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| Introduction: Statistical Questions | |
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| Data: Plots and Location | |
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| Plot the Data | |
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| Measures of Location: Single Observations | |
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| Measures of Location: Paired Observations | |
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| Robust Measures of Location: Paired Observations | |
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| Linear Algebra for Least Squares (Optional) | |
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| Exercises | |
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| Data: Dispersion and Correlation | |
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| Measures of Dispersion: Single Observations | |
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| Measures of Dispersion: Paired Observations | |
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| Robust Measures of Dispersion: Paired Observations | |
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| Analysis of Variance | |
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| Measures of Linear Relationship | |
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| Analysis of Variance using Linear Algebra (Optional) | |
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| Exercises | |
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| Random Variables: Probability and Density | |
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| Random Variables | |
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| Probability | |
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| Finding Probabilities | |
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| Densities: Discrete Random Variables | |
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| Densities: Continuous Random Variables | |
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| Binomial Random Variables | |
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| Normal Random Variables | |
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| Exercises | |
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| Random Variables: Expectation and Variance | |
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| Expectation of a Random Variable | |
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| Properties of Expectation | |
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| Independent Random Variables | |
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| Variance of a Random Variable | |
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| Correlation Coefficient | |
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| Properties of Normal Random Variables | |
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| Linear Algebra for Random Vectors (Optional) | |
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| Exercises | |
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| Statistical Inference | |
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| Populations and Samples | |
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| Unbiases Estimators | |
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| Distribution of X | |
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| Confidence Intervals | |
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| Hypothesis Testing | |
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| General Inference Problem | |
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| The Runs Test for Randomness | |
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| Testing for Normality | |
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| Linear Algebra for Inference (Optional) | |
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| Exercises | |
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| Simple Linear Models | |
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| Basics of the Simple Linear Model | |
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| Estimators for the Simple Linear Model | |
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| Inference for the Slope | |
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| Testing the Hypothesis b = 0 | |
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| Coefficient of Determination | |
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| Inference for the Intercept | |
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| Inference for the Variance | |
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| Prediction Intervals | |
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| Regression Through the Origin | |
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| Earthquake Example | |
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| Linear Algebra: The Simple Linear Model (Optional) | |
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| Exercises | |
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| Linear Model Diagnostics | |
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| Residual Plots | |
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| Standardized Residuals | |
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| Testing Assumption 1: Is X a Valid Predictor? | |
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| Testing Assumption 2: Does E([epsilon subscript i] = 0 for all i? | |
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| Testing Assumption 2: Does V ar([epsilon subscript i] = [sigma superscript 2] for all i? | |
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| Testing Assumption 3: Are the Errors Independent? | |
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| Testing Assumption 4: Are the Errors Normal? | |
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| Distribution of the Residuals | |
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| Linear Algebra for Residuals (Optional) | |
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| Exercises | |
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| Linear Models: Two Independent Variables | |
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| Calculating Parameters | |
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| Analysis of Variance | |
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| The Effects of Independent Variables | |
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| Inference for the Bivariate Linear Model | |
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| Diagnostics for the Bivariate Linear Model | |
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| Linear Algebra: Bivariate Linear Model (Optional) | |
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| Exercises | |
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| Linear Models: Several Independent Variables | |
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| A Multivariate Example | |
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| Analysis of Variance | |
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| Inference for the Multivariate Linear Model | |
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| Selecting Predictors | |
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| Diagnostics for the Multivariate Model | |
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| A Larger Example | |
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| A Curious Example | |
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| Linear Algebra: Multivariate Linear Model (Optional) | |
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| Exercises | |
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| Model Building | |
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| Transformations | |
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| Indicator Variables | |
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| Using R[superscript 2] Carefully | |
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| Selection of Predictors | |
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| Outliers and Influence | |
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| Comprehensive Example: College Presidents | |
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| Linear Algebra for Model Building (Optional) | |
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| Exercises | |
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| Extended Linear Models | |
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| Analysis of Variance Models | |
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| Analysis of Covariance Models | |
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| Diagnostics for ANOVA and ANCOVA | |
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| Binary Logistic Regression Models | |
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| Robust Regression Methods | |
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| Total Least Squares | |
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| Linear Algebra for ANOVA (Optional) | |
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| Exercises | |
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| Data References | |
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| MINITAB Reference | |
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| Introduction to Linear Algebra | |
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| Statistical Tables | |
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| References | |
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| Index | |