Consider the Following Symmetric and Idempotent Matrix A: a = $\frac { 1 } { n }$

question 9

Essay

Consider the following symmetric and idempotent Matrix A: A = I - $\frac { 1 } { n }$ ??' and ? = $\left[ \begin{array} { c } 1 \\1 \\\ldots \\1\end{array} \right]$ a. Show that by postmultiplying this matrix by the vector Y (the LHS variable of the OLS regression), you convert all observations of Y in deviations from the mean.
b. Derive the expression Y'AY. What is the order of this expression? Under what other name have you encountered this expression before?

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Definitions:

Variable Manufacturing Overhead

Indirect, fluctuating costs involved in the production process, such as utilities and maintenance, that are not directly tied to specific units produced.

Fixed Manufacturing Overhead

Costs related to manufacturing that do not vary with the level of production, such as factory rent, salaries of permanent staff, and depreciation of factory equipment.

Fixed Expenses

Costs that do not vary with the level of production or sales, such as rent, salaries, and insurance premiums.

Variable Expenses

These are costs that change in proportion to the activity of a business.