Question

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. For a random sample of tropical cyclones, let x be the lowest pressure as a cyclone approaches and let y be the maximum wind speed of the cyclone.

Clan Ul Lel.t Afai's. perceilage a Domestic as from insurance plan, and let y be the average administrative cost 75 35 25 30 35 40 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 E 135, 22 7133, 2y 148, 2y 4674, 3040. Compute r. As x increases, does the value of r imply that y and Sry should tend to increase or decrease? Explain. 9 leteorology: Cyclones Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? Data for this probiem are based on information taken from Weatherwise (vol. 46, no. 1), a publication of the Ameri- can Meteorological Society. For a random sample of tropical cyclones, let ax be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximu wind speed (in miles per hour) of the cyclone. 1004 975 992 935 985 932 40 100 65 145 80 150 Make a scatter diagram and draw the line you think best fits the data, (a) (b) Would you say the correlation is low, moderate, or strong? positive or negative? (c) Use a calculator to verify that 5823, 5,655,779, y580, 2y2 65,750, and Exy 556,315. Compute r: As x increases, does the value of r imply that y should tend to increase or decrease? Explain Geology: Earhauakes Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (o the Richter scale), and let y be the depth (in kilometers) of the quake below the sur face at the epicenter. The following is based on information taken from the National Earthquake Information Service of the U.S. Geological Survey. Additional d

Answer 1

9.

a) The scatter diagram is given by,

scatter plot 160 1400 120 TiHi 80 60 40 20 920 930940 950 960 970 980 990 1000 1010

b) Here we can see that, there is strong negative correlation .

c)

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$

6 556315 (5823 580) 6 5655779 - (5823)216 *65750- (580)

= -0.99

Here value of correlation coefficient is negative and it is close to 1. So we can say that there strong negative correlation between x and y. This imply that as value of x increases the value of y decreases.