Modern Regression Analysis in R

In this module, we introduce the basic conceptual framework for statistical modeling in general, and for linear regression models in particular. Topics include frameworks of statistical modeling, concept validity, linear regression models, matrix representation, and model interpretation.

In this module, we learn how to fit linear regression models with least squares. We study the properties of least squares and describe goodness of fit metrics for linear regression models. Topics include least squares estimation, linear algebra applications, and regression modeling in R.

In this module, we study the uses of linear regression modeling for justifying inferences from samples to populations. Topics include sampling distributions, t-tests, F-tests, and confidence intervals in the regression context.

In this module, we identify how models can predict future values and construct interval estimates. We explore the relationship between statistical modeling and causal explanations, including point estimates, interval estimates, and causality concepts.

In this module, we learn how to diagnose issues with the fit of a linear regression model. We use formal tests and visualizations to decide whether a linear model is appropriate for the data, including analysis of linearity, independence, variance, and normality assumptions.

In this module, we study methods for model selection and improvement. Topics include forward selection, backward selection, criterion-based methods, and the problem of multicollinearity. We explore various model selection techniques and their implementation in R.