課程資訊

Regression Analysis

104-1

MATH7606

221 U3940

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1041MATH7606_regress

Multiple regression and analysis of variance are the most often used statistical tools in applications.
1. Motivating Examples and Model Construction, Review of Basics such as MLE, Law of Large Numbers,
and Central Limit Theorem.
Simple and Multiple Linear Regressions: Estimation
2. Inference for Gaussian Linear Model.
3. Problems and Remedies - normality, unequal variances, correlated errors, outliers and
influential observations, and multicollinearity.
4. Generalized Linear Model.
5. More Complicated Models- nonlinear regression model, nonparametric and semiparametric
regression models.
6. Sparse high-dimensional regression and regularization

1. Give you some experience with basic regression techniques that you can apply in your research.
2. Expose you to situations where regression analysis is useful (and perhaps not useful).
3. Give you enough understanding that you can evaluate regression in papers your read. (it requires you to know how regression works to be able to evaluate a regression solution in a particular research situation.)

calculus, one semester of linear algebra (matrix theory), some programming experience, one semester introductory probability, and one semester mathematical statistics (Statistical Concepts: Random variables, normal and t distributions, mean and variance of a linear combination of random variables, hypothesis-testing including the concepts of significance level and p-value, t-tests and confidence intervals, sampling error, and the standard error of the mean.)
Depth of understanding comes from a systematic use of tools from linear algebra such assubspaces, projections, and matrix decompositions that allows an astonishing variety of applications to be comprehended via a small number of geometrical pictures and algebraic manipulations. Practical understanding comes from broad experience with and probing of the methods on particular data sets through use of a flexible computer data analysis language, which for us, will be R.

Office Hours

Rao, C. R. and Toutenburg, H. (1999). Linear Models: Least Squares and
Alternatives. Second Edition. Springer.
Grob, J. (2003). Linear Regression. Springer.
Sheather, S. (2005) A Modern Approach to Regression with R. 本校電子書

Textbook 1: An Introduction to Statistical Learning with Applications in R, 可由作者的網頁 http://www-bcf.usc.edu/~gareth/ISL/, 免費取得本書電子檔 (Chapter 2.1-2.2, Lab 2.3, Chapter 3.3-3.4, Lab 3.6, Chapter 4.3, Lab 4.6.2, Chapter 6.1-6.2, Lab 6.5-6.6, Chapter 7.1-7.6, Lab 7.8.1-7.8.2)
Textbook 2: Mathematical Statistics, Basic Ideas and Selected Topics Volume 1, Chapter 6.1 Inference for Gaussian Linear Models (p365-382)
http://faculties.sbu.ac.ir/~payandeh2/files/Books/Bickel,%20Mathematical%20Statistics,%20Basic%20Ideas%20and%20Selected%20Topics.pdf
Textbook 3: Applied Linear Regression, 3rd Ed. 電子書 Graphics and Residual Analysis http://onlinelibrary.wiley.com/book/10.1002/0471704091
 週次 日期 單元主題 第1週 9/14, 15 Monday: Review needed language and tool of probability and statistics and give an introduction of regression analysis (maximum likelihood estimate, method of least squares Tuesday 第2週 9/21, 22 Simple Linear Regression Tuesday: Finish up Chapter 1 and demo on setting up R-program to do linear regression, Finish the derivation of LS estimate and show that the estimator of $\beta_1$ is consistent. (Study A2.1~A2.3, A3.) Friday: Finish 2.3~2.6. 加退選截止 第3週 9/29 Monday: No class 中秋節 Tuesday: Chapter 6.1 Inference for Gaussian Linear Model, Bickel & Doksum Mathematical Statistics, Basic Ideas and Selected Topics Volume 1 (2nd edition, 2015) 第4週 10/5, 6 Tuesday: Chapter 6.1 Inference for Gaussian Linear Model, Bickel & Doksum Mathematical Statistics, Basic Ideas and Selected Topics Volume 1 (2nd edition, 2015) 第5週 10/12, 13 R project and Quiz 1 第6週 10/19, 20 Quiz 1: (Matrix representation, matrix derivative, constrained optimization, asymptotic analysis of linear combination of random variables, residual and scatter plot) Drawing Conclusions (in Regression Analysis) Emphasize on the last section on resampling method and measurement error in regressors 第7週 10/26, 27 Weights, Lack of Fit, and More 第8週 11/2, 3 Polynomials and Factors; 第10週 11/16, 17 期中考 (11/16, 15:30-17:50) Tuesday: brief introduction on the method of bootstrap 第11週 11/23, 24 Monday: regression in canonical form Tuesday: 自主學習 第12週 11/30, 12/01 Regression Diagnostics: Residuals 第13週 12/7, 8 Transformations; Variable Selection 停修申請截止日 12/11 第14週 12/14, 15 Variable Selection, Data can be download from www.itl.nist.gov/div898/handbook/pmd/ section6/pmd621.htm 第15週 12/21, 22 Nonlinear Regression; Logistic Regression 第16週 12/28, 29 Model Selection with Mallows Cp 第17週 1/4, 5 Quiz2 and Model Selection with Mallows Cp 授課結束 第18週 1/11, 12 期末考: January 11th (Monday)