課程大綱

課程資訊

課程名稱

迴歸分析
Regression Analysis

開課學期

103-1

授課對象

理學院數學研究所

授課教師

陳宏

課號

MATH7606

課程識別碼

221 U3940

班次

學分

全/半年

半年

必/選修

選修

上課時間

星期一7,8(14:20~16:20)星期二7(14:20~15:10)

上課地點

天數305天數305

備註

總人數上限：20人
外系人數限制：15人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1031MATH7606_reg

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課程概述

Multiple regression and analysis of variance are the most often used statistical tools in applications.
0. Review of Basics.
1. Motivating Examples and Model Construction.
2. Simple and Multiple Linear Regressions.
3. Problems and Remedies - normality, unequal variances, correlated errors, outliers and influential observations, and multicollinearity.
4. More Complicated Models.
5. Generalized Linear Model.
(http://www.springerlink.com/content/nujt764l16289558/fulltext.pdf)

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

每週五 15:30~17:30
每週二 16:30~17:30
每週一 14:00~15:00 備註：第一,二個為陳宏老師時間, 地點在天數465; 第三個為助教陳立榜時間,地點在天數538

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.
Ramsey, F. L. and Schafer, D. W. (2002). The Statistical Sleuth – A Course in
Methods of Data Analysis. Second Edition. Duxbury.
Sheather, S. (2005) A Modern Approach to Regression with R. 本校電子書

指定閱讀

Textbook: Applied Linear Regression, 3rd Ed. 電子書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 December 9, 2013 Sanford Weisberg http://z.umn.edu/alrprimer.

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Homework	20%
2.	Quiz	20%	Three Quizzes
3.	Midterm	30%
4.	Final	30%

課程進度

週次	日期	單元主題
第1週	09/15	Wednesday: Review needed language and tool of probability and statistics and give an introduction of regression analysis
第2週	09/22	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	09/29	Simple Linear Regression
第4週	10/06	Finish Simple Linear Regression and start on Multiple Linear Regression Multiple Regression
第5週	10/13	Multiple Linear Regression
第6週	10/20	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	10/27	Weights, Lack of Fit, and More
第8週	11/03	Polynomials and Factors;
第9週	11/10	Residuals, 期中考
第10週	11/17	Residuals; 彈性時間
第11週	11/24	Residuals
第12週	12/01	Regression Diagnostics: Residuals
第13週	12/08	Transformations; Variable Selection 停修申請截止
第14週	12/15	Variable Selection, Data can be download from www.itl.nist.gov/div898/handbook/pmd/ section6/pmd621.htm
第15週	12/22	Nonlinear Regression; Logistic Regression
第16週	12/29	Logistic Regression
第17週	01/05	Outliers and Influence; Review
第18週	01/12	期末考: January 12th (Tuesday)