Principles of Managerial Statistics and Data Science

ROBERTO RIVERA, PHD, is a Professor, at the College of Business, University of Puerto Rico, Mayagüez. He received his PhD in Statistics from the University of California, Santa Barbara. He founded the Puerto Rico Chapter of the American Statistical Association. Dr. Rivera is also the co-author of Applications of Regression Models in Epidemiology (2017).

• Preface xvAcknowledgments xviiAcronyms xixAbout the Companion Site xxiPrinciples of Managerial Statistics and Data Science xxiii1 Statistics Suck; So Why Do I Need to Learn About It? 11.1 Introduction 1Practice Problems 41.2 Data-Based Decision Making: Some Applications 51.3 Statistics Defined 91.4 Use of Technology and the New Buzzwords: Data Science, Data Analytics, and Big Data 111.4.1 A Quick Look at Data Science: Some Definitions 11Chapter Problems 14Further Reading 142 Concepts in Statistics 152.1 Introduction 15Practice Problems 172.2 Type of Data 19Practice Problems 202.3 Four Important Notions in Statistics 22Practice Problems 242.4 Sampling Methods 252.4.1 Probability Sampling 252.4.2 Nonprobability Sampling 27Practice Problems 302.5 Data Management 312.5.1 A Quick Look at Data Science: Data Wrangling Baltimore Housing Variables 342.6 Proposing a Statistical Study 36Chapter Problems 37Further Reading 393 Data Visualization 413.1 Introduction 413.2 Visualization Methods for Categorical Variables 41Practice Problems 463.3 Visualization Methods for Numerical Variables 50Practice Problems 563.4 Visualizing Summaries of More than Two Variables Simultaneously 593.4.1 A Quick Look at Data Science: Does Race Affect the Chances of a Driver Being Searched During a Vehicle Stop in San Diego? 66Practice Problems 693.5 Novel Data Visualization 753.5.1 A Quick Look at Data Science: Visualizing Association Between Baltimore Housing Variables Over 14 Years 78Chapter Problems 81Further Reading 964 Descriptive Statistics 974.1 Introduction 974.2 Measures of Centrality 99Practice Problems 1084.3 Measures of Dispersion 111Practice Problems 1154.4 Percentiles 1164.4.1 Quartiles 117Practice Problems 1224.5 Measuring the Association Between Two Variables 124Practice Problems 1284.6 Sample Proportion and Other Numerical Statistics 1304.6.1 A Quick Look at Data Science: Murder Rates in Los Angeles 1314.7 How to Use Descriptive Statistics 132Chapter Problems 133Further Reading 1395 Introduction to Probability 1415.1 Introduction 1415.2 Preliminaries 142Practice Problems 1445.3 The Probability of an Event 145Practice Problems 1485.4 Rules and Properties of Probabilities 149Practice Problems 1525.5 Conditional Probability and Independent Events 154Practice Problems 1595.6 Empirical Probabilities 1615.6.1 A Quick Look at Data Science: Missing People Reports in Boston by Day of Week 164Practice Problems 1655.7 Counting Outcomes 168Practice Problems 171Chapter Problems 171Further Reading 1756 Discrete Random Variables 1776.1 Introduction 1776.2 General Properties 1786.2.1 A Quick Look at Data Science: Number of Stroke Emergency Calls in Manhattan 183Practice Problems 1846.3 Properties of Expected Value and Variance 186Practice Problems 1896.4 Bernoulli and Binomial Random Variables 190Practice Problems 1976.5 Poisson Distribution 198Practice Problems 2016.6 Optional: Other Useful Probability Distributions 203Chapter Problems 205Further Reading 2087 Continuous Random Variables 2097.1 Introduction 209Practice Problems 2117.2 The Uniform Probability Distribution 211Practice Problems 2157.3 The Normal Distribution 216Practice Problems 2257.4 Probabilities for Any Normally Distributed Random Variable 2277.4.1 A Quick Look at Data Science: Normal Distribution, A Good Match for University of Puerto Rico SATs? 229Practice Problems 2317.5 Approximating the Binomial Distribution 234Practice Problems 2367.6 Exponential Distribution 236Practice Problems 238Chapter Problems 239Further Reading 2428 Properties of Sample Statistics 2438.1 Introduction 2438.2 Expected Value and Standard Deviation of x̄ 244Practice Problems 2468.3 Sampling Distribution of x̄ When Sample Comes From a Normal Distribution 247Practice Problems 2518.4 Central Limit Theorem 2528.4.1 A Quick Look at Data Science: Bacteria at New York City Beaches 257Practice Problems 2598.5 Other Properties of Estimators 261Chapter Problems 264Further Reading 2679 Interval Estimation for One Population Parameter 2699.1 Introduction 2699.2 Intuition of a Two-Sided Confidence Interval 2709.3 Confidence Interval for the Population Mean: 𝜎 Known 271Practice Problems 2769.4 Determining Sample Size for a Confidence Interval for 𝜇 278Practice Problems 2799.5 Confidence Interval for the Population Mean: 𝜎 Unknown 279Practice Problems 2849.6 Confidence Interval for 𝜋 286Practice Problems 2879.7 Determining Sample Size for 𝜋 Confidence Interval 288Practice Problems 2909.8 Optional: Confidence Interval for 𝜎 2909.8.1 A Quick Look at Data Science: A Confidence Interval for the Standard Deviation of Walking Scores in Baltimore 292Chapter Problems 293Further Reading 29610 Hypothesis Testing for One Population 29710.1 Introduction 29710.2 Basics of Hypothesis Testing 29910.3 Steps to Perform a Hypothesis Test 304Practice Problems 30510.4 Inference on the Population Mean: Known Standard Deviation 306Practice Problems 31810.5 Hypothesis Testing for the Mean (𝜎 Unknown) 323Practice Problems 32710.6 Hypothesis Testing for the Population Proportion 32910.6.1 A Quick Look at Data Science: Proportion of New York City High Schools with a Mean SAT Score of 1498 or More 333Practice Problems 33410.7 Hypothesis Testing for the Population Variance 33710.8 More on the p-Value and Final Remarks 33810.8.1 Misunderstanding the p-Value 339Chapter Problems 343Further Reading 34711 Statistical Inference to Compare Parameters from Two Populations 34911.1 Introduction 34911.2 Inference on Two Population Means 35011.3 Inference on Two Population Means – Independent Samples, Variances Known 351Practice Problems 35711.4 Inference on Two Population Means When Two Independent Samples are Used – Unknown Variances 36011.4.1 A Quick Look at Data Science: Suicide Rates Among Asian Men and Women in New York City 364Practice Problems 36611.5 Inference on Two Means Using Two Dependent Samples 368Practice Problems 37011.6 Inference on Two Population Proportions 371Practice Problems 374Chapter Problems 375References 378Further Reading 37812 Analysis of Variance (ANOVA) 37912.1 Introduction 379Practice Problems 38212.2 ANOVA for One Factor 383Practice Problems 39012.3 Multiple Comparisons 391Practice Problems 39512.4 Diagnostics of ANOVA Assumptions 39512.4.1 A Quick Look at Data Science: Emergency Response Time for Cardiac Arrest in New York City 399Practice Problems 40312.5 ANOVA with Two Factors 404Practice Problems 40912.6 Extensions to ANOVA 413Chapter Problems 416Further Reading 41913 Simple Linear Regression 42113.1 Introduction 42113.2 Basics of Simple Linear Regression 423Practice Problems 42513.3 Fitting the Simple Linear Regression Parameters 426Practice Problems 42913.4 Inference for Simple Linear Regression 431Practice Problems 44013.5 Estimating and Predicting the Response Variable 443Practice Problems 44613.6 A Binary X 448Practice Problems 44913.7 Model Diagnostics (Residual Analysis) 450Practice Problems 45613.8 What Correlation Doesn’t Mean 45813.8.1 A Quick Look at Data Science: Can Rate of College Educated People Help Predict the Rate of Narcotic Problems in Baltimore? 461Chapter Problems 466Further Reading 47214 Multiple Linear Regression 47314.1 Introduction 47314.2 The Multiple Linear Regression Model 474Practice Problems 47714.3 Inference for Multiple Linear Regression 478Practice Problems 48314.4 Multicollinearity and Other Modeling Aspects 486Practice Problems 49014.5 Variability Around the Regression Line: Residuals and Intervals 492Practice Problems 49414.6 Modifying Predictors 494Practice Problems 49514.7 General Linear Model 496Practice Problems 50214.8 Steps to Fit a Multiple Linear Regression Model 50514.9 Other Regression Topics 50714.9.1 A Quick Look at Data Science: Modeling Taxi Fares in Chicago 510Chapter Problems 513Further Reading 51715 Inference on Association of Categorical Variables 51915.1 Introduction 51915.2 Association Between Two Categorical Variables 52015.2.1 A Quick Look at Data Science: Affordability and Business Environment in Chattanooga 525Practice Problems 529Chapter Problems 532Further Reading 53216 Nonparametric Testing 53316.1 Introduction 53316.2 Sign Tests and Wilcoxon Sign-Rank Tests: One Sample and Matched Pairs Scenarios 533Practice Problems 53716.3 Wilcoxon Rank-Sum Test: Two Independent Samples 53916.3.1 A Quick Look at Data Science: Austin, Texas, as a Place to Live; Do Men Rate It Higher Than Women? 540Practice Problems 54316.4 Kruskal–Wallis Test: More Than Two Samples 544Practice Problems 54616.5 Nonparametric Tests Versus Their Parametric Counterparts 547Chapter Problems 548Further Reading 54917 Forecasting 55117.1 Introduction 55117.2 Time Series Components 552Practice Problems 55717.3 Simple Forecasting Models 558Practice Problems 56217.4 Forecasting When Data Has Trend, Seasonality 563Practice Problems 56917.5 Assessing Forecasts 57217.5.1 A Quick Look at Data Science: Forecasting Tourism Jobs in Canada 57517.5.2 A Quick Look at Data Science: Forecasting Retail Gross Sales of Marijuana in Denver 577Chapter Problems 580Further Reading 581Appendix A Math Notation and Symbols 583A.1 Summation 583A.2 pth Power 583A.3 Inequalities 584A.4 Factorials 584A.5 Exponential Function 585A.6 Greek and Statistics Symbols 585Appendix B Standard Normal Cumulative Distribution Function 587Appendix C t Distribution Critical Values 591Appendix D Solutions to Odd-Numbered Problems 593Index 643