| Description |
1 online resource (717 p.) |
| Series |
New York Academy of Sciences Ser |
|
New York Academy of Sciences Ser
|
| Contents |
Intro -- Methods and Applications of Linear Models -- Contents -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- PART I REGRESSION -- 1 Introduction to Linear Models -- 1.1 Background Information -- 1.2 Mathematical and Statistical Models -- 1.3 Definition of the Linear Model -- 1.4 Examples of Regression Models -- 1.4.1 Single-Variable, Regression Model -- 1.4.2 Regression Models with Several Inputs -- 1.4.3 Discrete Response Variables -- 1.4.4 Multivariate Linear Models -- 1.5 Concluding Comments -- Exercises |
|
2 Regression on Functions of One Variable -- 2.1 The Simple Linear Regression Model -- 2.2 Parameter Estimation -- 2.2.1 Least Squares Estimation -- 2.2.2 Maximum Likelihood Estimation -- 2.2.3 Coded Data: Centering and Scaling -- 2.2.4 The Analysis of Variance Table -- 2.3 Properties of the Estimators and Test Statistics -- 2.3.1 Moments of Linear Functions of Random Variables -- 2.3.2 Moments of Least Squares Estimators -- 2.3.3 Distribution of the Least Squares Estimators -- 2.3.4 The Distribution of Test Statistics -- 2.4 The Analysis of Simple Linear Regression Models |
|
2.4.1 Two Numerical Examples -- 2.4.2 A Test for Lack-of-Fit -- 2.4.3 Inference on the Parameters of the Model -- 2.4.4 Prediction and Prediction Intervals -- 2.5 Examining the Data and the Model -- 2.5.1 Residuals -- 2.5.2 Outliers, Extreme Points, and Influence -- 2.5.3 Normality, Independence, and Variance Homogeneity -- 2.6 Polynomial Regression Models -- 2.6.1 The Quadratic Model -- 2.6.2 Higher Ordered Polynomial Models -- 2.6.3 Orthogonal Polynomials -- 2.6.4 Regression through the Origin -- Exercises -- 3 Transforming the Data -- 3.1 The Need for Transformations |
|
3.2 Weighted Least Squares -- 3.3 Variance Stabilizing Transformations -- 3.4 Transformations to Achieve a Linear Model -- 3.4.1 Transforming the Dependent Variable -- 3.4.2 Transforming the Predictors -- 3.5 Analysis of the Transformed Model -- 3.5.1 Transformations with Forbes Data -- Exercises -- 4 Regression on Functions of Several Variables -- 4.1 The Multiple Linear Regression Model -- 4.2 Preliminary Data Analysis -- 4.3 Analysis of the Multiple Linear Regression Model -- 4.3.1 Fitting the Model in Centered Form -- 4.3.2 Estimation and Analysis of the Original Data |
|
4.3.3 Model Assessment and Residual Analysis -- 4.3.4 Prediction -- 4.3.5 Transforming the Response -- 4.4 Partial Correlation and Added-Variable Plots -- 4.4.1 Partial Correlation -- 4.4.2 Added-Variable Plots -- 4.4.3 Simple Versus Partial Correlation -- 4.5 Variable Selection -- 4.5.1 The Case of Orthogonal Predictors -- 4.5.2 Criteria for Deletion of Variables -- 4.5.3 Nonorthogonal Predictors -- 4.5.4 Computational Considerations -- 4.5.5 Selection Strategies -- 4.6 Model Specification -- 4.6.1 Application to Subset Selection -- 4.6.2 Improved Mean Squared Error |
| Notes |
Description based upon print version of record |
|
4.6.3 Development of the Cp Statistic |
| Genre/Form |
Electronic books
|
| Form |
Electronic book
|
| ISBN |
9781118593042 |
|
1118593049 |
|
