Consider the Model Y_i = β₁X_i + U_i, Where U_i $x _ { i } ^ { 2 }$

question 24

Essay

Consider the model Y_i = β₁X_i + u_i, where u_i = c $x _ { i } ^ { 2 }$ e_i and all of the X's and e's are i.i.d. and distributed N(0,1).
(a)Which of the Extended Least Squares Assumptions are satisfied here? Prove your assertions.
(b)Would an OLS estimator of β₁ be efficient here?
(c)How would you estimate β₁ by WLS?

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Definitions:

Psychosocial Developmental

Relating to the interrelation of social factors and individual thought and behavior throughout the lifespan.

Socioeconomic Status

Refers to an individual's or family's economic and social position in relation to others, based on income, education, and occupation.

Maturational Needs

The requirements essential for the natural progression and development of individuals, often related to physical or psychological growth.

Generativity

A stage of psychosocial development in which individuals focus on guiding the next generation or contributing to the well-being of younger people.