This question is a Ph.D. level question, and it has all the needed information.

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This question is a Ph.D. level question, and it has all the needed information. Please answer with details, many thanks!

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 X gender (1 if female, 0 if male), and marital if married, 0 if not). Table below gives the efficient estimates obtained in (i) Least squares regression and and, Nonlinear least-squares estimates of the logistic regression of Y on X1 X2, (ii) parenthesis model E(YIX1, X2) G(z), where Z Bo B1x1 +BrX2, and /(1 In of the are the conventional standard errors of the coefficient estimates Also tabulated are the means conditioning variables (regressors). Linear regression Logistic model Sample means 1.00 0.192 (0.26) (0.032 0.46 -0.13 (0.28). (0.032 -0.74 0.66 0.08 (0.29) (0.03) (a) Consider a married woman. According to the estimated logistic function which an single man and 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

Explanation / Answer

The given logistic regression can be written as

Log(p/(1-p)) =-1.65-1.01X1- 0.74 X2

For a single man both the variable X1 and X2=0 and for a married woman the variables X1 and X2 equal to 1.

Subsitute the value individually we get

Single Man,Log(p/1-p) =-1.65

Solve for p ,we get p= 0.1611

Married woman ,Lg(p/(1-p)) =-1.65-1.01*1-0.74*1 =-3.4

Solve for p,we get ,p = 0.0323

Odd ratio

Odd of being selected for single man = 0.1611/(1-0.1611)= 0.1920

Odds of being selected for married woman = 0.0323/(1-0.0323) = 0.0334

Odd ratio =-.1920/0.0334 =5.75

Thus the odds of being selected by a single man is 5.75 larger as compared to married woman.

b)Considering from the linear relation perspective,doing the same thing as above subsitite the value of X1 and X2 for both the single man and single woman,we get

For single man ,Y= 0.192

For married woman ,Y =0.192-0.13+0.08 = 0.142

We can see that the value of 0.192 is more than 0.142 therefore we can say that single man has more chance of getting into union as the expected value is more close to 1.Thus,we get the same answer as we got in case of logistic regression model.

However,Logitic regression model is the most appropriate to make a conclusion as the dependent variable is nominal.

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