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A Joint Hypothesis That Is Linear in the Coefficients and Imposes

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Short Answer

A joint hypothesis that is linear in the coefficients and imposes a number of restrictions can be written as a. (XX)1XY\left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 } \boldsymbol { X } ^ { \prime } \boldsymbol { Y } .
b. Rβ=r\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } .
c. β^β\hat { \beta } - \beta .
d. Rβ=0\boldsymbol { R } \boldsymbol { \beta } = \mathbf { 0 } .

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