Introduction to linear models and statistical inference / / Steven J. Janke, Frederick Tinsley

• Record Nr.: UNINA9910143571903321
• Autore: Janke Steven J. <1947->
• Pubbl/distr/stampa: Hoboken, NJ, : Wiley, c2005
• ISBN: 9786610277544; 9781280277542; 1280277548; 9780470315347; 0470315342; 9780471740117; 047174011X; 9780471740100; 0471740101
• Descrizione fisica: 1 online resource (600 p.)
• Altri autori (Persone): TinsleyFrederick <1951->
• Disciplina: 519.5/4
• Soggetti: Linear models (Statistics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 575-579) and index.
• Nota di contenuto: Introduction to Linear Models and Statistical Inference; Contents; INTRODUCTION: STATISTICAL QUESTIONS; 1. DATA: PLOTS AND LOCATION; 1.1 Plot the Data; 1.2 Measures of Location: Single Observations; 1.3 Measures of Location: Paired Observations; 1.4 Robust Measures of Location: Paired Observations; 1.5 Linear Algebra for Least Squares (Optional); Exercises; 2. DATA: DISPERSION AND CORRELATION; 2.1 Measures of Dispersion: Single Observations; 2.2 Measures of Dispersion: Paired Observations; 2.3 Robust Measures of Dispersion: Paired Observations; 2.4 Analysis of Variance; 2.5 Measures of Linear Relationship2.6 Analysis of Variance using Linear Algebra (Optional); Exercises; 3. RANDOM VARIABLES: PROBABILITY AND DENSITY; 3.1 Random Variables; 3.2 Probability; 3.3 Finding Probabilities; 3.4 Densities: Discrete Random Variables; 3.5 Densities: Continuous Random Variables; 3.6 Binomial Random Variables; 3.7 Normal Random Variables; Exercises; 4. RANDOM ; VARIABLES: EXPECTATION AND VARIANCE; 4.1 Expectation of a Random Variable; 4.2 Properties of Expectation; 4.3 Independent Random Variables; 4.4 Variance of a Random Variable; 4.5 Correlation Coefficient; 4.6 Properties of Normal Random Variables4.7 Linear Algebra for Random Vectors (Optional); Exercises; 5. STATISTICAL INFERENCE; 5.1 Populations and Samples; 5.2 Unbiases Estimators; 5.3 Distribution of X; 5.4 Confidence Intervals; 5.5 Hypothesis Testing; 5.6 General Inference Problem; 5.7 The Runs Test for Randomness; 5.8 Testing for Normality; 5.9 Linear Algebra for Inference (Optional); Exercises; 6. SIMPLE LINEAR MODELS; 6.1 Basics of the Simple Linear Model; 6.2 Estimators for the Simple Linear Model; 6.3 Inference for the Slope; 6.4 Testing the Hypothesis b = 0; 6.5 Coefficient of Determination6.6 Inference for the Intercept; 6.7 Inference for the Variance; 6.8 Prediction Intervals; 6.9 Regression Through the Origin; 6.10 Earthquake Example; 6.11 Linear Algebra: The Simple Linear Model (Optional); Exercises; 7. LINEAR MODEL DIAGNOSTICS; 7.1 Residual Plots; 7.2 Standardized Residuals; 7.3 Testing Assumption 1: Is X a Valid Predictor?; 7.4 Testing Assumption 2: Does E(ei) = 0 for all i?; 7.5 Testing Assumption 2: Does Var(ei) = s2 for all i?; 7.6 Testing Assumption 3: Are the Errors Independent?; 7.7 Testing Assumption 4: Are the Errors Normal?; 7.8 Distribution of the Residuals7.9 Linear Algebra for Residuals (Optional); Exercises; 8. LINEAR MODELS: TWO INDEPENDENT VARIABLES; 8.1 Calculating Parameters; 8.2 Analysis of Variance; 8.3 The Effects of Independent Variables; 8.4 Inference for the Bivariate Linear Model; 8.5 Diagnostics for the Bivariate Linear Model; 8.6 Linear Algebra: Bivariate Linear Model (Optional); Exercises; 9. LINEAR MODELS: SEVERAL INDEPENDENT VARIABLES; 9.1 A Multivariate Example; 9.2 Analysis of Variance; 9.3 Inference for the Multivariate Linear Model; 9.4 Selecting Predictors; 9.5 Diagnostics for the Multivariate Model
• Sommario/riassunto: A multidisciplinary approach that emphasizes learning by analyzing real-world data setsThis book is the result of the authors' hands-on classroom experience and is tailored to reflect how students best learn to analyze linear relationships. The text begins with the introduction of four simple examples of actual data sets. These examples are developed and analyzed throughout the text, and more complicated examples of data sets are introduced along the way. Taking a multidisciplinary approach, the book traces the conclusion of the analyses of data sets taken from geology, biology, econom