Assume the Existence of I Parameters $\alpha _ { 1 } , \alpha _ { 2 } , \ldots \ldots , \alpha _ { i }$

Assume the existence of I parameters $\alpha _ { 1 } , \alpha _ { 2 } , \ldots \ldots , \alpha _ { i }$ and J parameters $\beta _ { 1 } , \beta _ { 2 } , \ldots \ldots , \beta _ { i }$ such that $X _ { y } = \alpha _ { 2 } + \beta _ { j } + \varepsilon _ { y } ( i = 1 , \ldots \ldots , I \text { and } j = 1 , \ldots \ldots , J ) \text { and } \mu _ { y } = \alpha _ { 2 } + \beta _ { j } \text {. }$ The model specified by the above equations is called an __________ model because each mean response $\mu _ { y}$ is the __________ of an effect due to factor A at level $i \left( \alpha _ { 1 } \right)$ and an effect due to factor B at level $j \left( \beta _ { j } \right)$ .