LINEAR REGRESSION ANALYSIS
MODULE XVI
Lecture - 44
Exercises
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Exercise 1
The following data has been obtained on 26 patients on their systolic blood pressure and a
LINEAR REGRESSION ANALYSIS
MODULE X
Lecture - 32
Heteroskedasticity
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
In the multiple regression model
= X +,
y
it is assumed that
V ( ) = 2 I ,
i.e., Var ( i2 )= 2
LINEAR REGRESSION ANALYSIS
MODULE IX
Lecture - 31
Multicollinearity
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
6. Ridge regression
The OLSE is the best linear unbiased estimator of regression coefficient i
LINEAR REGRESSION ANALYSIS
MODULE IX
Lecture - 30
Multicollinearity
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Remedies for multicollinearity
Various techniques have been proposed to deal with the problems
LINEAR REGRESSION ANALYSIS
MODULE IX
Lecture - 29
Multicollinearity
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Multicollinearity diagnostics
An important question that arises is how to diagnose the presenc
LINEAR REGRESSION ANALYSIS
MODULE VIII
Lecture - 27
Indicator Variables
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Indicator variables versus quantitative explanatory variable
The quantitative explanatory
LINEAR REGRESSION ANALYSIS
MODULE IX
Lecture - 28
Multicollinearity
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
A basic assumption in multiple linear regression model is that the rank of the matrix of obser
LINEAR REGRESSION ANALYSIS
MODULE VIII
Lecture - 26
Indicator Variables
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
In general, the explanatory variables in any regression analysis are assumed to be quantit
LINEAR REGRESSION ANALYSIS
MODULE V
Lecture - 20
Correcting Model
Inadequacies Through
Transformation and Weighting
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
The graphical methods help in detecting the vi
LINEAR REGRESSION ANALYSIS
MODULE VII
Lecture 25
Generalized and Weighted
Least Squares Estimation
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
The usual linear regression model assumes that all the random e
LINEAR REGRESSION ANALYSIS
MODULE XI
Lecture - 34
Autocorrelation
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Tests of autocorrelation
Durbin-Watson (D-W) test
The Durbin-Watson (D-W) test is used for testi
LINEAR REGRESSION ANALYSIS
MODULE XI
Lecture - 33
Autocorrelation
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
One of the basic assumptions in linear regression model is that the random error components or d
LINEAR REGRESSION ANALYSIS
MODULE XV
Lecture - 43
Generalized Linear Models
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Linear predictors and link functions
The role of generalized model is basically to uni
LINEAR REGRESSION ANALYSIS
MODULE XV
Lecture - 42
Generalized Linear Models
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
The usual linear regression model assumes normal distribution of study variables where
LINEAR REGRESSION ANALYSIS
MODULE XIII
Lecture - 38
Variable Selection and Model
Building
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Evaluation of subset regression model
A question arises after the select
LINEAR REGRESSION ANALYSIS
MODULE XIV
Lecture - 40
Logistic and Poisson
Regression Models
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Logistic regression model
y
In the linear regression model= X , + there
LINEAR REGRESSION ANALYSIS
MODULE XIV
Lecture - 41
Logistic and Poisson
Regression Models
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Interpretation of parameters
To understand the interpretation of the rel
LINEAR REGRESSION ANALYSIS
MODULE XII
Lecture - 36
Polynomial Regression
Models
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Test of significance
To test the significance of highest order term, we test the n
LINEAR REGRESSION ANALYSIS
MODULE XIII
Lecture - 39
Variable Selection and Model
Building
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
5. Akaikes information criterion (AIC)
The Akaikes information criterion
LINEAR REGRESSION ANALYSIS
MODULE XIII
Lecture - 37
Variable Selection and Model
Building
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
The complete regression analysis depends on the explanatory variables pr
LINEAR REGRESSION ANALYSIS
MODULE XII
Lecture - 35
Polynomial Regression
Models
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
A model is said to be linear when it is linear in parameters. So the model
y = 0 +
LINEAR REGRESSION ANALYSIS
MODULE VI
Lecture - 24
Tests for Leverage and
Influential Points
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
2. DFFITS and DFBETAS
Cooks distance measure is a deletion diagnostic,
LINEAR REGRESSION ANALYSIS
MODULE V
Lecture - 22
Correcting Model
Inadequacies Through
Transformation and Weighting
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Computational procedure
The maximum- likelihoo
LINEAR REGRESSION ANALYSIS
MODULE II
Lecture - 7
Simple Linear Regression
Analysis
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Orthogonal regression method (or major axis regression method)
The direct and r
LINEAR REGRESSION ANALYSIS
MODULE III
Lecture - 10
Multiple Linear Regression
Analysis
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Maximum likelihood estimation
=
In the model y X + , it is assumed that the
LINEAR REGRESSION ANALYSIS
MODULE III
Lecture - 9
Multiple Linear Regression
Analysis
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Theorem:
i.
Let y = Xb be the empirical predictor of y. Then y has the same
LINEAR REGRESSION ANALYSIS
MODULE III
Lecture - 8
Multiple Linear Regression
Analysis
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
We consider now the problem of regression when study variable depends on mor
LINEAR REGRESSION ANALYSIS
MODULE II
Lecture - 6
Simple Linear Regression
Analysis
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Prediction of values of study variable
An important use of linear regression mo
LINEAR REGRESSION ANALYSIS
MODULE II
Lecture - 5
Simple Linear Regression
Analysis
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Joint confidence region for 0 and 1
A joint confidence region for 0 and 1 can a
LINEAR REGRESSION ANALYSIS
MODULE II
Lecture - 3
Simple Linear Regression
Analysis
Dr. Shalabh
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
2
Properties of the direct regression estimators
Unbiased property
s xy
=
Note th