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?

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Definitions:

Sociocultural Approach

The view that social and cultural factors may be just as powerful as evolutionary and physiological factors in affecting behavior and mental processing and that these factors must be understood when interpreting the behavior of others.

Systems Theory

An interdisciplinary study of systems in general, with the aim of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research.

Neuroscience

The scientific study of the nervous system, aimed at understanding the biological basis of behavior, thought, and emotion.

Eclectic

Deriving ideas, style, or taste from a broad and diverse range of sources, often resulting in a unique and comprehensive approach.