In the Case of a Simple Regression, Where the Independent

question 49

Multiple Choice

In the case of a simple regression, where the independent variable is measured with i.i.d. error,

• A) \(\hat { \beta } _ { 1 } \stackrel { p } { \longrightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }\)
• B) \(\hat { \beta } _ { 1 } \stackrel { p } { \longrightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w 1 } ^ { 2 } }\)
• C) \(\hat { \beta } _ { 1 } \stackrel { p } { \longrightarrow }
• \frac { \sigma _ { w } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }\)
• D) \(\hat { \beta } _ { 1 }\stackrel { p } { \longrightarrow }
• \beta _ { 1 } + \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } }\)

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Definitions:

Mathematical Equality

A statement indicating that two mathematical expressions or quantities are identical in value.

Debits And Credits

The two sides of every financial transaction in double-entry bookkeeping; debits must equal credits for each entry to balance.

Alphabetic Order

A method of arranging items or information according to the sequence of the letters in the English alphabet.

Journal

A record where all financial transactions are initially noted in chronological order before being transferred to accounts in the ledger.