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
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Chapter1: Making Economics Decisions
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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 = marital
status (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), where
Z=80+ B₁X1+B₂X2, and G(Z) = e²/(1+e2). In parenthesis are the conventional standard errors of the
coefficient estimates. Also tabulated are the means of the conditioning variables (regressors).
Transcribed Image Text: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 = marital status (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), where Z=80+ B₁X1+B₂X2, and G(Z) = e²/(1+e2). In parenthesis are the conventional standard errors of the coefficient estimates. Also tabulated are the means of the conditioning variables (regressors).
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.
Transcribed Image Text: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.
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