Dr. Hackney STA Solutions pg 194

Dr. Hackney STA Solutions pg 194 - 12-4Solutions Manual for...

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Unformatted text preview: 12-4Solutions Manual for Statistical InferenceFor the logit model we haveEstimateStd. Errorz valuePr(>|z|)Intercept15.04297.37192.041.0413temp-.2322.1081-2.147.0318and for the probit model we haveEstimateStd. Errorz valuePr(>|z|)Intercept8.770843.862222.271.0232temp-.13504.05632-2.398.0165Although the coefficients are different, the fit is qualitatively the same, and the probabilityof failure at 31, using the probit model, is.9999.12.19 a. Using the notation of Example 12.3.1, the likelihood (joint density) isJYj=1e+xj1 +e+xjy*j11 +e+xjnj-y*j=JYj=111 +e+xjnjejy*j+jxjy*j.By the Factorization Theorem,jy*jandjxjy*jare sufficient.b. Straightforward substitution.12.21 Sinceddlog(/(1-)) = 1/((1-)),Var log1-1(1-)2(1-)n=1n(1-)12.23 a. Ifai= 0,EXiaiYi=Xiai[+xi+(1-)] =Xiaixi=forai=xi-x.b.E(Y-x) =1nXi[+xi+(1-)]-x=+(1-),so the least squares estimateais unbiased in the modelYi=+xi+i, where...
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