SAS for Linear Models, Fourth Edition by Ramon Littell, Walter Stroup, Rudolf Freund

By Ramon Littell, Walter Stroup, Rudolf Freund

This transparent and entire consultant presents every little thing you would like for robust linear version research. utilizing an academic method and lots of examples, authors Ramon Littell, Walter Stroup, and Rudolf Freund lead you thru equipment relating to research of variance with fastened and random results. you'll discover ways to use the perfect SAS process for many scan designs (including thoroughly random, randomized blocks, and cut up plot) in addition to factorial remedy designs and repeated measures. SAS for Linear types, Fourth variation, additionally contains research of covariance, multivariate linear types, and generalized linear types for non-normal facts. locate within: regression versions; balanced ANOVA with either mounted- and random-effects types; unbalanced info with either mounted- and random-effects versions; covariance versions; generalized linear types; multivariate types; and repeated measures. New during this variation: combined and GENMOD methods, up to date examples, new software-related gains, and different new fabric.

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In matrix notation, the residual or error sum of squares is ERROR SS = Y ′(I − X(X ′X) −1X ′)Y = Y ′Y − Y ′X(X ′X) −1 X ′Y = Y ′Y − ȕˆ X ′Y The error mean square s 2 = MSE = ERROR SS / (n − m − 1) is an unbiased estimate of σ 2 , the variance of ε i . PROC REG and PROC GLM compute several sums of squares. Each sum of squares can be expressed as the difference between the regression sums of squares for two models, which are called complete and reduced models. This approach relates a given sum of squares to the comparison of two regression models.

32 SAS for Linear Models −1 where A11 is k×k and of rank k. Then Α11 exists, and a generalized inverse of X′X is ( X ′X)− −1 Α11 φ 21 = φ12 φ 22 where each φ ij is a matrix of zeros of the same dimensions as Aij. This approach to obtaining a generalized inverse can be extended indefinitely by partitioning a singular matrix into several sets of matrices, as shown above. Note that the resulting solution to − the normal equations, b = ( X ′X ) XY, has zeros in the positions corresponding to the rows filled with zeros in (X′X )− .

Note also that there are parameter estimates and associated t-tests for the two equations in the RESTRICT statement. These pertain to the Lagrangian parameters that are incorporated in the restricted minimization of the Error SS. 9 with results obtained by invoking the restrictions explicitly. , Walter W. Stroup, and Rudolf J. Freund. SAS® for Linear Models, Fourth Edition. , Cary, North Carolina, USA. ALL RIGHTS RESERVED. com/publishing. 20 SAS for Linear Models This is a three-variable model with an intercept of 0.

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