Question: On January 28, 1996, the space shuttle Challenger exploded and seven astronauts were killed. Prior to the launch, the predicted atmospheric temperature was for freezing weather at the launch site. Engineers for Morton Thiokol 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 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 attached in the Excel spreadsheet.

1. Construct a scatter diagram for the seven flights in which there was O-ring damage (O-ring damage index ≠ 0). What conclusions, if any, can you draw about the relationship between atmospheric temperature and O-ring damage?
2. Construct a scatter diagram for all 23 flights.
3. Explain any differences in the interpretation of the relationship between atmospheric temperature and O-ring damage in (a) and (b).
4. Based on the scatter diagram in (b), provide reasons for why a prediction should not be made for an atmospheric temperature of 31° F, the temperature on the morning of the launch of the Challenger.
5. Although the assumption of a linear relationship may not be valid, fit a simple linear regression model to predict O-ring damage based on atmospheric temperature.
6. Plot the straight line found in (e) on the scatter diagram developed in (b).
7. Based on the results of (f), do you think a straight line is an appropriate model for these data? Explain.
8. Perform a residual analysis. What conclusions do you reach?

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