Titlebook: Linear Regression; David J. Olive Textbook 2017 Springer International Publishing AG 2017 Regression.Prediction Interval.Bootstrap Confide

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Multivariate Models,ctor of ones: . = .. See Chapter . (Similarly, the location model is a special case of the multiple linear regression model. See Section .) The multivariate normal and elliptically contoured distributions are important parametric models for the multivariate location and dispersion model. The multiva

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Theory for Linear Models,es Propositions 2.1, 2.2, 2.3, 2.10, 3.1, 3.2, 4.1, 4.2, and Theorem 3.3. Some matrix manipulations are illustrated in Example 4.1. Unproved results include Propositions 2.4, 2.5, 2.6, 2.11, Theorems 2.6, 2.7, and 2.8.

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Multivariate Linear Regression, linear regression which has . = 1 response variable. Plots for checking the model are given, and prediction regions that are robust to nonnormality are developed. For hypothesis testing, it is shown that the Wilks’ lambda statistic, Hotelling Lawley trace statistic, and Pillai’s trace statistic are

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GLMs and GAMs, = .(.)), estimated sufficient predictor (.), generalized linear model (GLM), and the generalized additive model (GAM). When using a GAM to check a GLM, the notation . may be used for the GLM, and . (estimated additive predictor) may be used for the . of the GAM. Definition 1.2 defines the response

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Multivariate Models,riate normal distribution is useful in the large sample theory of the linear model, covered in Chapter ., while elliptically contoured distributions are useful for multivariate linear regression. Section . used prediction regions for iid multivariate data to bootstrap hypothesis tests.

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