Generalized inverse regression
We have just been studying the problems which can arise due to multicollinearities in regression. Examples quite frequently occur when there is an exact, rather than an approximate, linear relationship between the explanatory variables, and the problem we then face is that the matrix in the normal equations which we wish to invert is singular. Examples will be given below. In fact, it is possible to go through with much of least squares theory using what we call generalized inverses.
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