In the context of a controlled experiment, consider the simple linear regression formulation Yi = β0 + β1Xi + Ui. Let the Yi be the outcome, Xi the treatment level when the treatment is binary, and Ui contain all the additional determinants of the outcome. Then: a. the OLS estimator of the slope will be inconsistent in the case of a randomly assigned Xi since there are omitted variables present. b. Xi and Ui will not be independently distributed if the Xi are randomly assigned. c. β0 represents the causal effect of X on Y when X is zero. d. E(Y|X= 1) is the expected value for the treatment group. e. All of the above. f. None of the above.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.4: Linear Regression
Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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In the context of a controlled experiment, consider the simple linear regression formulation Yi = β0 + β1Xi + Ui. Let the Yi be the outcome, Xi the treatment level when the treatment is binary, and Ui contain all the additional determinants of the outcome. Then:

a.

the OLS estimator of the slope will be inconsistent in the case of a randomly assigned Xi since there are omitted variables present.

b.

Xi and Ui will not be independently distributed if the Xi are randomly assigned.

c.

β0 represents the causal effect of X on Y when X is zero.

d.

E(Y|X= 1) is the expected value for the treatment group.

e.

All of the above.

f.

None of the above.

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