Your textbook derives the OLS estimator as $\hat { \beta }$ = $\left( X ^ { \prime } \right.$ X)^-¹
$X ^ { \prime }$ ^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 $X ^ { \prime }$ X in this case?

Question

Your textbook derives the OLS estimator as

\hat { \beta }

=

\left( X ^ { \prime } \right.

X)^-¹

X ^ { \prime }

^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 ^ { \prime }

X in this case?

Quizplus · Accepted Answer

The Answer of Your textbook derives the OLS estimator as $\hat { \beta }$ = $\left( X ^ { \prime } \right.$ X)^-¹ $X ^ { \prime }$ ^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 $X ^ { \prime }$ X in this case?

Your Textbook Derives the OLS Estimator As β^\hat { \beta }β^​

Your Textbook Derives the OLS Estimator As $\hat { \beta }$