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Explain why two perfectly multicollinear regressors cannot be included in a linear multiple regression. If those...

Explain why two perfectly multicollinear regressors cannot be included in a linear multiple regression. If those same two regressors were not perfectly collinear but highly collinear what difference, or differences, would that make?

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Answer #1

Two perfectly multicollinear regressors cannot be included in a linear multiple regression because it undermines the statistical significance of the independent variables in the regression equation, thereby giving insignificant results of the regression equation, as the regressors would be affecting each other.

If instead of being perfectly multicollinear, the regressors were not perfectly collinear, they would still be affecting each other, leading to a wider confidence interval and thus lower statistical significance of the regressors.

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