MATH 5358: Regression analysis
Spring 2018
Table of Contents
Announcement
About this course
Welcome to the Regression Analysis course! This course introduces regression models, which relates an outcome to a set of predictors of interest. These models are the most important statistical technique that a data scientist needs to master.
You will learn the theory behind regression models and, through real-world examples, learn to fit, diagnose, and utilize regression models to examine the relationship between predictors and a continuous or discrete outcome, using the statistical software R. You will learn modern approaches on model selection and novel uses of regression models.
Before beginning the class make sure that you have the following:
- A basic understanding of linear algebra and calculus.
- A basic understanding of statistical inference.
- Basic knowledge of the R programming language. This is not required, but a big plus.
Course Syllabus
Course Schedule
The instructor reserves the right to adjust this schedule in any way that serves the educational needs of the students enrolled in this course.
Week | Date | Topics | Reading | Notes |
---|---|---|---|---|
Week1 | 1/17 | Introduction | MAR 1.1-3 | Lecture 1 |
Week2 | 1/22 | R tutorial | Lab 1, Lab 2 | |
Week2 | 1/24 | R markdown | Lab 3 | |
Week3 | 1/29 | Simple linear regression | MAR 2.1 | Lecture 2, HW 1 - Due |
Week3 | 1/31 | Inference for regression, Analysis of variance | MAR 2.2-5, 7 | Lab 4, Lab 5 |
Week4 | 2/5 | Dummy variable regression | MAR 2.6 | Lecture 3, HW 2 - Due 2/12 |
Week4 | 2/7 | Regression diagnostics | MAR 3.1-3.2.5 | Lab 6 |
Week5 | 2/12 | Transformation of variables | MAR 3.2.6-3.3.3 | HW 3 - Due 2/19 |
Week5 | 2/14 | Transformation of variables, weighted least squares | Lecture 4 | |
Week6 | 2/19 | Weighted least squares | MAR 4 | Lab 7, HW 4 - Due 2/26 |
Week6 | 2/21 | Weighted least squares / Polynomial regression | MAR 5.1 | Lecture 5 |
Week7 | 2/26 | Multiple linear regression | MAR 5.2 | Lab 8 |
Week7 | 2/28 | Midterm 1 | Midterm I | |
Week8 | 3/5 | Multiple linear regression | MAR 5.2 | HW 5 - Due 3/19 |
Week8 | 3/7 | Analysis of covariance | MAR 5.3 | |
Week9 | 3/12 | Spring vacation | ||
Week9 | 3/14 | Spring vacation | ||
Week10 | 3/19 | Regression diagnostics for multiple regression | MAR 6.1 | Lecture 6, HW 6 - Due 3/26 |
Week10 | 3/21 | Transformations | MAR 6.2-6 | Lab 9 |
Week11 | 3/26 | Multicollinearity | HW 7 - Due 4/2 | |
Week11 | 3/28 | Variable selection | MAR 7.1-2 | Lecture 7 |
Week12 | 4/2 | Assessing the predictive ability of regression models | MAR 7.3-4 | Lab 10 |
Week12 | 4/4 | Midterm 2 | Midterm II (SOLN) | |
Week13 | 4/9 | Logistic function and odds | MAR 8.1 | HW 8 - Due 4/16 |
Week13 | 4/11 | Logistic regression with a single predictor | MAR 8.2 | Lecture 8 |
Week14 | 4/16 | Binary logistic regression | HW 9 - Due 4/23 | |
Week14 | 4/18 | Binary logistic regression | Lab 11 | |
Week15 | 4/23 | Correlated error | MAR 9.1 | Lecture 9, Final HW - Due 5/4 |
Week15 | 4/25 | Autocorrelation | MAR 9.2 | Lab 12 |
Week16 | 4/30 | Presenatation - Fianl project | ||
Week16 | 5/2 | Presenatation - Fianl project | Final project |
Resources
R software
- Microsoft R Open
- Instructions
OS X: installing compilers for R ≥ 3.4.0
- Install gfortran-6.1 for OS X El Capitan (10.11)
- Install Homebrew
# Paste that at a Terminal prompt. /usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"
- Install clang4 and openssl
brew install llvm openssl cd /usr/local/clang4 sudo ln -s ../Cellar/llvm/5.0.1/bin
- R Studio
- R Markdown
- Cookbook for R graphs
- Introduction to R
- Rcpp for Seamless R and C++ Integration