Question

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 975 992 935 987 940

y 40 100 65 145 84 153

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

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

low

moderate

strong

Would you say the correlation is positive or negative?

positive

negative

(c) Use a calculator to verify that x = 5833, x2 = 5,674,699, y = 587, y2 = 67,315 and xy = 564,443. Compute r. (Round your answer to three decimal places.)

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, y should tend to decrease as x increases.

Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

Given our value of r, y should tend to increase as x increases.

Given our value of r, y should tend to remain constant as x increases.

Answer 1

a)

b)

strong

c)

negative

d)

ΣX =	5833.000
ΣY=	587.000
ΣX2 =	5674699.000
ΣY2 =	67315.000
ΣXY =	564443.000

	n=		6.0000
	X̅=ΣX/n		972.1667
	Y̅=ΣY/n		97.8333
	sx=(√(Σx2-(Σx)2/n)/(n-1))=		28.4634
	sy=(√(Σy2-(Σy)2/n)/(n-1))=		44.4676
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=		-1243.7667
	r=Cov/(Sx*Sy)=		-0.983

Given our value of r, y should tend to decrease as x increases.