Question: Assume that you have designed a small, lightweight engine that performs perfectly on the floor of your lab. You then attach it to a boat and test it again. Once again the performance is flawless. However, when you take your supervisor for a demonstration ride in the boat, the engine makes a horrible noise and fails. Now you run many more tests, and sometimes the engine runs perfectly and sometimes it fails. One or your colleagues suggests that it fails when the water is cold. Another suggests that it fails when the air is hot. A third wonders aloud if the failure is related to the mass in the boat. You collect the following data, where N is the number of failures per hour, T(air) is the average air tern perature during the testing hour, and T(water) is the average water temperature:

Write a program to determine which variables are linearly correlated with the number of failures per hour. Also check whether any of these variables are in turn linearly correlated with one another. Run your program once, looking for correlation coefficients satisfying

|r| ≥ 0.95

In a second run, try a threshold of 0.7. You may wish to use the class Data Set described in Programming Project 6. What are the implications of your program's results?