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\subsection{Fitted Empirical Orthogonal Functions}  Fitted EOF analysis explores covariance structure of fitted values. Fitted values are obtained by multivariate regression of response matrix (temperature) on independent variables (ENSO, volcanic aerosols). EOF analysis is carried out on fitted covariance matrix to identify fitted EOFs and fitted PCs. This approach differs from \cite{cook2007fisher} in a way that instead of inverse regression $(\begin{equation}E(\mathbf{X}/\mathbf{y})\end{equation})$, forward regression $(\begin{equation}E(\mathbf{y}/\mathbf{X})\end{equation})$ is used to obtain fitted EOFs. This is due to the fact that dimensionality of response $(\begin{equation}\mathbf{y}\end{equation})$ instead of predictors $(\begin{equation}\mathbf{X}\end{equation})$ is to be reduced to map leading spatial patterns accounting for the relationship of response and predictors.   Let $(\begin{equation}\mathbf{Y}\end{equation})$ be the ($n \times p$) matrix of response variables and $(\begin{equation}\mathbf{X}\end{equation})$ be the ($n \times q$) vector of independent variables. Then, multivariate regression model model\cite{johnson2007applied}  of $\begin{equation}\mathbf{Y}\end{equation}$ on $\begin{equation}\mathbf{X}\end{equation}$ is,\\ \begin{equation}  \mathbf{Y} = \mathbf{X B} + \mathbf{E}  \end{equation}\\ 
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