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• Preface
• Conventions Used in This Book
• Using Code Examples
• O’Reilly Online Learning
• How to Contact Us
• Acknowledgments
• 1. Exploratory Data Analysis
• Elements of Structured Data
• Further Reading
• Rectangular Data
• Data Frames and Indexes
• Nonrectangular Data Structures
• Further Reading
• Estimates of Location
• Mean
• Median and Robust Estimates
• Example: Location Estimates of Population and Murder Rates
• Further Reading
• Estimates of Variability
• Standard Deviation and Related Estimates
• Estimates Based on Percentiles
• Example: Variability Estimates of State Population
• Further Reading
• Exploring the Data Distribution
• Percentiles and Boxplots
• Frequency Tables and Histograms
• Density Plots and Estimates
• Further Reading
• Exploring Binary and Categorical Data
• Mode
• Expected Value
• Probability
• Further Reading
• Correlation
• Scatterplots
• Further Reading
• Exploring Two or More Variables
• Hexagonal Binning and Contours (Plotting Numeric Versus Numeric Data)
• Two Categorical Variables
• Categorical and Numeric Data
• Visualizing Multiple Variables
• Further Reading
• Summary
• 2. Data and Sampling Distributions
• Random Sampling and Sample Bias
• Bias
• Random Selection
• Size Versus Quality: When Does Size Matter?
• Sample Mean Versus Population Mean
• Further Reading
• Selection Bias
• Regression to the Mean
• Further Reading
• Sampling Distribution of a Statistic
• Central Limit Theorem
• Standard Error
• Further Reading
• The Bootstrap
• Resampling Versus Bootstrapping
• Further Reading
• Confidence Intervals
• Further Reading
• Normal Distribution
• Standard Normal and QQ-Plots
• Long-Tailed Distributions
• Further Reading
• Student’s t-Distribution
• Further Reading
• Binomial Distribution
• Further Reading
• Chi-Square Distribution
• Further Reading
• F-Distribution
• Further Reading
• Poisson and Related Distributions
• Poisson Distributions
• Exponential Distribution
• Estimating the Failure Rate
• Weibull Distribution
• Further Reading
• Summary
• 3. Statistical Experiments and Significance Testing
• A/B Testing
• Why Have a Control Group?
• Why Just A/B? Why Not C, D,…?
• Further Reading
• Hypothesis Tests
• The Null Hypothesis
• Alternative Hypothesis
• One-Way Versus Two-Way Hypothesis Tests
• Further Reading
• Resampling
• Permutation Test
• Example: Web Stickiness
• Exhaustive and Bootstrap Permutation Tests
• Permutation Tests: The Bottom Line for Data Science
• Further Reading
• Statistical Significance and p-Values
• p-Value
• Alpha
• Type 1 and Type 2 Errors
• Data Science and p-Values
• Further Reading
• t-Tests
• Further Reading
• Multiple Testing
• Further Reading
• Degrees of Freedom
• Further Reading
• ANOVA
• F-Statistic
• Two-Way ANOVA
• Further Reading
• Chi-Square Test
• Chi-Square Test: A Resampling Approach
• Chi-Square Test: Statistical Theory
• Fisher’s Exact Test
• Relevance for Data Science
• Further Reading
• Multi-Arm Bandit Algorithm
• Further Reading
• Power and Sample Size
• Sample Size
• Further Reading
• Summary
• 4. Regression and Prediction
• Simple Linear Regression
• The Regression Equation
• Fitted Values and Residuals
• Least Squares
• Prediction Versus Explanation (Profiling)
• Further Reading
• Multiple Linear Regression
• Example: King County Housing Data
• Assessing the Model
• Cross-Validation
• Model Selection and Stepwise Regression
• Weighted Regression
• Further Reading
• Prediction Using Regression
• The Dangers of Extrapolation
• Confidence and Prediction Intervals
• Factor Variables in Regression
• Dummy Variables Representation
• Factor Variables with Many Levels
• Ordered Factor Variables
• Interpreting the Regression Equation
• Correlated Predictors
• Multicollinearity
• Confounding Variables
• Interactions and Main Effects
• Regression Diagnostics
• Outliers
• Influential Values
• Heteroskedasticity, Non-Normality, and Correlated Errors
• Partial Residual Plots and Nonlinearity
• Polynomial and Spline Regression
• Polynomial
• Splines
• Generalized Additive Models
• Further Reading
• Summary
• 5. Classification
• Naive Bayes
• Why Exact Bayesian Classification Is Impractical
• The Naive Solution
• Numeric Predictor Variables
• Further Reading
• Discriminant Analysis
• Covariance Matrix
• Fisher’s Linear Discriminant
• A Simple Example
• Further Reading
• Logistic Regression
• Logistic Response Function and Logit
• Logistic Regression and the GLM
• Generalized Linear Models
• Predicted Values from Logistic Regression
• Interpreting the Coefficients and Odds Ratios
• Linear and Logistic Regression: Similarities and Differences
• Assessing the Model
• Further Reading
• Evaluating Classification Models
• Confusion Matrix
• The Rare Class Problem
• Precision, Recall, and Specificity
• ROC Curve
• AUC
• Lift
• Further Reading
• Strategies for Imbalanced Data
• Undersampling
• Oversampling and Up/Down Weighting
• Data Generation
• Cost-Based Classification
• Exploring the Predictions
• Further Reading
• Summary
• 6. Statistical Machine Learning
• K-Nearest Neighbors
• A Small Example: Predicting Loan Default
• Distance Metrics
• One Hot Encoder
• Standardization (Normalization, z-Scores)
• Choosing K
• KNN as a Feature Engine
• Tree Models
• A Simple Example
• The Recursive Partitioning Algorithm
• Measuring Homogeneity or Impurity
• Stopping the Tree from Growing
• Predicting a Continuous Value
• How Trees Are Used
• Further Reading
• Bagging and the Random Forest
• Bagging
• Random Forest
• Variable Importance
• Hyperparameters
• Boosting
• The Boosting Algorithm
• XGBoost
• Regularization: Avoiding Overfitting
• Hyperparameters and Cross-Validation
• Summary
• 7. Unsupervised Learning
• Principal Components Analysis
• A Simple Example
• Computing the Principal Components
• Interpreting Principal Components
• Correspondence Analysis
• Further Reading
• K-Means Clustering
• A Simple Example
• K-Means Algorithm
• Interpreting the Clusters
• Selecting the Number of Clusters
• Hierarchical Clustering
• A Simple Example
• The Dendrogram
• The Agglomerative Algorithm
• Measures of Dissimilarity
• Model-Based Clustering
• Multivariate Normal Distribution
• Mixtures of Normals
• Selecting the Number of Clusters
• Further Reading
• Scaling and Categorical Variables
• Scaling the Variables
• Dominant Variables
• Categorical Data and Gower’s Distance
• Problems with Clustering Mixed Data
• Summary
• Bibliography
• Index