Assume That You Had Found Correlation of the Residuals Across

question 17

Essay

Assume that you had found correlation of the residuals across observations.This may
happen because the regressor is ordered by size.Your regression model could therefore
be specified as follows: $$\begin{array} { c } Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \\u _ { i } = \rho u _ { i - 1 } + v _ { i } ; | \rho | < 1 .\end{array}$$
Furthermore, assume that you had obtained consistent estimates for $\beta _ { 0 } , \beta _ { 1 } , \rho$ . If asked to make a prediction for $Y$ , given a value of $X \left( = X _ { j } \right)$ and $\hat { u } _ { j - 1 }$ , how would you proceed? Would you use the information on the lagged residual at all? Why or why not?

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Definitions:

Predetermined Overhead Rate

A rate used to allocate manufacturing overhead to individual products or job orders, calculated before the accounting period begins based on estimated costs and activity levels.

Direct Labor-hours

Refers to the total hours worked by employees who are directly involved in the production process, directly affecting the manufacturing of goods.

Predetermined Overhead Rate

A rate used to allocate manufacturing overhead costs to products, calculated based on estimates rather than actual expenses.

Manufacturing Overhead

Refers to the indirect factory-related costs incurred when producing a product, which may include the cost of materials, labor, and utility expenses that are not directly tied to the production of goods.