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Can we test the hypothesis that no regressor has a nonzero effect on the response variable. Answer using only mathematical proofs. Please relate this to

Can we test the hypothesis that no regressor has a nonzero effect on the response variable. Answer using only mathematical proofs.

Please relate this to sum of squares, and the multiple linear regression model: y = B₀ + B₁x₁ + B₂x₂ + e

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