Analysis of Variance and Covariance

Annette J. Dobson
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Annette J. Dobson: University of Newcastle

Chapter 7 in Introduction to Statistical Modelling, 1983, pp 57-73 from Springer

Abstract: Abstract This chapter concerns linear models of the form % MathType!MTEF!2!1!+- % feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iaadIfacqaHYoGycqGHRaWkcaWGLbaaaa!3C41! $$ y = X\beta + e $$ with e ~ N(0, σ 2 Iwhere y and e are random vectors of length N, X is an N × p matrix of constants, ß is a vector of p parameters and I is the unit matrix. These models differ from the regression models of the previous chapter in that X, called the design matrix, consists entirely of dummy variables for analysis of variance (ANOVA) or dummy variables and measured covariates for analysis of covariance (ANCOVA). Since the choice of dummy variables is to some extent arbitrary, a major consideration is the optimal choice of X. The main questions addressed by analysis of variance and covariance involve comparisons of means. Traditionally the emphasis is on hypothesis testing rather than estimation or prediction.

Keywords: Full Model; Constraint Equation; Normal Equation; Design Matrix; Factor ANOV (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4899-3174-0_7

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