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1.1 Bivariate Relationships 1.2 Probabilistic Models 1.3 Estimation of the Line 1.4 Properties of the Least Squares Estimators 1.5 Estimation of the Variance
2.1 The Normal Errors Model 2.2 Inferences for the Slope 2.3 Inferences for the Intercept 2.4 Correlation and Coefficient of Determination 2.5 Estimating the Mean Response 2.6 Predicting the Response
3.1 Residual Diagnostics 3.2 The Linearity Assumption 3.3 Homogeneity of Variance 3.4 Checking for Outliers 3.5 Correlated Error Terms 3.6 Normality of the Residuals
4.1 More Than One Predictor Variable 4.2 Estimating the Multiple Regression Model 4.3 A Primer on Matrices 4.4 The Regression Model in Matrix Terms 4.5 Least Squares and Inferences Using Matrices 4.6 ANOVA and Adjusted Coefficient of Determination 4.7 Estimation and Prediction of the Response
5.1 Multicollinearity and Its Effects 5.2 Adding a Predictor Variable 5.3 Outliers and Influential Cases 5.4 Residual Diagnostics 5.5 Remedial Measures
6.1 Indicator Variables 6.2 Interaction Between Predictors
7.1 Model Selection Criteria 7.2 Best Subsets Procedure 7.3 Stepwise Regression Procedures 7.4 Lasso 7.5 Model Validation
8.1 Logistic Regression 8.2 Multinomial Logistic Regression 8.3 Ordinal Regression 8.4 Poisson Regression
Introduction to Regression Analysis
with Examples in R

This is the course material for STA 3386 taught at Baylor University by Joshua Patrick Ph.D.

The reader is assumed to have already taken an Introductory Statistics course. Throughout these notes, matrices are used for ease in notation. Whenever not too cumbersome, non-matrix versions of equations are also given.

Examples are given using the stastical programming language R 3.5.3. Readers that are not too familiar with R should start by visiting any of the number of intro to R pages such as Introduction to R DataCamp or R-tutor.com. Note that some examples utilize the functions in the tidyverse packages.

The menu at the top left can be used to navigate chapters and sections.

There are some underlined blank spaces in the notes. These are used during in-class lectures. By clicking on the underlined blank space, the word will appear in red. In the left menu, all the blanks can be filled in by clicking on "Fill in Blanks".

Normal text that is undelined provides a pop-up of a referenced Figure or of text when the mouse hovers over the underlined word. Blue text that are underlined is a link that opens in a new tab when clicked.







Updates:
2019-12-02 Chapter 8 added
2019-11-21 Chapter 7 added
2019-11-01 Chapter 6 added
2019-10-15 Chapter 5 added
2019-10-08 Chapter 4 added
2019-09-16 Chapter 3 added
2019-08-28 Corrected the mean for model (2.1)
2019-08-27 Chapter 2 added
2019-08-22 Fixed issue with latex equations not rendering
2019-08-14 Fixed plots to scale to smaller screen sizes; Fixed toggle to fill in all blanks
2019-08-11 Fixed side menu
2019-08-08 Launch