Downer data For unknown reasons, dairy cows sometimes become recumbent—they lay down. Called downers, these cows may have a serious illness that may lead to death of the cow. These data are from a study of blood samples of over 400 downer cows studied at the Ruakura New Zealand Animal Health Laboratory during 1983–1984. A variety of blood tests were performed, and for many of the animals, the outcome (survived, died, or animal was killed) was determined. The goal is to see if survival can be predicted from the blood measurements. The variables in the data file downer.txt are described in Table 12.7. These data were collected from veterinary records, and not all variables were recorded for all cows.

1.       Consider first predicting Outcome from Myopathy. Find the fraction of surviving cows of Myopathy = 0 and for Myopathy = 1.

2.       Fit the logistic regression with response Outcome, and the single predictor Myopathy. Obtain a 95% confidence interval for coefficient for Myopathy, and compute the estimated decrease in odds of survival when Myopathy = 1. Obtain the estimated probability of survival when Myopathy = 0 and when Myopathy = 1, and compare with the observed survival fractions in Problem 12.1.1.