In the Case When the Errors Are Homoskedastic and Normally $\hat \beta$

question 1

Multiple Choice

In the case when the errors are homoskedastic and normally distributed, conditional on X, then

• A) \(\hat \beta\) is distributed N(?, \(\sum _ { \hat { \beta } \mid X }\) ),where \(\sum _ { \hat { \beta } \mid X }\) = \(\sigma _ { u } ^ { 2 }\) I_(k+1).
• B) \(\hat \beta\) is distributed N(?, \(\sum _ { \hat { \beta } }\) ), where \(\sum _ { \hat { \beta } }\) = \(\sum _ { \sqrt { n } \left( \hat { \boldsymbol { \beta } } _ { - } \boldsymbol { \beta } \right) }\) /n = \(Q _ { X } ^ { - 1 }\) \(\sum _ { V }\) \(Q _ { X } ^ { - 1 }\) /n.
• C) \(\hat \beta\) is distributed N(?, \(\sum _ { \hat { \beta } \mid X }\) ),where \(\sum _ { \hat { \beta } \mid X }\) = \(\sigma _ { u } ^ { 2 }\) ( \(X ^ { \prime }\) X)^-1.
• D) \(\hat { u }\) = P_XY where P_X = X( \(X ^ { \prime }\) X)^-1 \(X ^ { \prime }\)

Evaluate the influence of modern social theories on understanding power dynamics.

Understand the impact of the principal's bankruptcy on the agent's power.

Recognize the requirements for terminating an agent's apparent authority.

Distinguish between actual, implied, and express authority of an agent.

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