Using the Model Y = Xβ + U, and the Extended

question 5

Essay

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

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Definitions:

DDT

A synthetic organic compound used as an insecticide, known for its environmental impacts, including the accumulation in the food chain.

Pyrethrum

A natural insecticide made from the dried flower heads of certain chrysanthemum species.

Chrysanthemums

A type of flowering plant, often grown for its brightly colored flowers and used in floral arrangements and festivals.

Carbamates

A class of chemical compounds used as insecticides, herbicides, and in some medications, known for their ability to inhibit cholinesterase enzymes.