Your Textbook Derives the OLS Estimator As Show That the Estimator Does Not Exist If There Are

question 38

Essay

Your textbook derives the OLS estimator as $\hat { \boldsymbol { \beta } } = \left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 } \boldsymbol { X } ^ { \prime } \boldsymbol { Y }$ Show that the estimator does not exist if there are fewer observations than the number of
explanatory variables, including the constant.What is the rank of X′X in this case?

---

Definitions:

Data Collection

The process of gathering and measuring information on variables of interest in an organized and systematic way for research purposes.

Causal Relationship

A connection between two variables where a change in one directly influences the change in the other.

Spurious

Relating to a relationship or finding that appears to be valid but is actually due to unrelated factors or variables.

Sociology Mid-Term

A Sociology Mid-Term usually refers to a midterm examination in a sociology course, assessing students' understanding of sociological theories, concepts, and methodologies studied in the first half of the course.