Chapter 7
Generalized and Weighted Least Squares Estimation
The usual linear regression model assumes that all the random error components are identically and
independently distributed with constant variance. When this assumption is violated, then ordinar

Chapter 8
Indicator Variables
In general, the explanatory variables in any regression analysis are assumed to be quantitative in nature. For
example, the variables like temperature, distance, age etc. are quantitative in the sense that they are recorded
o

Chapter 3
Multiple Linear Regression Model
We consider the problem of regression when study variable depends on more than one explanatory or
independent variables, called as multiple linear regression model. This model generalizes the simple linear
regres

Chapter 1
Introduction
Linear models play a central part in modern statistical methods. On the one hand, these models are able to
approximate a large amount of metric data structures in their entire range of definition or at least piecewise.
Linear Models

Chapter 12
Polynomial Regression Models
A model is said to be linear when it is linear in parameters. So the model
y = 0 + 1 x + 2 x 2 +
and
y = 0 + 1 x1 + 2 x2 + 11 x12 + 22 x22 + 12 x1 x2 +
are also the linear model. In fact, they are the second order

Chapter 9
Multicollinearity
A basic assumption is multiple linear regression model is that the rank of the matrix of observations on
explanatory variables is same as the number of explanatory variables. In other words, such matrix is of
full column rank.

Chapter 11
Autocorrelation
One of the basic assumption in linear regression model is that the random error components or disturbances
are identically and independently distributed. So in the model=
y X + u , it is assumed that
u2 if s = 0
E (ut , ut s )

Chapter 6
Diagnostic for Leverage and Influence
The location of observations in x -space can play an important role in determining the regression
coefficients. Consider a situation like in the following
yi
A
Xi
The point A in this figure is remote in x sp

Chapter 5
Transformation and Weighting to Correct Model Inadequacies
The graphical methods help in detecting the violation of basic assumptions in regression analysis. Now we
consider the methods and procedures for building the models through data transfo

Chapter 4
Model Adequacy Checking
The fitting of linear regression model, estimation of parameters testing of hypothesis properties of the
estimator are based on following major assumptions:
1. The relationship between the study variable and explanatory v

Chapter 10
Heteroskedasticity
In the multiple regression model
=
y X +,
it is assumed that
V ( ) = 2 I ,
i.e.,
Var ( i2 ) = 2 ,
Cov( i j )= 0, i j = 1, 2,., n.
In this case, the diagonal elements of covariance matrix of are same indicating that the varian

Chapter 2
Simple Linear Regression Analysis
The simple linear regression model
We consider the modeling between the dependent and one independent variable. When there is only one
independent variable in the
linear regression model, the model is generally