## Table of Contents

1. Linear Regression

1.1 Introduction to simple linear regression (SLR)

1.2 SLR assumptions

1.3 Correlation and coefficient of determination

1.4 Interpreting SLR models

1.5 Confidence and prediction intervals for SLR models

1.6 Testing SLR parameters

2. Multiple Linear Regression

2.1 Introduction to multiple regression

2.2 Multiple regression assumptions and diagnostics

2.3 Coefficient of multiple determination

2.4 Multicollinearity

2.5 Interpreting multiple regression models

2.6 Confidence and prediction intervals for MLR models

2.7 Testing multiple regression parameters

2.8 Multiple regression example

3. Higher Order Regression

3.1 Interaction terms

3.2 Categorical predictor variables

3.3 Quadratic models

3.4 Complete second order models

3.5 Comparing nested models: F-test

3.6 Higher order models

4. Logistic Regression

4.1 Introduction to logistic regression (LR)

4.2 Estimating LR parameters

4.3 LR models with multiple predictors

4.4 LR assumptions and diagnostics

4.5 Testing LR parameters

4.6 Interpreting LR models

4.7 Comparing nested models: Likelihood ratio tests and AIC

4.8 Classification using LR models

5. Transformations

5.1 Logarithmic transformations

5.2 Ladder of powers

5.3 Box-Cox transformation

6. Stepwise Regression

6.1 Introduction to stepwise regression

6.2 Forward selection

6.3 Backward selection

6.4 Stepwise selection

7. Principal Component Analysis

7.1 Introduction to principal component analysis (PCA)

7.2 Calculating principal components for two variables

7.3 Extending PCA to more variables

7.4 Determining the number of components

7.5 Interpreting principal components

8. Time Series

8.1 What is a time series?

8.2 Time series patterns and stationarity

8.3 Moving average and exponential smoothing forecasting

8.4 Forecasting using regression

9. Monte Carlo Methods

9.1 What is a Monte Carlo simulation?

9.2 Building simulations

9.3 Optimization and forecasting

9.4 What-if analysis

9.5 Advanced simulations

10. Non-parametric Analysis

10.1 Parametric vs. nonparametric statistics

10.2 Resampling: Randomization and bootstrapping

10.3 Wilcoxon rank-sum test

10.4 Kruskal-Wallis test

10.5 Multiple tests

11. Appendix A: Distribution Tables

11.1 t-distribution table

11.2 z-distribution table

11.3 Chi-squared distribution table

12. Appendix B: CSV Files

12.1 Data sets

## What You’ll Find In This zyBook:

### More action with less text.

- An exceptionally student-focused introduction to regression analysis.
- Traditionally difficult topics are made easier using animations and learning questions.
- R coding environments are provided throughout to allow students to experiment.
- Commonly combined with “Applied Statistics with Data Analytics” with numerous configurations possible.

## The zyBooks Approach

### Less text doesn’t mean less learning.

This zyBook builds on the techniques introduced in linear regression and provides the tools needed to analyze the relationship between two or more variables. Ideal for students enrolled in a second applied statistics course, Applied Regression Analysis dives deeper into model selection and evaluation. The following questions are answered: Which variables should be included or removed to better predict the target variable? Are the conditions for a specific technique satisfied? Which transformations can be performed on the data when certain conditions are violated? Additional topics covered are time series, Monte-Carlo methods, bootstrapping and randomization, and non-parametric statistics.