Chapter 8 Polynomial Regression Models
1.0
logx
1.6
0.5
1.4
0.0
1.2
1.0
x
1.8
2.0
1.5
2.2
Use of polynomial regression models
Most frequently used curvilinear response models
Can be used in two cases
as true model or
to approximate a nonlinear relati
Chapter 9 Transformation of the Response
Variable
Use of transformations
Corrections for violations of model assumptions (e.g.
nonconstant variance, nonnormality)
Trial and error
Rules of thumb:
Square root of counts
Log of positive numbers with larg
Chapter 7 Worthwhile Regressions
20
16
Regression
Sample Mean
14
0.1073
Is the model statistically significant?
Are you satisfied with the model?
18
y
Example: A SLR model is fitted
for data with 50 observations
5.767
4.04
, , .
22
24
Is my regression a
Chapter 2 Regression in Matrix Terms
Fitting a straight line
1
1
1
,
,
,
Assume
~ 0,
(all columns are linearly independent)
We can write ~
,
Use
1, , , , ,
to denote the th row in
1
Least square estimate of
LS seeks
( ) that minimizes
,
This is mi
Chapter 5 Multiple Linear Regression:
Special Topics
Testing a general linear hypothesis
Linear hypothesis:
Test a linear function of the s
:
0
:
2
0
:
0
:
1
General form:
:
0
0
0
:
Or written in matrix form as
. i.e.,
has
,
linearly independ
Chapter3ExtraSumofSquaresandTests
Test whether it is worthwhile to include certain terms in the model
T-test for :
0( ,
)
F-test for the significance of the whole regression model
including all predictor variables (
)
,
More general test involving se
Chapter 4 More on Model Checking
Case diagnostics Outliers
Individual cases can be
outliers in
detected as usual in a single sample
outliers in
influential cases (high leverage)
regression outliers
outliers in for a given
1
Regression outliers
Re
Chapter 6 Bias in Regression Estimates
Bias in regression estimates
Least squares estimate:
If the specified model is correct:
If the specified model is incorrect:
Bias depends on
The true model
The specified model
experimental design
1
Specified