Solved: Suppose that we have assumed the straight-line

Chapter , Problem 112MEE

(choose chapter or problem)

Suppose that we have assumed the straight-line regression model

$Y=\beta_{0}+\beta_{1} x+\epsilon$

but the response is affected by a second variable $x 2$ such that the true regression function is

$E(Y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}$

Is the estimator of the slope in the simple linear regression model unbiased?

Equation Transcription:

$Y={\beta{}}_{0}+{\beta{}}_{1}x+ϵ$

$x2$

$E(Y)={\beta{}}_{0}+{\beta{}}_{1}{x}_{1}+{\beta{}}_{2}{x}_{2}$

Text Transcription:

Y=\beta_0+\beta_1 x+\epsilon

E(Y)=\beta_0+\beta_1 x_1+\beta_2 x_2

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