A sample of subjects were asked their opinion about refurbishing the subway in New York (support, oppose). For the explanatory variables gender (female, male), religious affiliation (Protestant, Catholic, Jewish), and political party affiliation (Democrat, Republican, Independent), the model for the probability π of supporting legalized abortion, logit(pi) = alpha + betagh + betari + betapj has reported parameter estimates (setting the parameter for the last category of a variable equal to 0.0 and alpha^ = -0.11, beta^g1 = 0.16, beta^g2 = 0.0, beta^r1 = -0.57, beta^r2 = -0.66, beta^r3 =0.0, beta^p1 =0.84, beta^p2 = -1.67, beta^p3 =0.00) . Interpret how the odds of supporting refurbishment depend on gender. Find the estimated probability of supporting refurbishment for (i) male Catholic Republicans and (ii) female Jewish Democrats. If we defined parameters such that the first category of a variable has value 0, then what would beta^g2 equal? Show then how to obtain the odds ratio that describes the conditional effect of gender. If we defined parameters such that they sum to 0 across the categories of a variable, then what would beta^g1 and beta^g2 equal? Show then how to obtain the odds ratio that describes the conditional effect of gender.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4A: Problems In Applying The Linear Regression Model

Section: Chapter Questions

Problem 2E

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A sample of subjects were asked their opinion about refurbishing the subway in New York (support, oppose). For the explanatory variables gender (female, male), religious affiliation (Protestant, Catholic, Jewish), and political party affiliation (Democrat, Republican, Independent), the model for the probability π of supporting legalized abortion,

logit(pi) = alpha + beta^g_h+ beta^r_i + beta^p_j

has reported parameter estimates (setting the parameter for the last category of a variable equal to 0.0 and alpha^ = -0.11, beta^^g₁ = 0.16, beta^^g₂ = 0.0, beta^^r₁ = -0.57, beta^^r₂ = -0.66, beta^^r₃ =0.0, beta^^p₁ =0.84, beta^^p₂ = -1.67, beta^^p₃ =0.00) .

Interpret how the odds of supporting refurbishment depend on gender.
Find the estimated probability of supporting refurbishment for (i) male Catholic Republicans and (ii) female Jewish Democrats.
If we defined parameters such that the first category of a variable has value 0, then what would beta^^g₂equal? Show then how to obtain the odds ratio that describes the conditional effect of gender.
If we defined parameters such that they sum to 0 across the categories of a variable, then what would beta^^g₁ and beta^^g₂ equal? Show then how to obtain the odds ratio that describes the conditional effect of gender.

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