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.

(a) Each column of the table above represents a different shuttle mission. Examine these data and describe what you observe with respect to the relationship between temperatures and damaged O-rings.

(b) Failures have been coded as 1 for a damaged O-ring and 0 for an undamaged O-ring, and a logistic regression model was t to these data. A summary of this model is given below. Describe the key components of this summary table in words.

(c) Write out the logistic model using the point estimates of the model parameters.

(d) Based on the model, do you think concerns regarding O-rings are justified? Explain.

Shuttle Mission Temperature Damaged Undamaged Shuttle Mission Temperature Damaged Undamaged 1 2 3 53 57 58 5 1 1 1 1.0 5 F 5 13 14 15 70 70 72 1 0 0 5 6 6 4 5 63 66 1 0 5 6 16 73 0 6 6 67 7 8 67 67 0 6 0 0 6 6 17 18 19 75 75 76 0 1 0 6 5 6 9 10 11 68 69 70 0 0 1 6 6 5 20 21 76 78 0 6 22 23 79 81 0 6 0 0 6 6 12 70 0 6