Suppose that X₁ is measured with error. Y_i = $\beta$₀ + $\beta$₁X_1i + $\varepsilon$_i X_i = X*_1i + $\nu$_i Which of the following is most accurate? A) The estimate of $\beta$₁hat will be larger than it should be. B) The estimate of $\beta$₁hat will be smaller than it should be. C) $\beta$₁hat will be biased toward zero. D) We know $\beta$₁hat will be biased, but do not know which direction.

Question

Quizplus · Accepted Answer

According to the equation, the estimate of F1F1F1S1βF1F1F10₁ will be biased towards zero because of the error term in the equation. This means that the estimated value of F1F1F1S1βF1F1F10₁ will be consistently lower than the true value, even with infinite amounts of data. Therefore, option C is the most accurate.

Suppose That X1 Is Measured with Error β\betaβ 0 β\betaβ

Suppose That X₁ Is Measured with Error $\beta$ ₀ $\beta$