A GLM can be related to a standard regression model:

Design & Analysis of Experiments 8E 2012 Montgomery

A GLM can be related to a standard regression model: Design & Analysis of Experiments 8E 2012 Montgomery

Approximate Methods • Estimating missing values • Setting dada aside Design & Analysis of Experiments 8E 2012 Montgomery

15.3 The Analysis of Covariance A useful technique for dealing with uncontrollable but observable nuisance factors Design & Analysis of Experiments 8E 2012 Montgomery

The Basic ANCOVA Model • The model is a combination of an ANOVA and a regression model • The analysis is an “adjusted” ANOVA • The procedure actually fits the covariate first, then fids the contribution of the treatment factor over and above the covariate • Details of computing are in the text • JMP, Minitab, and SAS can do the analysis Design & Analysis of Experiments 8E 2012 Montgomery

Design of Experiments with Known Covariates • In many situations the covariates are observed along with the response variable(s), so there is no opportunity to use information about the covariates to design the experiment • Sometimes the covariates are known in advance, and when this is the case, this information can be used in constructing a design Design & Analysis of Experiments 8E 2012 Montgomery

Motor Oil Additive Experiment • Properties of the product depend on two controllable factors • They also depend on the viscosity and molecular weight of a raw material used to manufacture the product • The raw material properties are known in advance, because there are 40 samples of this material available for use in the experiment Design & Analysis of Experiments 8E 2012 Montgomery

A GLM can be related to a standard regression model: