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