a Y i \u03b1 log \u03b2 1 \u03b2 2 x i e i where e i N 0 \u03c3 2 b Y i exp \u03b1 log \u03b2 1 x 1 i \u03b2 2 log

# A y i α log β 1 β 2 x i e i where e i n 0 σ 2 b y

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(a)Yi=α+ log(β1+β2xi) +eiwhereei∼ N(0, σ2).(b)Yi= exp{α+ log(β1)x1i+β2log(x2i)}whereYiis a Poisson random variable.(c)Yi=α+β1(x1i+x21i) +eiwhereei∼ N(0, σ2).(d)πi=exp{α+βexi}1+exp{α+βexi}whereYiis binomial with probabilityπiandntrials.(e)Yij= exp[λ+λRi+λCj+βRiβCj] whereYiis a Poisson random variable, andRandCare categorical variables explanatory variables withIandJlevels,respectively.2
2. The data for this problem comes from a study by Brown et al (1983) and concernshow toxaemia in mothers during pregnancy of their first child is related to number ofcigarettes smoked and social class. Variables indicating signs of toxaemia arehypertension and protein urea. The data, which are given below and are availableform the course web-site, consist of the frequency of toxaemic signs exhibited bymothers during pregnancy cross-classified by smoking habits and social class.Analyzed these data. Be sure to explain you model selection strategy, check whetherthe model you select fits the data well, and give an interpretation of the results.HypertensionYesNoCigarettesSocialProtein ureasmokesclassYesNoYesNo0I2882212861–1952457120+130130II50266347851–1913921728420+0153340III278110116431601–19120492142230020+1692323830IV63213526561–19351294664920+740121630V2078232451–1922743432120+7144653
3. The data given below are from the National Longitudinal Survey of Youth (NLSY).

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• Spring '08
• Hong
• Probability theory, Births Exposure Births, Exposure Births Exposure