Consider the Simple Regression Model $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$

question 32

Essay

Consider the simple regression model $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$ where $X _ { \mathrm { i } } > 0$ for all $i$ , and the conditional variance is $\operatorname { var } \left( u _ { i } \mid X _ { i } \right) = \theta X _ { i } ^ { 2 }$ where $\theta$ is a known constant with $\theta > 0$ . (a) Write the weighted regression as $\tilde { Y } _ { i } = \beta _ { 0 } \tilde { X } _ { 0 i } + \beta _ { 1 } \tilde { X } _ { 1 i } + \tilde { u } _ { i }$ . How would you construct $\tilde { Y } _ { i }$ , $\tilde { X } _ { 0 i }$ and $\tilde { X } _ { 1 i } ?$

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Definitions:

Spoilage of Materials

Wastage or damage of raw materials during production that cannot be recovered or used.

Direct Labor Time Variance

The difference between the expected (or standard) time to produce goods and the actual time taken, often used in cost control.

Overhead

The ongoing administrative and general expenses of a business that are not directly attributable to specific products or services.

Standard Labor Hours

The estimated amount of time that should be required to produce a unit of product or to complete a process, task, or project.