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| Introduction | |
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| Building Valid Models | |
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| Motivating Examples | |
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| Assessing the Ability of NFL Kickers | |
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| Newspaper Circulation | |
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| Menu Pricing in a New Italian Restaurant in New York City | |
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| Effect of Wine Critics' Ratings on Prices of Bordeaux Wines | |
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| Level of Mathematics | |
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| Simple Linear Regression | |
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| Introduction and Least Squares Estimates | |
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| Simple Linear Regression Models | |
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| Inferences About the Slope and the Intercept | |
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| Assumptions Necessary in Order to Make Inferences About the Regression Model | |
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| Inferences About the Slope of the Regression Line | |
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| Inferences About the Intercept of the Regression Line | |
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| Confidence Intervals for the Population Regression Line | |
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| Prediction Intervals for the Actual Value of Y | |
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| Analysis of Variance | |
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| Dummy Variable Regression | |
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| Derivations of Results | |
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| Inferences about the Slope of the Regression Line | |
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| Inferences about the Intercept of the Regression Line | |
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| Confidence Intervals for the Population Regression Line | |
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| Prediction Intervals for the Actual Value of Y | |
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| Exercises | |
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| Diagnostics and Transformations for Simple Linear Regression | |
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| Valid and Invalid Regression Models: Anscombe's Four Data Sets | |
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| Residuals | |
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| Using Plots of Residuals to Determine Whether the Proposed Regression Model Is a Valid Model | |
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| Example of a Quadratic Model | |
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| Regression Diagnostics: Tools for Checking the Validity of a Model | |
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| Leverage Points | |
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| Standardized Residuals | |
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| Recommendations for Handling Outliers and Leverage Points | |
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| Assessing the Influence of Certain Cases | |
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| Normality of the Errors | |
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| Constant Variance | |
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| Transformations | |
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| Using Transformations to Stabilize Variance | |
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| Using Logarithms to Estimate Percentage Effects | |
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| Using Transformations to Overcome Problems due to Nonlinearity | |
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| Exercises | |
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| Weighted Least Squares | |
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| Straight-Line Regression Based on Weighted Least Squares | |
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| Prediction Intervals for Weighted Least Squares | |
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| Leverage for Weighted Least Squares | |
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| Using Least Squares to Calculate Weighted Least Squares | |
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| Defining Residuals for Weighted Least Squares | |
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| The Use of Weighted Least Squares | |
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| Exercises | |
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| Multiple Linear Regression | |
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| Polynomial Regression | |
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| Estimation and Inference in Multiple Linear Regression | |
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| Analysis of Covariance | |
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| Exercises | |
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| Diagnostics and Transformations for Multiple Linear Regression | |
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| Regression Diagnostics for Multiple Regression | |
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| Leverage Points in Multiple Regression | |
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| Properties of Residuals in Multiple Regression | |
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| Added Variable Plots | |
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| Transformations | |
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| Using Transformations to Overcome Nonlinearity | |
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| Using Logarithms to Estimate Percentage Effects: Real Valued Predictor Variables | |
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| Graphical Assessment of the Mean Function Using Marginal Model Plots | |
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| Multicollinearity | |
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| Multicollinearity and Variance Inflation Factors | |
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| Case Study: Effect of Wine Critics' Ratings on Prices of Bordeaux Wines | |
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| Pitfalls of Observational Studies Due to Omitted Variables | |
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| Spurious Correlation Due to Omitted Variables | |
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| The Mathematics of Omitted Variables | |
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| Omitted Variables in Observational Studies | |
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| Exercises | |
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| Variable Selection | |
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| Evaluating Potential Subsets of Predictor Variables | |
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| Criterion 1: R2-Adjusted | |
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| Criterion 2: AICc, Akaike's Information Criterion | |
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| Criterion 3: AICc, Corrected AIC | |
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| Criterion 4: BIC, Bayesian Information Criterion | |
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| Comparison of AIC, AICc and BIC | |
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| Deciding on the Collection of Potential Subsets of Predictor Variables | |
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| All Possible Subsets | |
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| Stepwise Subsets | |
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| Inference After Variable Selection | |
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| Assessing the Predictive Ability of Regression Models | |
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| Stage 1: Model Building Using the Training Data Set | |
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| Stage 2: Model Comparison Using the Test Data Set | |
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| Recent Developments in Variable Selection-LASSO | |
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| Exercises | |
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| Logistic Regression | |
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| Logistic Regression Based on a Single Predictor | |
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| The Logistic Function and Odds | |
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| Likelihood for Logistic Regression with a Single Predictor | |
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| Explanation of Deviance | |
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| Using Differences in Deviance Values to Compare Models | |
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| R2 for Logistic Regression | |
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| Residuals for Logistic Regression | |
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| Binary Logistic Regression | |
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| Deviance for the Case of Binary Data | |
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| Residuals for Binary Data | |
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| Transforming Predictors in Logistic Regression for Binary Data | |
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| Marginal Model Plots for Binary Data | |
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| Exercises | |
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| Serially Correlated Errors | |
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| Autocorrelation | |
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| Using Generalized Least Squares When the Errors Are AR(1) | |
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| Generalized Least Squares Estimation | |
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| Transforming a Model with AR(1) Errors into a Model with iid Errors | |
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| A General Approach to Transforming GLS into LS | |
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| Case Study | |
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| Exercises | |
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| Mixed Models | |
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| Random Effects | |
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| Maximum Likelihood and Restricted Maximum Likelihood | |
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| Residuals in Mixed Models | |
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| Models with Covariance Structures Which Vary Over Time | |
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| Modeling the Conditional Mean | |
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| Exercises | |
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| Appendix: Nonparametric Smoothing | |
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| References | |
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| Index | |