課程資訊

Regression Analysis

103-1

MATH7606

221 U3940

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1031MATH7606_reg

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.

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.
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

Textbook: Applied Linear Regression, 3rd Ed. 電子書http://onlinelibrary.wiley.com/book/10.1002/0471704091
 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)