## 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

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

13. Appendix C: Additional Material

13.1 What is statistics?

13.2 What is data?

13.3 What is data visualization?

13.4 Python for data visualization

13.5 Data frames

13.6 Scatter plots

13.7 Box plots

13.8 Histograms

13.9 Normal distribution

13.10 Student’s t-Distribution

13.11 F-distribution

13.12 Chi-square distribution

13.13 Confidence intervals

13.14 Confidence intervals for population means

13.15 Hypothesis testing

13.16 Hypothesis test for a population mean

13.17 Hypothesis test for the difference between two population means

13.18 Chi-square tests for categorical variables

13.19 One-way analysis of variance (one-way ANOVA)

## 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.
- Python 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.

## Senior Contributors

**Joel Berrier**

*Assistant Professor, Dept. of Physics and Astronomy, Univ. of Nebraska, Kearny, Ph.D. Physics and Astronomy, UC Irvine*

**Chris Chan**

*Content lead: Mathematics, zyBooks, M.A. Mathematics, San Francisco State Univ.*

**Iain Pardoe**

*Mathematics and Statistics Instructor, Thompson Rivers Univ., Pennsylvania State Univ., and Statistics.com, PhD Statistics, Univ. of Minnesota*

**Rodney X. Sturdivant**

*Professor, Dept. of Mathematics and Physics, Azusa Pacific Univ., Ph.D. Biostatistics, U Mass Amherst*

**Krista Watts**

*Assistant Professor, Director—Center for Data Analysis and Statistics, United States Military Academy, West Point, Ph.D. Biostatistics, Harvard*