III. Ordinary least squares regression In the multiple regression setting, y is a Ixn vector of...

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III. Ordinary least squares regression In the multiple regression setting, y is a Ixn vector of observations on the dependent variable. X is an nx(m+1) matrix of the observations of the independent variables where m<<n consisting of n I's in its first column and m nxl vectors of independent variables XI,...,Xm. The independent variables and the dependent variable are related through the equation y = Xb, where b is an mxl vector of unknown coefficients. X is not square since m<<n, so does not have the "usual" matrix inverse. The minimum distance inverse of X is (XX)-¹X¹. Use this pseudo-inverse to solve for b.< III. Ordinary least squares regression In the multiple regression setting, y is a Ixn vector of observations on the dependent variable. X is an nx(m+1) matrix of the observations of the independent variables where m<<n consisting of n I's in its first column and m nxl vectors of independent variables XI,...,Xm. The independent variables and the dependent variable are related through the equation y = Xb, where b is an mxl vector of unknown coefficients. X is not square since m<<n, so does not have the "usual" matrix inverse. The minimum distance inverse of X is (XX)-¹X¹. Use this pseudo-inverse to solve for b.<

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Answer b XTX1XTy Explanation y is an Ixndimensional vector of observations on the dependent variable ... View the full answer