that indicates which levels were observed for each factor the model assumption is that depends in linear way on the indicator featuresapart from an error term that isy pj = = jk { ke{ jk where we have omitted one indicator feature (corresponding to level for each factor for independent responses yn where each yi corresponds to the factor values ui uir let xi jk {ui kthenthe linear model for the data becomes yi pj jk xi jk ei ( = = where the {ei are independent with expectation and some variance by gathering the and { jk into vector band the {xi jk into matrix xwe have again linear model of the form ( the model matrix has rows and rj= ( columns using the above convention that the parameters are subsumed in the parameter (corresponding to the "constantfeature)we can interpret as baseline response when using the explanatory vector xfor which for all factors the other parameters { jk can be viewed as incremental effects relative to this baseline effect for exampleb describes by how much the response is expected to change if level is used instead of level for factor incremental effects example (crop yield (cont )in example the linear model ( has eight parametersb and the model matrix depends on how the crop yields are organized in vector and on the ordering of the factors let us order column-wise from table as in [ ]and let treatment be factor and block be factor then we can write ( as ewhere { |{zb and with [ ]and [ ]estimation of and model selectionand prediction can now be carried out in the usual manner for linear models in the context of factorial experimentsthe model matrix is often called the design matrixas it specifies the design of the experimente how many replications are taken for each combination of factor levels the model ( can be extended by adding products of indicator variables as new features such features are called interaction terms design matrix interaction