Suppose we omit X₂ from the following in a bivariate model Y_i = $\beta$₀ + $\beta$₁X_1i + $\varepsilon$_i And suppose X₂ is positively related to X₁ and $\beta$₂ is positive, while $\beta$₁is negative. What is the likely effect of omitting X₂ on our estimate of $\beta$₁? A) No effect; $\beta$₁ hat will be unbiased. B) $\beta$₁ hat will be more negative than it should be. C) $\beta$₁ hat will be less negative than it should be. D) $\beta$₁ hat will be biased toward zero.

Question

Quizplus · Accepted Answer

When X₂ is positively related to X₁ and $\beta$₂ is positive, while $\beta$₁is negative, omitting X₂ from the model will result in a more negative estimate of $\beta$₁ than it should be. This is because the positive relationship between X₂ and X₁ will cause X₁ to act as a proxy for X₂ in the model, and the negative relationship between X₂ and Y will be reflected in a more negative estimate of $\beta$₁.

Suppose We Omit X2 from the Following in a Bivariate β\betaβ

Suppose We Omit X₂ from the Following in a Bivariate $\beta$