11 Analysis of Variance and Regression

11.1 Introduction

11.2 Oneway Analysis of Variance

11.2.1 Model and Distribution Assumptions

11.2.2 The Classical ANOVA Hypothesis

11.2.3 Inferences Regarding Linear Combinations of Means

11.2.4 The ANOVA F Test

11.2.5 Simultaneous Estimation of Contrasts

11.2.6 Partitioning Sums of Squares

11.3 Simple Linear Regression

11.3.1 Least Squares: A Mathematical Solution

11.3.2 Best Linear Unbiased Estimators: A Statistical Solution

11.3.3 Models and Distribution Assumptions

11.3.4 Estimation and Testing with Normal Erros

11.3.5 Estimation and Prediction at a Specified x = x0

11.3.6 Simultaneous Estimation and Confidence Bands

11.4 Miscellanea