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=1eα+βxj1 +eα+βxjy*j11 +eα+βxjnj-y*j=JYj=111 +eα+βxjnjeα∑jy*j+β∑jxjy*j.By the Factorization Theorem,∑jy*jand∑jxjy*jare sufficient.b. Straightforward substitution.12.21 Sinceddπlog(π/(1-π)) = 1/(π(1-π)),Var logˆπ1-ˆπ≈1π(1-π)2π(1-π)n=1nπ(1-π)12.23 a. If∑ai= 0,EXiaiYi=Xiai[α+βxi+μ(1-δ)] =βXiaixi=βforai=xi-¯x.b.E(¯Y-β¯x) =1nXi[α+βxi+μ(1-δ)]-β¯x=α+μ(1-δ),so the least squares estimateais unbiased in the modelYi=α+βxi+i, where...
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