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:

Capital Intensity Ratio

A metric that measures the amount of capital needed per unit of output, indicating the extent to which a firm or economy relies on capital to produce goods and services.

Retention Ratio

The proportion of earnings that is not distributed as dividends to shareholders, but is retained by the company for reinvestment.

Cash Dividends

Distributions of profits from a corporation to its shareholders as payments.

Selling and Administrative Expenses

Indirect costs not directly tied to product production, including marketing, management, rent, and utilities.