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(21) 4. Logistic regression is applied in a study on low birth weights of babies for a sample of size n = 189. The response

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(21) 4. Logistic regression is applied in a study on low birth weights of babies for a sample of size n = 189. The response variable is y : low : 1 if the birth weight is g 2500g and y : 0 otherwise. Explanatory variables are: age:age of mother; lwt:weight (in pounds) of mother at last menstrual period; race:l white (baseline), race:2 for black, race:3 for other; smoke:1 for smoker and :0 otherwise; ptl:# of previous premature labour; ht:l for history of hypertension and :0 otherwise; ui:1 for presence of uterine irritability and :0 otherwise. Summaries of regression equations tted to (i) all of these explanatory variables and (ii) a subset are given below. fit 1=glm(low\"age+lwt+race+smoke+ptd+ht+ui , family=binomial) fit2=glm(low\"lwt+race+smoke+ht , family=binomial) Note that race2 and race3 below are binary dummy variables. fit1 fit2 Estimate Std.Err0r 2 value Estimate Std.Error 2 value (Intercept) 0.4644 1.2047 0.39 0.3520 0.9244 0.38 age -0.0271 0.0364 -0.74 th 0.0152 0.0069 -2.19 0.0179 0.0068 2.63 race2 1.2632 0.5265 2.40 1.2877 0.5216 2.47 race3 0.8616 0.4392 1.96 0.9436 0.4234 2.23 smoke 0.9233 0.4008 2.30 1.0716 0.3875 2.77 ptl 0.5418 0.3463 1.56 ht 1.8337 0.6918 2.65 1.7492 0.6908 2.53 ui 0.7586 0.4594 1.65 Residual deviance: 201.43 Residual deviance: 208.25 AIC: 219.4 AIC: 220.2 Explain the binary dummy variable race2 (that is, how is it dened). Based on the summaries, which of the two tted logistic regressions appear to be better. Mention the criterion or criteria for your decision. With the logistic model fit2, what is the predicted probability of low birth weight for a black mother with lwt:130 pounds, nonsmoking and no history of hypertension. With the logistic model fit2 and lwt, race and ht held at xed values (such as 150, white, 1 respectively), what is the odds ratio for the increased risk of low birth weight for a smoking versus nonsmoking mother. For the odds ratio is (d), what is an interval estimate with 95% condence. [This is a thinking question without much calculations] Everything else being constant, which of the three races (white, black, other) has highest probability of low birth weight. Indicate the summaries/coefcients above used to make this conclusion. For the model summarized as glm(y\"x1+x2+x3,family:binomial), with data (yi,xi1,:ci2,:ci3), 7L : 1,. . . ,n, write the loglikelihood that leads to the maximum likelihood estimate (80, 31,32, 5'3)

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