STAT 136: Introduction to Regression Analysis
Midyear 2024
COURSE SYLLABUS
Course Description
Linear regression model; model selection; regression diagnostics; use of dummy variables; remedial measures. Prereq: Stat 131, Stat 135. 3h. 3 u.
Course Objectives
The course shall equip the learners with the foundation necessary to perform linear regression analysis.
In this course, we specifically aim to:
 introduce the concept of regression, its limitations, interpretations, and uses.
discuss linear regression modeling as a methodology built upon the theories of statistical inference and matrix algebra
apply regression theory to reallife data, solve research questions, and distinguish between proper modeling practices and improper data mining.
The learners are also expected to apply the learnings in this course to higher Stat courses.
Course Outline
The course is mainly divided into 3 parts: (1) Preliminaries and Introduction, (2) Model Building, and (3) Diagnostic Checking. The following is the complete outline:
Chapter  Topics  Duration 


Review of Matrix Theory and Inference  1 

The Linear Model and Assumptions  12 

Least Squares and Other Estimation Procedures  1 

Fitted Values, Residuals, Sum of Squares, ANOVA, Properties of Estimators in OLS  34 

Inference about \(E(Y_i)\), predicting new observation \(Y_{h(new)}\), Assessment of predictability  1 

Full vs Reduced Models, General Linear Test, Partial Ftest, Sequential Ftest  1 

Allpossible regressions, automatic search procedures  1 

Categorical Independent Variables, Regime Switching  1 

Residual Plots  1 

Effects and Causes of Nonlinearity, Nonlinearity Test, Transforming Variables  1 

Effects and Causes of Nonnormality and Heteroskedasticity, Testing for Nonnormality and Heteroskedasticity, Remedial Measures  1 

Effects and Causes of Autocorrelation, Testing for Autocorrelation, Remedial Measures  1 

Causes of Multicollinearity, Testing for Multicollinearity, Remedial Measures  1 

Effects and Causes of Outliers and Influential Observations, Testing for Presence of Outliers and Influential Observations, Remedial Measures  1 
Book Guide
White boxes are used to highlight the objectives or to summarize a section.
Definition 0.1 Blue boxes are for definitions. These are for new concepts introduced in the class.
Theorem 0.1 Green boxes are for theorems. I may ask you to prove some of them either through ungraded exercises or board works.
Exercise 0.1 Yellow boxes are for exercises. These are part of your problem sets which will be graded.
Gray boxes are for notes, mostly related to the limitations of the course.
Click me!
Watch out for this clickable text. You may find here important remarks, examples, illustration, or hints.
# There are also R Code chunks in this book to visualize some concepts, and of course for application.
Make sure that the following packages are installed in your devices:
# for reading files
install.packages("readr")
# for plots and data manipulation
install.packages("tidyverse")
# for datasets and some tests
install.packages("car")
# for variable selection, diagnostic plots
install.packages("olsrr")
# for normality test
install.packages("nortest")
Needed files can be accessed through this link. You can only access this using a UP Email.
References
 Neter, J., Kutner, M. H., Nachtsheim, C. J., and Wasserman, W. (1996). Applied Linear Regression Models (4th ed.). Irwin, Chicago
 Chatterjee, S., Hadi, A., Price, B. (2000). Regression Analysis by Example (5th ed.). Wiley Interscience Publications, John Wiley and Sons, Inc.
 Cook, RD (1998). Regression Graphics. Wiley Interscience Publications, John Wiley and Sons, Inc.
 Draper, N, Smith, H (1998). Applied Regression Analysis (3rd ed.). Wiley Series in Probability and Statistics, John Wiley and Sons, Inc.
 Searle, S (1982). Matrix Algebra Useful for Statistics. Wiley Series in Probability and Mathematical Statistics, John Wiley and Sons, Inc.
This book is being maintained by Instructor Siegfred Roi L. Codia of UP School of Statistics.
Special thanks to Asst. Prof. Joemari Olea and Asst. Prof. Angela Nalica of UP School of Statistics for the outline and content of this course material.