Chapter 13, Problem 80PS

On January 28, 1986, the space shuttle Challenger exploded, and seven astronauts were killed. Prior to the lunch, the predicted atmospheric temperature was for freezing weather at the lunch site. Engineers for Morton Thiokol (the manufacturer of the racket motor) prepared charts to make the case that the launch should not take place due to the cold weather. These arguments were rejected, and the launch, and the launch tragically took place. Upon investigation after the tragedy, experts agreed that the disaster occurred because of leaky rubber O-rings that did not seal properly due to the cold temperature. Data indicating the atmospheric temperature at the time of 23 previous launches and the O-ring damage index are stored in O-Ring.

O -ring damage index are stored in O-Ring.

Note: Data from flight 4 is omitted due to unknown O-ring condition.

a. Construct a scatter plot for the seven flights in which there was O-ring damage (O-ring damage index $\ne$ 0). What conclusions, if any, can you reach about the relationship between atmospheric temperature and O-ring damage?

b. Construct a scatter plot for all 23 flights.

c. Explain a difference in the interpretation of the relationship between atmospheric temperature and O-ring damage in (a) and (b).

d. Based on the scatter plot in (b), provide reason why a prediction should not be made for an atmospheric temperature of ${31}^{\circ }\text{F,}$ The temperature on the morning of the launch of the Challenger.

e. Although the assumption of a linear relationship may not be valid for the set of 23 flights, fit a simple linear regression model to predict O-ring damage, based on atmospheric temperature.

f. Include the prediction line found in (e) on the scatter plot developed in (b).

g. Based on the results in (f), do you think a linear model is appropriate for these data? Explain.

h. Perform a residual analysis. What conclusions do you reach?