Your Textbook Only Analyzed the Case of an Error-In-Variables Bias$\bar X$

Question

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The Answer is This would have an effect similar to changing the units of measurement. The measurement error is not random here, and the bias can be determined exactly.
For the case

\bar X

_i= X_i + a, the slope will be unaffected and the usual properties for the OLS slope estimator will hold. However, since

\bar { X }

=

\bar { X }

+ a and

\hat { \beta }

₀ =

\bar { Y }

-

\hat { \beta }

₁

\bar { X }

)-

\hat { \beta }

₁a, the intercept will be underestimated by the constant measurement error times the slope.
For the case

\bar { X }

_i = bX_i, the intercept is unaffected, but the ratio of the estimated slope with measurement error to the slope without measurement error is b.

Your Textbook Only Analyzed the Case of an Error-In-Variables Bias $\bar X$

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Your Textbook Only Analyzed the Case of an Error-In-Variables Bias Xˉ\bar XXˉ

Definitions:

Your Textbook Only Analyzed the Case of an Error-In-Variables Bias $\bar X$