Project (Fall 2018-2019): Distribution Theory of
Simple Linear Regression
Student: Mariam A. Orabi U14123143
Supervisor: Dr. Luai M. Al-Labadi
Regression analysis is a statistical methodology that utilizes the
relation between two or more variables so that one variable can be
predicted from the other, or the others (Neter, Kutner, Nachtsheim
and Wasserman, 1996).
Building valid models for real-life data is one of the most important
approaches of statistics for analyzing data which is widely used today.
Successful applications require understanding of both the underlying
theory and the practical problems that are encountered when building
models for real-life data.
The simplest form of regression is the simple linear regression,
which considers only one explanatory variable linearly related to the
response variable. Understanding simple linear regression enables the
reader to look at many aspects of regression in the simplest possible
In this project, we thoroughly demonstrated the concept of simple
linear regression. The model parameters are estimated using two methods, namely, least squares method and maximum likelihood method.
It is shown that the estimators are equal in both methods, and proven
to be good estimates, for which, the proof of Gauss-Markov theorem
is provided. In order to check the validity of the model, statistical
inferences about the parameters along with diagnostic methods to assure the validity of the model’s assumptions are explained. When
encountering specific problems, suggestions and some transformations
are provided to overcome such problems. An example is included, and
used to apply all the illustrated theory using RStudio software. The
R-code and the results are shown in complete details.
Project (Spring 2017-2018): Bayesian Inference: One-parameter Models
Students: Israa F.M. Alhamarna
Ragad W.A. Albarghash
There are two main opposing schools of statistical reasoning, frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong impulse that is starting to change the situation. The basic notions about these two approaches to inference are presented and the corresponding terminology is introduced.
Project II(Spring 2017-2018): Bayesian Inference: Multi-parameter Models
Student: Maitha khalid AlAli
Two main methods of statistical inference can be found in the literature of statistics. The first one is known as the frequentist (or classical) approach. This approach has been studied in 1440-361 (Mathematical Statistics). The second method to inference, which will be the choice of this project, is called the Bayesian approach. This approach can be viewed as the modern statistics to inference and it differs from the classical one in that it specifies a probability distribution for the parameter(s) of interest. The goal of this project is to extend the one-parameter Bayesian approach to the Multi-parameter case. Examples and real life applications are also considered. Section 1 - Section 6 are done jointly with Israa Alhamarna and Ragad Albarghash.