Probability and Statistics for Economics and Business
An Introduction Using R
by Abrevaya
| ISBN: 9780262553360 | Copyright 2025
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Designed for an introductory course in probability and statistics for economics and business undergraduates, this comprehensive textbook introduces students to the R statistical programming language. While covering the standard topics found in traditional textbooks, Jason Abrevaya takes a modern approach that directly integrates R, highlights the use of simulation methods, and provides a general treatment of statistical inference for asymptotically normal estimators. Coverage emphasizes concepts that are useful to economists and data analysts, including general statistical-inference results that apply well beyond averages and variances. The book offers a higher level of mathematical rigor than traditional business statistics textbooks to prepare students for future coursework and for a professional climate where employers increasingly emphasize competence in data science and statistics.
- Introduces students to the R statistical programming language
- Uses real-world examples and datasets related to economics and business
- Provides extensive coverage of simulation methods
- Focuses on large-sample (asymptotic) results
- Is classroom tested at Emory University, the University of Texas at Austin, Princeton University, and elsewhere
- Suits undergraduate and graduate students in business, economics, data science, and statistics with knowledge of calculus
- Offers companion website and extensive instructor resources
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| Contents (pg. vii) | |
| Preface (pg. xi) | |
| Acknowledgments (pg. xix) | |
| 1. The Basics of R (pg. 1) | |
| 1.1. Installing R (pg. 1) | |
| 1.2. Arithmetic Operations and Mathematical Functions (pg. 2) | |
| 1.3. Variables and Data Types (pg. 5) | |
| 1.4. Vectors (pg. 10) | |
| 1.5. Output (pg. 20) | |
| 1.6. Programming (pg. 20) | |
| 1.7. Writing Functions (pg. 24) | |
| 1.8. Data Frames and File Input (pg. 26) | |
| 1.9. Missing Values (pg. 33) | |
| 1.10. R Packages (pg. 34) | |
| Notes (pg. 35) | |
| Exercises (pg. 36) | |
| 2. Introduction to Probability Theory (pg. 41) | |
| 2.1. Experiments and Sample Spaces (pg. 43) | |
| 2.2. Events (pg. 47) | |
| 2.3. What Is a Probability (pg. 51) | |
| 2.4. Properties of Probabilities (pg. 57) | |
| Notes (pg. 62) | |
| Exercises (pg. 62) | |
| 3. Conditional Probabilities and Independence (pg. 67) | |
| 3.1. Definition and Properties of Conditional Probabilities (pg. 67) | |
| 3.2. Multiplication Rule and Bayes’ Theorem (pg. 69) | |
| 3.3. Probability Tables (pg. 73) | |
| 3.4. Independence (pg. 76) | |
| 3.5. Examples with an Infinite Number of Outcomes (pg. 81) | |
| Exercises (pg. 84) | |
| 4. Combinatorics (Counting Methods) (pg. 91) | |
| 4.1. Product Rule and Sum Rule (pg. 91) | |
| 4.2. Permutations and Combinations (pg. 92) | |
| 4.3. Probabilities for Equally Likely Choices (pg. 96) | |
| Exercises (pg. 99) | |
| 5. Economic Data and Sampling (pg. 105) | |
| 5.1. Types of Data (pg. 105) | |
| 5.2. Types of Variables (pg. 107) | |
| 5.3. The Population and Sampling (pg. 111) | |
| Note (pg. 114) | |
| Exercises (pg. 114) | |
| 6. Descriptive Statistics and Visuals: Univariate Data (pg. 117) | |
| 6.1. Data Set Examples (pg. 117) | |
| 6.2. Categorical Data: Sample Proportions and Bar Charts (pg. 121) | |
| 6.3. Numerical Data: Histograms (pg. 124) | |
| 6.4. Numerical Data: Measures of Location (pg. 129) | |
| 6.5. Numerical Data: Measures of Dispersion (pg. 137) | |
| 6.6. Modal Outcomes (pg. 147) | |
| 6.7. Linear Transformations of Univariate Data (pg. 149) | |
| 6.8. Time-Series Plots (pg. 156) | |
| Notes (pg. 159) | |
| Exercises (pg. 160) | |
| 7. Descriptive Statistics and Visuals: Bivariate Data (pg. 165) | |
| 7.1. Categorical Variables (pg. 166) | |
| 7.2. Numerical Data: Scatter Plots, Sample Covariance, and Sample Correlation (pg. 173) | |
| 7.3. Correlation Is Not Causation (pg. 198) | |
| Notes (pg. 199) | |
| Exercises (pg. 200) | |
| 8. Discrete Random Variables (pg. 205) | |
| 8.1. Using Sample Proportions to Calculate Descriptive Statistics (pg. 205) | |
| 8.2. Random Variables and Discrete Random Variables (pg. 207) | |
| 8.3. Population-Descriptive Statistics (pg. 215) | |
| 8.4. Multiple Discrete Random Variables (pg. 220) | |
| 8.5. Linear Transformations (pg. 233) | |
| 8.6. Linear Combination of Multiple Random Variables (pg. 235) | |
| 8.7. Expected Values of Functions of Discrete Random Variables (pg. 240) | |
| Notes (pg. 241) | |
| Exercises (pg. 241) | |
| 9. Models of Discrete Random Variables (pg. 249) | |
| 9.1. Bernoulli Random Variable (pg. 249) | |
| 9.2. Binomial Random Variable (pg. 251) | |
| 9.3. Geometric Random Variable (pg. 257) | |
| 9.4. Negative Binomial Random Variable (pg. 260) | |
| 9.5. Poisson Random Variable (pg. 263) | |
| Note (pg. 267) | |
| Exercises (pg. 268) | |
| 10. Continuous Random Variables (pg. 275) | |
| 10.1. Continuous Random Variables Versus Discrete Random Variables (pg. 275) | |
| 10.2. Probability Density Function (pg. 277) | |
| 10.3. Cumulative Distribution Function (pg. 282) | |
| 10.4. Population-Descriptive Statistics (pg. 289) | |
| 10.5. Linear Transformations of One Random Variable (pg. 297) | |
| 10.6. Multiple Continuous Random Variables (pg. 299) | |
| 10.7. Linear Transformations and Combinations of Multiple Random Variables (pg. 311) | |
| 10.8. Expected Values of Functions of Continuous Random Variables (pg. 319) | |
| 10.9. Strictly Increasing Transformations of Random Variables (pg. 320) | |
| 10.10. Random Variables with Discrete and Continuous Outcomes (pg. 323) | |
| Notes (pg. 324) | |
| Exercises (pg. 324) | |
| 11. Models of Continuous Random Variables (pg. 333) | |
| 11.1. Normal Random Variable (pg. 333) | |
| 11.2. Log-Normal Random Variable (pg. 347) | |
| 11.3. Chi-Square Random Variable (pg. 351) | |
| 11.4. Exponential Random Variable (pg. 354) | |
| 11.5. Mixture of Normal Random Variables (pg. 358) | |
| Notes (pg. 360) | |
| Exercises (pg. 360) | |
| 12. Sampling Distributions: Exact (pg. 367) | |
| 12.1. Sampling Distribution of the Sample Mean (pg. 369) | |
| 12.2. Sampling Distribution of the Sample Variance (pg. 376) | |
| 12.3. Sampling Distribution of Other Statistics (pg. 383) | |
| Notes (pg. 386) | |
| Exercises (pg. 386) | |
| 13. Sampling Distributions: Asymptotic (pg. 391) | |
| 13.1. Asymptotic Distribution of the Sample Mean (pg. 391) | |
| 13.2. Asymptotic Distribution of the Sample Variance (pg. 401) | |
| 13.3. Asymptotic Distribution of Other Statistics (pg. 404) | |
| Notes (pg. 411) | |
| Exercises (pg. 412) | |
| 14. Estimation and Confidence Intervals (pg. 417) | |
| 14.1. Estimation and Properties of Estimators (pg. 417) | |
| 14.2. Finite-Sample Confidence Intervals: Population Mean of i.i.d. Normal Random Variables (pg. 422) | |
| 14.3. Asymptotic Confidence Intervals: Population Mean of i.i.d. Random Variables (pg. 432) | |
| 14.4. Asymptotic Confidence Intervals: Parameters with Asymptotically Normal Estimators (pg. 438) | |
| 14.5. Functions of Consistent Estimators (pg. 455) | |
| 14.6. Asymptotic Predictive Intervals for Continuous Random Variables (pg. 457) | |
| Notes (pg. 459) | |
| Exercises (pg. 459) | |
| 15. The Bootstrap (pg. 467) | |
| 15.1. Bootstrap Sampling (pg. 468) | |
| 15.2. Bootstrap Sampling Distribution (pg. 471) | |
| 15.3. Bootstrap Standard Errors and Bootstrap Confidence Intervals (pg. 473) | |
| Notes (pg. 482) | |
| Exercises (pg. 483) | |
| 16. Hypothesis Testing (pg. 487) | |
| 16.1. Finite-Sample Hypothesis Testing: Population Mean of i.i.d. Normal Random Variables (pg. 489) | |
| 16.2. Asymptotic Hypothesis Testing: Parameters with Asymptotically Normal Estimators (pg. 501) | |
| 16.3. Statistical Significance Versus Practical Significance (pg. 510) | |
| 16.4. Hypothesis Testing for Multiple Hypotheses: The Wald Test (pg. 512) | |
| Appendix: Details of the Wald test (pg. 519) | |
| Notes (pg. 525) | |
| Exercises (pg. 525) | |
| 17. Simple Linear Regression (pg. 531) | |
| 17.1. The Simple Linear Regression Model (pg. 531) | |
| 17.2. The Least-Squares Estimator (pg. 538) | |
| 17.3. Fitted Values, Estimated Residuals, and Regression Fit (pg. 547) | |
| 17.4. Asymptotic Normality and Statistical Inference (pg. 557) | |
| 17.5. Causality and Prediction (pg. 569) | |
| Notes (pg. 572) | |
| Exercises (pg. 573) | |
| 18. Multiple Linear Regression (pg. 581) | |
| 18.1. The Multiple Linear Regression Model (pg. 581) | |
| 18.2. The Least-Squares Estimator (pg. 584) | |
| 18.3. Standard Errors and Confidence Intervals (pg. 596) | |
| 18.4. Inference for Linear Combinations of Regression Parameters (pg. 602) | |
| 18.5. Hypothesis Testing (pg. 604) | |
| 18.6. Modeling Approaches and Explanatory Variables (pg. 608) | |
| 18.7. Log-Transformed Outcome Variable (pg. 619) | |
| 18.8. Asymptotic Predictive Intervals (pg. 622) | |
| 18.9. Linear Probability Model (pg. 628) | |
| Notes (pg. 633) | |
| Exercises (pg. 634) | |
| References (pg. 641) | |
| Index (pg. 643) | |
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