Linear Regression Models

MATH27711 Linear Regression Models 10 Semester 1 Undergraduate Level 2 Saralees Nadarajah Unit coordinator School of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 In many areas of science, technology and medicine, researchers are often interested in two objectives: one is to explore the relationship between one observable random response and a number of explanatory variables; the other is to analyze the variability of the responses. Many statistical techniques investigate these objectives through the use of linear regression models. This course presents the theory and practice of these models.  Syllabus:1.Basic theory: multivariate normal and normal-related distributions, quadratic form. 2. Simple linear regression least squares method, analysis of variance, coefficient of determination, hypothesis tests and confidence intervals for regression parameters, prediction. 3. Multiple linear regression: least squares method, analysis of variance, coefficient of determination, reduced vs full models, hypothesis tests and confidence intervals for regression parameters, prediction. 4. One-way classification models: one-way ANOVA, analysis of treatment effects, contrasts. 5. Two-way classification models: interactions, two-way ANOVA for balanced data structures, analysis of treatment effects, contrasts. 6. Universal approach to linear modelling: dummy variables, ‘multiple linear regression’ representation of one-way and two-way (unbalanced) models, ANCOVA models, and concomitant variables. 7. Regression diagnostics: leverage, residual plot, normal probability plot, outlier, studentized residual, influential observation, Cook’s distance. The particular aims are to enable the students to: 1. Understand linear regression model with one or multiple independent variables.  2. Understand general linear model with continuous independent variables.  3. Understand classification models for one and two factors. 4. Understand ANCOVA models for one factor and multiple continuous independent variables. <ul> <li>formulate, estimate and use regression linear models that are suitable for relevant statistical studies</li> <li>formulate statistical hypotheses in terms of the model parameters and test such hypotheses</li> <li>obtain confidence intervals for linear combinations of the model parameters</li> <li>obtain prediction intervals for linear combinations of future responses</li> <li>identify the impact of outliers on regression line</li> <li>use R to implement methods covered in the course</li></ul> Teaching is composed of two hours of lectures per week and one tutorial class per fortnight. And one Examples class in the week there is no tutorial.  Some lecture time will be delivered through pre-recorded videos posted online. Teaching materials will be uploaded to Blackboard for reference and review. 0 Other 20% 1 Written exam 80% Written Exam - 80% One mid-term online timed Blackboard test - 20%   Generic feedback will be provided after marks are released MATH11022 Linear Algebra Pre-Requisite Compulsory MATH11711 Probability I Pre-Requisite Compulsory MATH11712 Statistics I Pre-Requisite Compulsory N Applied regression analysis    Draper, Norman Richard, author.    John Wiley & Sons, Inc.    1998    ISBN: 0471170828 Introduction to linear regression analysis    Montgomery, Douglas C.,    John Wiley & Sons Ltd    2012    ISBN: 9781119180173 Applied linear regression    Weisberg, Sanford, 1947-, author.    Wiley    2014    ISBN: 9781118789551 Lectures 22 Practical classes & workshops 6 Tutorials 6 0 66