Chapter 4.1, Problem 15P

Meteorology: Cyclones Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? Data for this problem are based on information taken from Weatherwise (Vol. 46, No. 1), a publication of the American Meteorological Society. 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

(a) Make a scatter diagram and draw the line you think best fits the data.

(b) Would you say the correlation is low. moderate, or strong? positive or negative?

(c) Use a calculator to verify that $\sum x=5823,\sum x^2=5,655,779,\sum y=580,\sum y^2=65,750,\text{and }\sum xy=556,315.$ Compute r. As x increases, does the value of r imply that y should tend to increase or decrease? Explain.