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Preface | |

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Introduction and Fundamental Ideas | |

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Statistics as Science | |

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What You Will Learn in This Chapter | |

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Introduction | |

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Statistics: A Framework for Decision Making | |

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Statistics and the Methodology of Science | |

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Statistics as a Science | |

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The Subject Matter of Statistics | |

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Statistics and Science Interwined | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Addendum for the Reader | |

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Exercises | |

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Types of Variables, Measurements, and Explanation | |

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What You Will Learn in This Chapter | |

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Introduction | |

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Types of Variables | |

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Cardinal Measurement | |

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Ordinal Measurement | |

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Categorical Variables | |

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Indices | |

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Time Series | |

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Random and Deterministic Variables | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Descriptive Statistics | |

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How to Describe and Summarize Random Data by Graphical Procedures | |

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What You Will Learn in This Chapter | |

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Introduction | |

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Describing Data by Box-and-Whisker Plots | |

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The Median | |

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The Range | |

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Quartiles | |

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Box-and-Whisker Plots | |

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Plotting Relative Frequencies | |

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Cumulative Frequencies | |

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Histogram | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Moments and the Shape of Histograms | |

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What You Will Learn in This Chapter | |

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Introduction | |

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The Mean, a Measure of Location | |

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An Aside on Notation | |

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Averaging Grouped Data | |

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Interpreting the Mean | |

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The Second Moment as a Measure of Spread | |

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General Definition of Moments | |

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The Third Moment as a Measure of Skewness | |

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The Fourth Moment as a Measure of Peakedness, or "Fat Tails" | |

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Standardized Moments | |

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Some Practical Uses for Higher Moments | |

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Standardization of Variables | |

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The Higher Moments about the Origin | |

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Higher Moments and Grouped Data | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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The Description of Bivariate Data | |

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What You Will Learn in This Chapter | |

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Introduction | |

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Three-Dimensional Histograms | |

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Scatter Plots | |

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Standardization for Pairs of Random Variables | |

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Covariation and m[subscript 11], the First Cross Product Moment | |

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Linear Statistical Relationships and the Correlation Coefficient | |

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The Correlation Coefficient and Slope | |

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Rank Correlation | |

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Bivariate Categorical Data | |

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Row Comparisons | |

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Column Comparisons | |

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Joint Comparisons | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Probability and Distribution Theory | |

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The Theory of Statistics: An Introduction | |

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What You Will Learn in This Chapter | |

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Introduction | |

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The Theory: First Steps | |

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The Sample Space | |

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Introducing Probabilities | |

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Probabilities of Unions and Joint Events | |

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A Mathematical Digression | |

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Calculating the Probabilities of the Union of Events | |

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The Definition of Probability for Sample Spaces of Discrete Events | |

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Conditional Probability | |

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Summing Up the Many Definitions of Probability | |

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Random Variables: Intuition Made Formal | |

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An Example Using Two Random Variables | |

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Statistical Independence | |

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Application of the Results to Continuous Random Variables | |

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Consequences of the Equally Likely Principle | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Excercises | |

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The Generation and Description of Discrete Probability Distributions | |

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What You Will Learn in This Chapter | |

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Introduction | |

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Combinations and Permutations | |

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Generating Binomial Probabilities | |

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The Convolution Sum | |

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Deriving the Binomial Distribution | |

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Parameters and the Shape of the Probability Distribution | |

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Theoretical Moments and the Shape of the Probability Distribution | |

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Expectation | |

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Moment-Generating Functions for Discrete Variables | |

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The Cumulative Distribution Function | |

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The Poisson Probability Distribution | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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The Generation of Some Continuous Probability Distributions | |

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What You Will Learn in This Chapter | |

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Introduction | |

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How to Express Probability in Terms of Continuous Random Variables | |

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Theoretical Moments and Density Functions | |

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The Uniform Distribution | |

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The Normal, or Gaussian, Density Function and the Central Limit Theorem | |

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Standard Deviation and the Nonstandard Gaussian | |

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The Gaussian, or Normal, Distribution as an Approximation to the Binomial Distribution | |

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Moment-Generating Functions for Continuous Variables | |

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The Chebyshev Inequality | |

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Terminology | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Basic Principles of Inference | |

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Elementary Sampling Theory | |

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What You Will Learn in This Chapter | |

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Introduction | |

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An Illustrative Example | |

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An Introduction to the Theory of Simple Random Sampling | |

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Stratified Random Sampling | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Estimation of Theoretical Moments and the Parameters of Probability Distributions | |

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What You Will Learn in This Chapter | |

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Introduction | |

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Estimating Theoretical Moments: Large Sample Results | |

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Estimating Moments and Parameters: Confidence Intervals and Small Sample Results | |

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Estimating a Binomial Probability | |

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Estimating the Poisson Parameter | |

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The Student's T Distribution | |

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The Chi-square Distribution and Confidence Intervals for the Variance | |

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Maximum Likelihood Estimators | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Hypothesis Testing: How to Discriminate between Two Alternatives | |

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What You Will Learn in This Chapter | |

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Introduction | |

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The Basic Idea of Hypotheses Tests | |

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A Digression on the Interpretation of Rejection Regions | |

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How to Choose an Optimal Decision Rule | |

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Why Type I Error Is Usually Small | |

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The Special Rofe of the Null Hypothesis | |

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Simple and Composite Hypotheses Tests | |

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Two-Sided Hypotheses Tests | |

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Tests of Proportions | |

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Hypotheses Tests When the Variance Is Unknown | |

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Testing the Difference between Two Means | |

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An Aside on Statistical Significance | |

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P Values | |

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Some Practical Examples | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Bivariate Distributions, Regression, and ANOVA | |

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The Generation of Bivariate and Conditional Probability Distributions | |

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What You Will Learn in This Chapter | |

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Introduction | |

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Some Pragmatic Examples | |

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The Generation of a Bivariate Discrete Distribution | |

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The Generation of a Bivariate Continuous Distribution | |

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The Conditional Normal Density Function | |

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Moments of Joint and Conditional Density Functions | |

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Bivariate and Conditional Distributions Obtained by Sampling | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Unility? | |

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Exercises | |

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The Theory and Practice of Regression Analysis | |

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What You Will Learn in This Chapter | |

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Introduction | |

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The Regression Model | |

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Estimation and Inference: The Basics | |

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The Coefficient of Determination and the Degree of Fit | |

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Estimation and Inference: Confidence Intervals and Hypotheses Tests | |

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Confidence Intervals for the Regression Parameters | |

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Predicting the Dependent Variable | |

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Confidence Intervals for the Error Term Standard Deviation | |

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The F Distribution and Measuring the Goodness of Fit | |

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Testing Hypotheses in Regression Equations | |

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Calculations | |

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The "Regression" in Regression Analysis | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Comparing Populations through the Analysis of Variance | |

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What You Will Learn in This Chapter | |

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Introduction | |

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An Introduction to One-Way Analysis of Variance | |

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For Multiple Treatments, Which Is Best? | |

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The Link to Regression Analysis | |

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Summary | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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Exercises | |

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Retrospective | |

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Retrospective | |

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What You Will Learn in This Chapter | |

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Introduction | |

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A Schematic Review of What You Have Learned | |

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The Role of Statistics in Everyday Life | |

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Case Study: Was There Age Discrimination in a Public Utility? | |

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The Relationship between Science and Statistics | |

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What Might You Learn Next in Statistics? | |

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Exercises | |

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Appendixes | |

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Mathematical Appendix: Review of Concepts and Conventions | |

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Notational Conventions | |

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Indexing | |

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Sigma Notation | |

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Elementary Set Theory | |

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Elements of Calculus | |

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Exercises | |

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Directions for Using the Student Version of S-Plus 4.5 | |

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Installing, Starting, and Closing S-Plus | |

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Using S-Plus in This Text | |

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General Notes about S-Plus | |

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Data Files | |

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Windows in S-Plus | |

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Menu Bar Commands | |

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Probability and Density Calculations | |

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Statistical Tables | |

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Supplemental Material | |

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Nonparametric Measures | |

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Bayesian Inference | |

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Index | |