Using the Model $\boldsymbol { Y } = \boldsymbol { X } \boldsymbol { \beta } + \boldsymbol { U }$

question 13

Essay

Using the model $\boldsymbol { Y } = \boldsymbol { X } \boldsymbol { \beta } + \boldsymbol { U }$ and the extended least squares assumptions, derive the OLS estimator $\hat { \beta }$ . Discuss the conditions under which $\boldsymbol { X } ^ { \prime } \boldsymbol { X }$ is invertible.

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Definitions:

Subcontracting

The act of assigning another company the responsibility to complete a portion of the work or services originally undertaken by oneself.

Overtime

Time worked beyond the standard hours set by a company policy or national regulation, often compensated at a higher pay rate.

Stockouts

Occurrences where items are not available for sale or use due to insufficient stock.

Linear Programming

A mathematical method used to achieve the optimal outcome in a model whose requirements are represented by linear relationships.