University of Applied Sciences and Arts Western SwitzerlandENGINEERIN 100Logistic regression solutions

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Summative Quiz 2 (Simple Logistic Regression) Solutions: 1. Observational data were collected by researchers on 189 consecutive births at Baystate Medical Center in Springfield, Massachusetts (USA)1... . The researchers were interested in using logistic regression to identify maternal and other factors associated with the low birth weight births (as per the World Health Organization’s definition of low birth weight as < 2500 grams). The average birth weight for the 189 infants in the sample was 2,945 grams (s= 729, range -709 -4,990 grams) with 59 infants (30%) meeting the low birth weight criteria. The first regression relates the log (ln) odds of low birth weight (LBW) to mother’s smoking status during pregnancy: ln(???? ?? ???) = -1.09 + 0.70?7, where x1= 1 if the mother smoked during pregnancy (and 0 if not). The estimated standard error of the slope of x1 is 0.32. What is the estimated odds ratio for being low birth weight for children of mothers who smoked during pregnancy, compared to mothers who did not smoke during pregnancy? Answer: 2. (this item references the same logistic regression results as item #1) Compute and report a 95% CI for the odds ratio from the previous question (theodds ratio for being low birth weight for children of mothers who smoked during pregnancy, compared to mothers who did not smoke during pregnancy). Answer: 3. (this item references the same linear regression results as item #1) What is the estimated probability of being low-weight (proportion of low birth weight infants) for babies born to mothers who did not smoke during pregnancy? Answer: 4. (this item references the same logisitic regression results as item #1) What is the estimated probability of being low-weight (proportion of low birth weight infants) for babies born to mothers who smoked during pregnancy? Answer: 5. (this item references the same logistic regression results as item #1) What is the estimated relative risk for being low birth weight for children of mothers who smoked during pregnancy, compared to mothers who did not smoke during pregnancy? Answer: 6. The next analysis involves estimating the association between low birth weight and age of the mother (at the time of birth). The following “lowess” plot show the association between the log (ln) odds of infants being low birthright and the age of the mothers. = The following logistic regression relates the two measures: ln(???? ?? ???) = 0.38 + -0.05?7, where x1= 1 age of the mother. The estimated standard error of the slope of x1 is 0.03, and the range of mother’s ages is 14-45 years. What is the nature of the estimated relationship between the risk infants being low birth weight and the age of the mother? Answer: 7. (This item references the same logistic regression results as item #6) What is the estimated odds ratio, and 95% CI for the odds of delivering a low birth weight baby for two groups of mothers who differ by 1 year in age? Answer: 8. (This item references the same logistic regression results as item #6) Is the relationship between low birth weight and mothers' ages statistically significant (α=0.05)? Answer: 9. (This item references the same logistic regression results as item #6) What is the estimated odds ratio, and 95% CI for the odds of delivering a low birth weight baby for 40 years old mothers compared to 30 year old mothers? Answer: 10. (This item references the same logistic regression results as item #6) What is the estimated probability of a 30 year old mother giving birth to a low birth weight baby? Answer: [Show More]

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