Dataset: variable grmhem is a dichotomous random variable (germinal matrix hemorrhage) --> 1 hemorrhage occurred, 0 it did not. toxemia = tox variable; 1 = yes, 0 = no.

sbp sex tox grmhem gestage apgar5 43 Male No No 29 7 51 Male No No 31 8 42 Female No No 33 0 39 Female No No 31 8 48 Female Yes No 30 7 31 Male No Yes 25 0 31 Male Yes No 27 7 40 Female No No 29 9 57 Female No No 28 6 64 Female Yes No 29 9 46 Female No No 26 7 47 Female No Yes 30 6 63 Female No No 29 8 56 Female No No 29 1 49 Male No No 29 8 87 Male No No 29 7 46 Female No No 29 8 66 Female No No 33 8 42 Female Yes No 33 8 52 Female No No 29 7 51 Male No No 28 7 47 Female No No 30 9 54 Male No No 27 4 64 Male No No 33 9 37 Female No No 32 7 36 Male Yes No 28 3 45 Female No Yes 29 7 39 Male No No 28 7 29 Female No No 29 4 61 Female No No 30 3 53 Male No No 31 7 64 Female No No 30 7 35 Female No No 31 6 34 Male No No 29 9 62 Female No No 27 7 59 Female No No 27 8 36 Male No No 27 9 47 Female No No 32 8 45 Male No Yes 31 2 62 Female No Yes 28 5 75 Male Yes No 30 7 44 Male No No 29 0 39 Male No No 28 8 48 Female No Yes 31 7 43 Female Yes No 27 6 19 Female No Yes 25 4 63 Male No No 30 7 42 Male No No 28 6 44 Female No No 28 9 25 Female No No 25 8 26 Female No No 23 8 27 Male No No 27 9 35 Male No No 28 8 40 Male No No 27 7 44 Female No No 27 6 66 Male No No 26 8 59 Female No No 25 3 24 Female No No 23 7 40 Female No Yes 26 3 49 Female No No 24 5 53 Male Yes No 29 9 45 Female No No 29 9 50 Male No Yes 27 8 64 Male No No 30 7 48 Female No No 30 6 48 Female No Yes 32 4 58 Female Yes No 33 7 67 Female No No 27 8 40 Female No Yes 31 8 48 Female No No 26 8 36 Male No No 27 5 44 Male No No 27 6 53 Female Yes No 35 9 45 Female Yes No 28 6 54 Male No No 30 8 44 Male Yes No 31 2 42 Male No No 30 5 50 Female No No 27 0 48 Female No No 25 5 29 Female No Yes 25 5 30 Female No Yes 26 2 36 Female No No 29 0 44 Female No No 29 0 46 Female Yes No 34 9 51 Male Yes No 30 4 51 Male No No 29 5 43 Male Yes No 33 7 48 Male No No 30 5 52 Male No No 29 8 43 Male No No 24 6 42 Male Yes No 33 8 48 Male No Yes 25 5 49 Female Yes No 32 8 62 Male Yes No 31 7 45 Male No No 31 9 51 Female Yes Yes 31 6 52 Male No No 29 8 47 Male Yes No 32 5 40 Female Yes No 33 8 50 Female No No 28 7 

a. Using germinal matrix hemorrhage as the response, fit a logistic model where x₁ is five minute Apgar score. Write the equation and interpret ₁, the estimated coefficient of Apgar score.

b. If a particular child has a five-minute Apgar score of 3, what is the predicted probability that this child will experience a brain hemorrhage? What is the probability if the child's score is 7?

c. At the 0.05 level of significance, test the null hypothesis that the population parameter ₁ is equal to 0. What do you conclude?

d. Now fit the regression model where x₂ represents toxemia status. Interpret ₂, the estimated coefficient of toxemia.

e. For a child whose mother was diagnosed with toxemia during pregnancy, what is the predicted probability of experiencing a germinal matrix hemorrhage? What is the probability for a child who was not diagnosed with toxemia?

f. What are the estimated odds of suffering a germinal matrix hemorrhage for children whose mothers were diagnosed with toxemia relative to children whose mothers are not.

g. Construct 95% confidence interval for the population odds ratio. Does this interval contain the value 1? What does this tell you?

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