Applied Linear Models I
- The course gives students an important foundation to develop and conduct their own research as well as to evaluate research of others.
- To know the theoretical foundation of applied linear modeling, starting with the univariate models
- To know modern extensions to applied regression, including working with “problem data”
- To know the basic principles behind working with all types of data for building regression models
- Be able to explore the advantages and disadvantages of various linear modeling instruments, and demonstrate how they relate to other methods of analysis
- Be able to work with major linear modeling programs, especially SAS, so that they can use them and interpret their output.
- Be able to develop and/or foster critical reviewing skills of published empirical research using applied statistical methods
- Be able to criticize constructively and determine existing issues with applied linear models in published work
- Have an understanding of the basic principles of linear models and lay the foundation for future learning in the area
- Have the skill to meaningfully develop an appropriate model for the research question
- Have the skill to work with statistical software, required to analyze the data
- Introduction to the Framework of Regression AnalysisThe first session will introduce the main concepts of preparation for regression analysis. We will discuss data types and levels, sampling techniques, variable types and transformations, and graphical representation of the data.
- Simple Linear Regression IThe session sets up the framework for fitting the linear curve. We will discuss both the algebraic and the geometric meaning of linear regression.
- Simple Linear Regression IIThe session provides the theoretical basis and the derivation of the Ordinary Least Squares (OLS) and the Goodness of Fit measures (Pearson’s r and R2). Practical part will include running and interpreting the regression output in R.
- Statistical Inference in a Simple Linear Regression IThis sessions builds the understanding of model assumptions and properties of the OLS esti-mates, as well as running and interpreting the Analysis of Variance output.
- Statistical Inference in a Simple Linear Regression IIThis session covers the foundation of the hypothesis testing and building confidence intervals for regression coefficients. Also, we will discuss the derivation of confidence intervals for predictors (for a given criterion) and a criterion (for a given predictor).
- Statistical Inference in a Simple Linear Regression IIThis session will continue the derivation of confidence intervals, provide an understanding of prediction intervals, and discuss regression through the origin.
- Model diagnostics in a Simple Linear RegressionThis session will focus on the residual analysis, including evaluation of regression assumptions of homoscedasticity and normality. We will also look at graphical tools to evaluate the residuals.
- Multivariate regression IThis session will extend the basics of univariate regression to two independent variables, includ-ing specifics of OLS estimates, goodness of fit, and inference.
- Multivariate regression IIThis session will generalize regression to the multivariate case, with OLS estimates, Goodness of Fit, interpretation of adjusted R2, inference, ANOVA, analysis of residuals.
- Model Building IThis session will focus on variable selection and information measures (Akaike, Schwarz, ad-justed R2). It will also introduce the use of machine learning for variable selection.
- Model Building IIThis session will continue with building appropriate models, with a special focus on influential observations and multicollinearity.
- Model Building IIIThis session introduces variable transformation and models with categorical predictors. Special attention will be paid to coding categorical predictors in SAS.
- Quizzes (Best 9 of 10, Varied points)
- Final In-Class or Take-home exam (at the discretion of the instructor)
- Homework Assignments (5 x Varied points)
- In-Class Labs (9-10 x Varied points)
- Interim assessment (2 module)0.5 * Final In-Class or Take-home exam (at the discretion of the instructor) + 0.2 * Homework Assignments (5 x Varied points) + 0.2 * In-Class Labs (9-10 x Varied points) + 0.1 * Quizzes (Best 9 of 10, Varied points)
- Montgomery, D. C., Vining, G. G., & Peck, E. A. (2012). Introduction to Linear Regression Analysis (Vol. 5th ed). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1021709
- Weisberg, S. (2005). Applied Linear Regression (Vol. 3rd ed). Hoboken, N.J.: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=128514
- Yan, X., Su, X., & World Scientific (Firm). (2009). Linear Regression Analysis: Theory And Computing. Singapore: World Scientific. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=305216
- Elliott, A. C., & Woodward, W. A. (2016). SAS Essentials : Mastering SAS for Data Analytics (Vol. Second edition). Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1051725
- Hocking, R. R. (2013). Methods and Applications of Linear Models : Regression and the Analysis of Variance (Vol. Third edition). Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=603362