11.1 Least squares estimation11.1.1 Examples11.1.2 Method of least squares11.1.3 Linear regressionEstimation in linear regression11.1.4 Regression and correlation11.1.5 Overfitting a model11.2 Analysis of variance, prediction, and further inference11.2.1 ANOVA and R-square11.2.2 Tests and confidence intervalsDegrees of freedom and variance estimationInference about the regression slopeANOVA F-testF-test and T-test11.2.3 PredictionConfidence interval for the mean of responsesPrediction interval for the individual responsePrediction bands11.3 Multivariate regression11.3.1 Introduction and examples11.3.2 Matrix approach and least squares estimationMatrix approach to multivariate linear regressionLeast squares estimates11.3.3 Analysis of variance, tests, and predictionTesting significance of the entire modelVariance estimatorTesting individual slopesPrediction11.4 Model building11.4.1 Adjusted R-square11.4.2 Extra sum of squares, partial F-tests, and variable selectionStepwise (forward) selectionBackward elimination11.4.3 Categorical predictors and dummy variablesAvoid singularity by creating only (C − 1) dummiesInterpretation of slopes for dummy variablesMatlab notesSummary and conclusionsExercisesFigure 11.1Figure 11.2Figure 11.3Figure 11.4Figure 11.5Figure 11.6Table 11.1