On January 28, 1986, a routine launch was anticipated for the Challenger space shuttle. Seventy-three seconds into the flight, disaster happened: the shuttle broke apart, killing all seven crew members on board. An investigation into the cause of the disaster focused on a critical seal called an O-ring, and it is believed that damage to these O-rings during a shuttle launch may be related to the ambient temperature during the launch. The table below summarizes observational data on O-rings for 23 shuttle missions, where the mission order is based on the temperature at the time of the launch. temp gives the temperature in Fahrenheit, damaged represents the number of damaged O-rings, and undamaged represents the number of O-rings that were not damaged.
orings = read.csv('http://people.hsc.edu/faculty-staff/blins/classes/spring17/math222/data/challenger.csv')
orings## temp damaged undamaged
## 1 53 5 1
## 2 57 1 5
## 3 58 1 5
## 4 63 1 5
## 5 66 0 6
## 6 67 0 6
## 7 67 0 6
## 8 67 0 6
## 9 68 0 6
## 10 69 0 6
## 11 70 1 5
## 12 70 0 6
## 13 70 1 5
## 14 70 0 6
## 15 72 0 6
## 16 73 0 6
## 17 75 0 6
## 18 75 1 5
## 19 76 0 6
## 20 76 0 6
## 21 78 0 6
## 22 79 0 6
## 23 81 0 6Make a scatterplot that shows the relationship between temperature and the proportion of the O-rings that were damaged.
Find the best fit logistic regression model for this data.
The actual ambient temperature on the day of the Challneger launch was 36 degrees Fahrenheit. That was 15 degrees colder than the next coldest shuttle launch up to that point. It’s not a great idea to extrapolate beyond the data you have in any model, but what does the model say about the probability of O-ring failure on a day that cold?