Multiple Linear Regression

1
Multiple Linear Regression
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
2
The Multiple Regression Model
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
3
Assumptions of the Multiple Regression Model

• The errors follow a normal distribution, centered
  at zero, with common variance
• The errors are independent

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
4
Multiple Regression Model Assumptions
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 15.3
5
Hypothesis Test for the Significance of the Model
Ho ?1 ?2 ?k Ha at least one of the ?s
? 0
Reject Ho if F gt F?,k,n-k-1
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
6
F Statistic
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 15.5
7
Test for Ho ?i 0
Ho ?1 0 Ha ?1 ? 0
Reject Ho if t gt t ?./2, n-k-1
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
8
(1- ?) 100 Confidence Interval for ?i
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
9
Coefficient of Determination
SSR
R

2
SST
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
10
Curvilinear Models
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
11
Curvilinear Models
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 15.10
12
Extrapolation with Curvilinear Models
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 15.12
13
Multicollinearity- VIFs
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
14
Dummy Variables

• The use of dummy or indicator variables in a
  regression analysis allows you to include
  qualitative variables in the model.

For example
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
15
Stepwise Procedures
Stepwise Procedures allow the evaluation of an
additional variable in an established
model. There are three methods Forward
Regression Backward Regression and Stepwise
Regression
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
16
Figure 15.18
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
17
(1-?) 100 Confidence Interval for ? yx
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
18
Prediction Interval for YXo
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
19
Interaction Effects
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
20
Interaction Effects
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 15.23