Alternative Equation Formats
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\begin{eqnarray*} \Strong{X}_0 & = & \mbox{ the columns of } \mb{X} \text { whose associated effects do not contain } F1 \\ \Strong{X}_1 & = & \mbox{ the columns of }\mb{X} \text { associated with } F1 \\ \Strong{X}_2 & = & \mbox{the columns of }\mb{X} \text { associated with an } F2 \text { effect that contains} F1 \\ \Strong{M} & = & \Strong{I} - \Strong{X}_0(\Strong{X}_0'\Strong{X}_0)^{-} \Strong{X}_0' \end{eqnarray*}
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