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Does the inclusion of the irrelevant variable x3 affect the

Suppose that the "true" model is

Yi = β1 + β2 X2i + ut (1)

but we add an "irrelevant" variable X3 to the model (irrelevant in the sense that the true β3 coef?cient attached to the variable X3 is zero) and estimate

Yi = β1 + β2 X2i + β3 X3i + vi (2)

a. Would the R2 and the adjusted R2 for model (2) be larger than that for model (1)?

b. Are the estimates of β1 and β2 obtained from (2) unbiased?

c. Does the inclusion of the "irrelevant" variable X3 affect the variances of βˆ1 and βˆ2 ?

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