-order model with two predictor variables. 2
2
y = β0 +β1x1 +β2x2 +β3x1 + β4x2 +β5x1x2 + ε
Second-order model with one predictor variable: Variable z5 = x1x2 is added to account for the potential effects of the two variables acting together. 2 y = β 0 + β 1x1 + β 2 x1 + ε
This type of effect is called interaction.
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
Slide 5
Dr. Kameliia Petrova
School of Business and Economics
SUNY Plattsburgh
Slide 6
1
Nonlinear Models That Are
Intrinsically Linear
Transformations Involving the
Dependent