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:

DNA

A molecule known as Deoxyribonucleic acid, DNA serves as the carrier of genetic guidelines necessary for the life processes, including growth, development, operation, and reproduction, in every known living entity and several viruses.

RNA

RNA, or ribonucleic acid, is a nucleic acid involved in coding, decoding, regulation, and expression of genes, playing a key role in protein synthesis and regulation.

Chemical Composition

The identity and relative number of the elements that make up any particular compound.

Missense Mutation

A type of base-pair substitution mutation that causes one amino acid to be substituted for another in the resulting protein product. Compare with nonsense mutation.