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課程名稱 |
迴歸分析
Regression Analysis |
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開課學期 |
104-1 |
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授課對象 |
理學院 應用數學科學研究所 |
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授課教師 |
陳 宏 |
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課號 |
MATH7606 |
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課程識別碼 |
221 U3940 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期一8,9(15:30~17:20)星期二8(15:30~16:20) |
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上課地點 |
天數305天數305 |
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備註 |
總人數上限：20人
外系人數限制：15人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1041MATH7606_regress |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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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 |
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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.)
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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.
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預期每週課後學習時數 |
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Office Hours |
每週一 14:00~15:00
每週二 16:30~17:30 備註： 第一,二個為陳宏老師時間, 地點在天數465 |
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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
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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 December 9, 2013 Sanford Weisberg http://z.umn.edu/alrprimer. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
20% |
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2. |
Quiz |
20% |
Three Quizzes |
3. |
Midterm |
30% |
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4. |
Final |
30% |
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週次 |
日期 |
單元主題 |
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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 |
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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 |
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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) |
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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)
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第5週 |
10/12, 13 |
R project and Quiz 1 |
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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 |
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第7週 |
10/26, 27 |
Weights, Lack of Fit, and More |
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第8週 |
11/2, 3 |
Polynomials and Factors;
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第10週 |
11/16, 17 |
期中考 (11/16, 15:30-17:50)
Tuesday: brief introduction on the method of bootstrap |
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第11週 |
11/23, 24 |
Monday: regression in canonical form Tuesday: 自主學習 |
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第12週 |
11/30, 12/01 |
Regression Diagnostics: Residuals |
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第13週 |
12/7, 8 |
Transformations; Variable Selection
停修申請截止日 12/11 |
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第14週 |
12/14, 15 |
Variable Selection, Data can be download from www.itl.nist.gov/div898/handbook/pmd/
section6/pmd621.htm |
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第15週 |
12/21, 22 |
Nonlinear Regression; Logistic Regression |
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第16週 |
12/28, 29 |
Model Selection with Mallows Cp |
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第17週 |
1/4, 5 |
Quiz2 and Model Selection with Mallows Cp 授課結束 |
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第18週 |
1/11, 12 |
期末考: January 11th (Monday) |
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