If the Three Least Squares Assumptions Hold, Then the Large $\widehat { \beta } _ { 1 }$

question 49

Multiple Choice

If the three least squares assumptions hold, then the large sample normal distribution of $\widehat { \beta } _ { 1 }$ is

• A) \(N \left( 0 , \frac { 1 } { n } \frac { \left. \operatorname { var } \left[ X _ { i } - \mu _ { X } \right) u _ { i } \right] } { \left[ \operatorname { var } \left( X _ { i } \right) \right] ^ { 2 } } \right)\)
• B) \(N \left( \beta _ { 1 } , \frac { 1 } { n } \frac { \left. \operatorname { var } \left( u _ { i } \right) \right] ^ { 2 } } { \left[ \operatorname { var } \left( X _ { i } \right) \right] ^ { 2 } } \right)\)
• C) \(N \left( \beta _ { 1 } , \frac { \sigma _ { u } ^ { 2 } } { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) ^ { 2 } } \right.\)
• D) \(N \left( \beta _ { 1 } , \frac { 1 } { n } \frac { \left. \operatorname { var } \left( u _ { i } \right) \right] } { \left[ \operatorname { var } \left( X _ { i } \right) \right] ^ { 2 } } \right)\)

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Definitions:

Average Inventory

The mean value of the inventory of goods held over a certain period of time, usually calculated by averaging the beginning and ending inventory of a given period.

Quarterly Inventories

An accounting practice where a company counts and records its inventory four times a year, typically at the end of each fiscal quarter.

Beginning Inventory

The recorded value of inventory held by a business at the start of an accounting period.

Average Inventory

The mean value of inventory within a certain period, calculated by averaging the sum of starting and ending inventory.