Suppose We Omit X₃ (A Variable That Does Not Affect $\beta$

question 2

Multiple Choice

Suppose we omit X₃ (a variable that does not affect Y) from the following in a bivariate model
Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\beta$ ₂X_2i + $\varepsilon$ _i
And suppose each of the independent variables are correlated with the other independent variables. What is the consequence of omitting X₃ on $\beta$ ₁hat?

• A) No effect; \(\beta\)₁hat will be unbiased.
• B) The bias will depend only on the correlation of X₁ and X_3.
• C) The bias will depend on the correlations of all the independent variables_.
• D) The bias will depend only on the correlation of X₁ and X_2.

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Definitions:

Issued Shares

Represents the total number of shares that have been allocated by a corporation and are held by shareholders, including both public investors and company officers or insiders.

Stockholders' Equity

The remaining stake in a company's assets once all debts are subtracted, indicating the shareholders' ownership claim.

Authorized Shares

The maximum number of shares that a corporation is legally allowed to issue, as specified in its charter.

Common Stock

A form of corporate equity ownership, a type of security that represents ownership in a corporation and entitles the shareholder to vote on corporate matters.