Question: Meteorology: Cyclones Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone.

X 1004 975 992 935 985 932

Y 40 100 65 145 80 150

Complete Parts (a) through (c) for these data, and comment on the meaning of r and r² in the context of this problem.

1. Draw a scatter diagram for the data.
2. From the scatter diagram, would you estimate the correlation coefficient r to be closest 1, 0, or –1?
3. Compute the correlation coefficient r and the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x by using the least-squares line? What percent of the variation is unexplained?

Answers may vary slightly due to the rounding

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