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
13. Appendix C: Additional Material
13.1 What is statistics?
13.2 What is data?
13.3 What is data visualization?
13.4 R 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.
- 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.
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
