Question

The Report of the Presidential Commission on the Space Shuttle Challenger Accident in 1986 shows a plot of the calculated joint temperature in Fahrenheit and the number of O-rings that had some thermal distress. You collect the data for the seven flights for which thermal distress was identified before the fatal flight and produce the accompanying plot. 4 C0 2 50 60 70 80 Temperature (a) Do you see any relationship between the temperature and the number of O-ring failures? If you fitted a linear regression line through these seven observations, do you think the slope would be positive or negative? Significantly differ- ent from zero? Do you see any problems other than the sample size in your procedure?

Answer 1

There is a relationship between the temperature and the number of failures

The regression line can be fitted to have positive slope

The sample size is the major challenge of this procedure. It is too small and makes the relationship unclear.

Explanation:

a) There is a relationship between the temperatures and the number of O - ring failures.

If we observe from the graph, when the temperature is 55⁰F, the number of O rings is 3, as the temperature increases from 55 to around 57, the number of O ring decreases to 1, from 57⁰F to 70⁰F, the number of O rings remains constant at 1, and beyond 70⁰F, the number of O rings increases back to 2. This shows that there is a relationship between the two variables

A linear regression line with positive slope can be fitted through these observations because the linear regression line will pass through the average of the observation.

The sample size is the only observed problem. It makes the relationship between the temperature and the number of O rings to be unclear.

Answer 2

NO, as per study, I cant see any other problem than the sample size in the procedure.

From the graph there is a slight quadratic relationship between temperature and number of O-rings.

As in the graph, we can see that above 50°F but below 55°F number of O-rings in 3 but after 55°F as temperature goes on increasing the number of O-rings decreases and remains constant up to 70°F and above 70°F the number of O-rings increases to 2. Hence, we can say that there is a relationship between temperature and number of O-rings.

If we want to fit a linear regression through these seven observations, the slope would be positive as linear regression line passes through the average.

Looking at the relationship, slope must be significantly different from zero as there is a relationship between two variables, where as slope significantly zero implies no relationship. However, we have only seven points so drawing a conclusion is difficult as the nature of the relationship is not clearly visualized by this graph.