Alternative Equation Formats

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MathML

\begin{aligned} S w e e p (C, X) = & [\begin{array}{cc} {(X^{'} X)}^{-} & {(X^{'} X)}^{-} X^{'} Y \\ - Y^{'} X {(X^{'} X)}^{-} & Y^{'} Y - Y^{'} X {(X^{'} X)}^{-} X^{'} Y \end{array}] \\ = & [\begin{array}{cc} {(X^{'} X)}^{-} & \hat{β} \\ - \hat{β} & Y^{'} M Y \end{array}] = [\begin{array}{cc} {(X^{'} X)}^{-} & \hat{β} \\ - \hat{β} & S S R \end{array}] \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} \mr{Sweep}(\bC ,\bX ) =& \left[\begin{array}{cc} \left(\bX '\bX \right)^{-} & \left(\bX '\bX \right)^{-}\bX '\bY \cr -\bY '\bX \left(\bX '\bX \right)^{-} & \bY '\bY - \bY '\bX \left(\bX '\bX \right)^{-}\bX '\bY \end{array}\right] \\[0.1in] =& \left[\begin{array}{cc} \left(\bX '\bX \right)^{-} & \widehat{\bbeta } \cr -\widehat{\bbeta } & \bY '\bM \bY \end{array}\right] = \left[\begin{array}{cc} \left(\bX '\bX \right)^{-} & \widehat{\bbeta } \cr -\widehat{\bbeta } & \mr{SSR} \end{array}\right] \end{align*}