For the OLS Estimator $\hat { \beta}$ = $X ^ { \prime }$

question 33

Essay

For the OLS estimator $\hat { \beta}$ = ( $X ^ { \prime }$ X)^-1
$X ^ { \prime }$ Y to exist, X'X must be invertible. This is the case when X has full rank. What is the rank of a matrix? What is the rank of the product of two matrices? Is it possible that X could have rank n? What would be the rank of X'X in the case n<(k+1)? Explain intuitively why the OLS estimator does not exist in that situation.

---

Definitions:

Equal Employment Opportunity

Policies and regulations ensuring that all individuals have an equal chance for employment, without discrimination on the basis of race, color, religion, sex, or national origin.

Equal Pay

A principle requiring that men and women be given equal pay for equal work in the same establishment.

Broad Bands

A strategy in pay structure where a wide range of salaries is offered within a single pay band, allowing for greater flexibility in employee payment.

Promoting Employees

The process of advancing an employee's rank or position within a company, often accompanied by an increase in salary and responsibilities.