**Problem 2. (SW 11.8(a-c))** Consider the linear probability model $ Y_i = \beta_0 + \beta_1 X_i + u_i $, and assume that $ E(u_i | X_i) = 0 $.(a) Show that $ P(Y_i = 1 | X_i) = \beta_0 + \beta_1 X_i $.(b) Show that $ \text{var}(u_i | X_i) = (\beta_0 + \beta_1 X_i)[1 - (\beta_0 + \beta_1 X_i)] $. [*Hint: You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).](c) Is $ u_i $ heteroskedastic? Explain.

Answered: Image /qna-images/answer/75ca2087-105f-480e-b635-666874a867fe.jpg

(a) Show that Pr(Yį = 1|X) = Bo+®ıX. (b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (Bo + B₁X;)]. [Hint: You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).] (c) Is u, heteroskedastic? Explain.

(a) Show that Pr(Yį = 1|X) = Bo+®ıX. (b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (Bo + B₁X;)]. [Hint: You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).] (c) Is u, heteroskedastic? Explain.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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**Problem 2. (SW 11.8(a-c))** Consider the linear probability model $ Y_i = \beta_0 + \beta_1 X_i + u_i $, and assume that $ E(u_i | X_i) = 0 $.

(a) Show that $ P(Y_i = 1 | X_i) = \beta_0 + \beta_1 X_i $.

(b) Show that $ \text{var}(u_i | X_i) = (\beta_0 + \beta_1 X_i)[1 - (\beta_0 + \beta_1 X_i)] $. [*Hint: You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).]

(c) Is $ u_i $ heteroskedastic? Explain.

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