7. Suppose we are interested in the relationship of the union status variable Y (= 1; if in union, = 0,if not in union) to the conditioning variables X₁ = gender (1 if female, 0 if male), and X2 = maritalstatus (1 if married, 0 if not).Table below gives the coefficient estimates obtained in (i) Least squares regression of Y on X₁ and X₂,and, (ii) Nonlinear least-squares estimates of the logistic regression model E(YX1, X2) = G(Z), whereZ=80+ B₁X1+B₂X2, and G(Z) = e²/(1+e2). In parenthesis are the conventional standard errors of thecoefficient estimates. Also tabulated are the means of the conditioning variables (regressors). 1X₁X₂Linear regression Logistic model Sample means0.192(0.03)-0.13(0.03)0.08(0.03)-1.65(0.26)-1.01(0.28)-0.74(0.29)1.000.460.66(a) Consider an married man and a unmarried woman. According to the estimated logistic function,which of them has the higher probability of being a union member? How much larger?(b) Determine whether the linear function gives approximately the same answer to those questionsabove.

Given,linear regressionLogistic modelsample…

1 X₁ X₂ Linear regression Logistic model Sample means 0.192 (0.03) -0.13 (0.03) 0.08 (0.03) -1.65 (0.26) -1.01 (0.28) -0.74 (0.29) 1.00 0.46 0.66 (a) Consider an married man and a unmarried woman. According to the estimated logistic function, which of them has the higher probability of being a union member? How much larger? (b) Determine whether the linear function gives approximately the same answer to those questions above.

1 X₁ X₂ Linear regression Logistic model Sample means 0.192 (0.03) -0.13 (0.03) 0.08 (0.03) -1.65 (0.26) -1.01 (0.28) -0.74 (0.29) 1.00 0.46 0.66 (a) Consider an married man and a unmarried woman. According to the estimated logistic function, which of them has the higher probability of being a union member? How much larger? (b) Determine whether the linear function gives approximately the same answer to those questions above.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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