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

question 17

Short Answer

In the case when the errors are homoskedastic and normally distributed, conditional on X, then a. $\hat { \boldsymbol { \beta } }$ is distributed $N \left( \boldsymbol { \beta } , \Sigma _ { \hat { \beta } \mid X } \right)$ , where $\Sigma _ { \hat { \beta } \mid X } = \sigma _ { u } ^ { 2 } \boldsymbol { I } _ { ( \mathrm { k } + 1 ) }$ .
b. $\hat { \boldsymbol { \beta } }$ is distributed $\mathrm { N } \left( \boldsymbol { \beta } , \Sigma _ { \hat { \beta } } \right)$ , where $\Sigma _ { \hat { \beta } } = \Sigma _ { \sqrt { n } ( \dot { \beta } - \beta ) } / n = \boldsymbol { Q } _ { X } ^ { - 1 } \Sigma _ { V } \boldsymbol { Q } _ { X } ^ { - 1 } / n$ .
c. $\hat { \beta }$ is distributed $N \left( \boldsymbol { \beta } , \Sigma _ { \dot { \beta } \mid X } \right)$ , where $\Sigma _ { \dot { \beta } \mid X } = \sigma _ { u } ^ { 2 } ( \boldsymbol { X } \boldsymbol { X } ) ^ { - 1 }$ .
d. $\hat { U } = \boldsymbol { P } _ { \boldsymbol { X } } \boldsymbol { Y }$ where $\boldsymbol { P } _ { \boldsymbol { X } } = \boldsymbol { X } \left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 } \boldsymbol { X } ^ { \prime }$ .

Comprehend the realm and implications of canon law.

Realize the hierarchical structure of courts and the obligation to follow higher court decisions.

Learn the importance and limitations of judge-made law over statutory law.

Understand the concept of equity and its meaning within the legal system.

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Definitions:

Convert Technique

A method or approach used to change someone's beliefs, behavior, or perception towards a product, idea, or another entity.

Postpone

The action of delaying or deferring an event or arrangement to a later time.

Prospect's Objection

The concerns or hesitations expressed by potential customers or clients during the sales process, which need to be addressed by the seller to successfully close a sale.

Showing a Diagram

The act of presenting a graphical representation of information to visualize concepts, data, or processes.