One of the most prominent tools in statistics is linear regression. It can be stated as a linear vector model

where |y contains the observed manifestations of the response variable, the matrix X contains the socalled regressors, |? is a parameter vector to be estimated, and is a vector of uncorrelated random fluctuations. Show that by minimizing the square error functional F = ??|??with respect to ?|, the socalled least-squares estimator

is obtained. Remember that the chain rule of differentiation has to be obeyed in vector calculus also. This may again be a tough one.

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ly) = X\B) + |e) 8) = (X' Xy-' x'v»>