Subject: STA 206
Title: Statistical Methods for Research I
Units: 4.0
School: College of Letters and Science LS
Department: Statistics STA
Effective Term: 2013 Fall Quarter
Learning Activities
- Lecture - 3.0 hours
- Discussion/Laboratory - 1.0 hours
Description
Focus on linear statistical models. Emphasis on concepts, method and data analysis; formal mathematics kept to minimum. Topics include simple and multiple linear regression, polynomial regression, diagnostics, model selection, factorial designs and analysis of covariance. Use of professional level software.
Prerequisites
Introductory statistics course; some knowledge of vectors and matrices.
Expanded Course Description
Summary of Course Content:
1. Simple linear regression: Data sets, model, estimation of parameters, estimation of variance, inference for regression coefficients, confidence intervals for the mean response, prediction intervals, coefficient of determination, general linear test, ANOVA decomposition of total sum of squares (4 lectures)
2. Diagnostics: residual plot, normal probability plots etc, Box-Cox transformation (1 lecture)
3. Vector-Matrix notations: Re-expression of the simple linear model and the associated methodologies in vector-matrix notations.(1 lecture)
4. Multiple regression: Data sets, model, parameter estimation, coefficient of determination, problems of multicollinearity, partial F-tests, partial coefficient of determination, polynomial regression, interaction models, coding of qualitative variables (6 lectures)
5. Diagnostics and Model building: All subsets regression, stepwise methods, models selection criteria such as Mallows’ Cp, AIC, BIC (4 lectures)
6. One-factor fixed effects ANOVA: Data sets, model, estimation of overall mean and factor effects, hypothesis testing and confidence intervals (including simultaneous confidence intervals), coding of factors and rewriting of one factor ANOVA model as a regression model (4 lectures)
7. Diagnostics: residual plot, normal probability plot, unequal variance, Box-Cox transformation (1 lecture)
8. Two factor fixed effects ANOVA (including the case with one observation per cell): Data sets, additive and interaction models, estimation and testing, coding of variables and modeling two-factor ANOVA by the regression method (3 lectures)
9. Analysis of covariance: Data sets, models, regression approach, inference (2 lectures)
Illustrative Reading:
1. A Second Course in Statistics: Regression Analysis: by Mendenhall, W. and Sincich, T. 2003, Prentice Hall.
2. Regression and ANOVA: An Integrated Approach Using SAS Software, by Muller, K. E. and Fetterman, B. A.
3. Applied Regression Analysis and other Multivariable Methods, by Kleinbaum, D,. Kupper, L. Nizam, A. and Muller, K. Thompson, Brooks-Cole.
4. Linear Models with R, by J. Faraway, Chapman and Hall / CRC 2009
Potential Course Overlap:
There is some overlap with materials taught in Statistics 106 and Statistics 108. However, Statistics 206 covers much more materials than each of these courses. It will be taught at a level that is more advanced mathematically and computationally. This course also has some overlap with Statistics 232AB. Since Statistics 232 series is a requirement for the Ph.D. students in Statistics, its coverage is far wider and deeper and this course is taught at a substantially higher level.