A study was conducted to determine if a relationship existed between infant birthweight and the likelihood of that infant surviving severe idiopathic respiratory distress syndrome ( SIRDS).18 Data from 50 infants who displayed this syndrome are in the SIRDS file.
a. Create a logistic regression model using birthweight to estimate the probability of survival. Interpret the model in terms of the odds ratio.
b. Use the Wald statistic to create a 90% confidence interval for the odds ratio.
c. Test H0: β1 = 0 versus Ha: β1 ≠ 0 using both Wald’s test and the likelihood ratio test. State your conclusion based on these tests.
d. Conduct the Hosmer-Lemeshow test to assess how well the model fits the data. Ensure that you have appropriate sample sizes in each group.
e. Explain why the Pearson and deviance goodness-of-fit tests are not appropriate.
f. Report and interpret Somers’D, Goodman-Kruskal gamma, or Kendall’s tau-a for this logistic regression model.
g. Create histograms of the standardized Pearson residuals and deviance residuals.
h. Create scatterplots of delta deviance, delta chi-square, and delta beta (standardized) versus the expected probabilities.
i. Create scatterplots of delta deviance, delta chi- square, and delta beta (standardized) versus the leverage.
j. Identify any observations (covariate patterns) that appear to be outliers or influential observations.