課程資訊
課程名稱
迴歸分析
Regression Analysis 
開課學期
106-1 
授課對象
理學院  應用數學科學研究所  
授課教師
陳宏 
課號
MATH7606 
課程識別碼
221 U3940 
班次
 
學分
3.0 
全/半年
半年 
必/選修
必修 
上課時間
星期一8,9(15:30~17:20)星期二8(15:30~16:20) 
上課地點
天數304天數304 
備註
總人數上限:40人
外系人數限制:15人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH7606_ 
課程簡介影片
 
核心能力關聯
核心能力與課程規劃關聯圖
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

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.
(Two chapters from http://www.springerlink.com/content/nujt764l16289558/fulltext.pdf)
6. Sparse high-dimensional regression and regularization 

課程目標
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.)
 
課程要求
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.
 
預期每週課後學習時數
 
Office Hours
每週二 13:30~14:30
每週一 13:30~14:30 備註: 第一,二個為陳宏老師時間, 地點在天數465 
參考書目
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




 
指定閱讀
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
Sanford Weisberg, published by Wiley/Interscience in 2005 (ISBN 0-471-66379-4).
Computing Primer for Applied Linear Regression, 4th Edition, Using R
Version of October 27, 2014 http://users.stat.umn.edu/~sandy/alr4ed/links/alrprimer.pdf. 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Final 
30% 
 
2. 
Midterm 
30% 
 
3. 
Quiz 
20% 
Three Quizzes 
4. 
Homework  
20% 
 
 
課程進度
週次
日期
單元主題
第1週
9/11, 12  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
9/18, 19  Monday and Tuesday: Classical Linear Regression based on BickelDoksumV1p365-382
加退選截止 
第3週
9/25, 26, 30  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
10/2, 3  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
9/30  10/8, 9 調整放假, 9/30 調整上課 
第6週
10/16, 17  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
10/23, 24  Weights, Lack of Fit, and More 
第8週
10/30, 31  Polynomials and Factors;
 
第9週
11/6, 7  期中考 (11/06, 15:30-17:20) Mallows Cp (11/07, model selection) 
第10週
11/13, 14  自主學習周
Tuesday: brief introduction on the method of bootstrap 
第11週
11/20, 21  Monday: regression in canonical form Tuesday: 自主學習? 
第12週
11/27, 28  Regression Diagnostics: Residuals  
第13週
12/04, 05  Transformations; Variable Selection
停修申請截止日 12/11 
第14週
12/11, 12  Variable Selection, Data can be download from www.itl.nist.gov/div898/handbook/pmd/
section6/pmd621.htm 
第15週
12/18, 19  Nonlinear Regression; Logistic Regression 
第16週
12/25, 26  Model Selection with Mallows Cp 
第17週
1/02  Quiz2 and Model Selection with Mallows Cp 授課結束 
第18週
1/08  期末考: January 8th (Monday)