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MAT 3375
This course covers linear statistical inference, hypothesis testing, and estimation, with applications to simple, multiple, and non-linear regression analysis. The course introduces students to the methods and approaches to linear and non-linear regression, with the aim of allowing them to apply these techniques to concrete problem-solving in both simple and multiple regression scenarios.
✔ (Summary) What You Will Learn:
- Simple Linear Regression: Focusing on the concept of linear regression with one predictor variable, this topic delves into parameter estimation, hypothesis testing, and result interpretation. The aim is to model the relationship between a response variable and a single predictor variable.
- Multiple Linear Regression: Expanding on simple linear regression, this topic incorporates multiple predictor variables, allowing for more intricate relationships between variables to be modeled and analyzed.
- Model Adequacy Checking: Centered around methods for assessing the validity of a regression model, this topic covers residual analysis and tests for violations of regression assumptions, such as linearity, normality, and homoscedasticity.
- Transformations & Weighting to Correct Model Inadequacies: Addressing issues with model fit, this topic explores techniques for dealing with non-linearity or heteroscedasticity, such as transforming the response variable or applying weights to observations to improve model fit and meet regression assumptions.
- Indicator Variables: Introducing the use of indicator (dummy) variables to represent categorical predictors in regression models, this topic teaches how to incorporate categorical variables into regression models and interpret the results.
- Multicollinearity: Discussing the issue of multicollinearity, which arises when predictor variables are highly correlated, this topic covers the impact of multicollinearity on regression models and methods for detecting and addressing it.
- Model Selection and Validation: Covering techniques for selecting the best regression model among a set of candidate models and methods for validating the chosen model, this topic includes model selection criteria, such as adjusted R-squared and Akaike information criterion (AIC), and cross-validation techniques.
- Generalized Linear Models: Introducing generalized linear models, which extend linear regression to accommodate non-normal response variables and non-linear relationships between variables, this topic covers different types of generalized linear models, such as logistic regression and Poisson regression, and how to fit and interpret these models.
Learning Outcomes:
Throughout the course, students will gain an understanding of various regression models, including simple linear regression, multiple linear regression, and non-linear regression. They will also learn about estimation and hypothesis testing, which are essential components of statistical inference. This course equips students with essential skills and knowledge in regression analysis, preparing them for various roles in the fields of statistics, data analysis, and research.
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