# 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 real-life 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
1. Preliminaries
Review of Matrix Theory and Inference 1
1. Introduction to Regression and Linear Models
The Linear Model and Assumptions 1-2
1. Estimation Procedures
Least Squares and Other Estimation Procedures 1
1. Least Squares Theory and ANOVA
Fitted Values, Residuals, Sum of Squares, ANOVA, Properties of Estimators in OLS 3-4
1. Inference about the Mean Response and Prediction of New Observations
Inference about $$E(Y_i)$$, predicting new observation $$Y_{h(new)}$$, Assessment of predictability 1
1. Model Evaluation in Multiple Linear Regression
Full vs Reduced Models, General Linear Test, Partial F-test, Sequential F-test 1
1. Variable Selection Procedures
All-possible regressions, automatic search procedures 1
1. Dummy Variables
Categorical Independent Variables, Regime Switching 1
1. Overview of Diagnostic Checking
Residual Plots 1
1. Linearity and Transformations
Effects and Causes of Nonlinearity, Nonlinearity Test, Transforming Variables 1
1. Non-normality and Heteroskedasticity
Effects and Causes of Non-normality and Heteroskedasticity, Testing for Non-normality and Heteroskedasticity, Remedial Measures 1
1. Autocorrelation
Effects and Causes of Autocorrelation, Testing for Autocorrelation, Remedial Measures 1
1. Multicollinearity
Causes of Multicollinearity, Testing for Multicollinearity, Remedial Measures 1
1. On Outliers and Influential Observations
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

# 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.