Question

Consider the following regression output: Suppose the true relationship of Y and X, Z is given by $Y_i = \beta_1 X_i + \beta_2 Z_i + \epsilon_i$ under classical assumptions. Now, assume that you estimate $\beta_1$ by regressing $Y_i$ on $X_i$ only as $Y_i = \hat{\beta}_1 X_i + \hat{\epsilon}_i$ Then, find $E(\hat{\beta}_1)$. Is $\hat{\beta}_1$ unbiased?

          Consider the following regression output:
Suppose the true relationship of Y and X, Z is given by
$Y_i = \beta_1 X_i + \beta_2 Z_i + \epsilon_i$
under classical assumptions. Now, assume that you estimate $\beta_1$ by regressing $Y_i$ on $X_i$ only as
$Y_i = \hat{\beta}_1 X_i + \hat{\epsilon}_i$
Then, find $E(\hat{\beta}_1)$. Is $\hat{\beta}_1$ unbiased?

Consider the following regression output:
Suppose the true relationship of Y and X, Z is given by
Yi = β1 Xi + β2 Zi +
under classical assumptions. Now, assume that you estimate β1 by regressing Yi on Xi only as
Yi = β̂1 Xi + ϵ̂i
Then, find E(β̂1). Is β̂1 unbiased?

Added by Rocio G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

04/12/2023

Step 1

An estimator is unbiased if its expected value is equal to the true value of the parameter being estimated. In this case, we want to determine if the estimator of B, denoted as B̂, is unbiased. Show more…

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Consider the following regression output: Suppose the true relationship of Y and X,Z is given by Yi = B1Xi + B2Zi + ei under classical assumptions. Now, assume that you estimate , by regressing Yi on Xi only as Yi= BXi + ei Then, find E(). Is unbiased?