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	973	934
y	40	100	65	145	79	149

(c) Use a calculator to verify that

x = 5813,

x² = 5,636,015,

y = 578,

y² = 65,292

and

xy = 553,748.

Compute r. (Round your answer to three decimal places.)

Answer 1

Solution :

X	Y	XY	X^2	Y^2
1004	40	40160	1008016	1600
975	100	97500	950625	10000
992	65	64480	984064	4225
935	145	135575	874225	21025
973	79	76867	946729	6241
934	149	139166	872356	22201

n	6
sum(XY)	553748.00
sum(X)	5813.00
sum(Y)	578.00
sum(X^2)	5636015.00
sum(Y^2)	65292.00
Numerator	-37426.00
Denominator	38061.50
r	-0.9833
r square	0.9669
Xbar(mean)	968.8333
Ybar(mean)	96.3333
SD(X)	26.4160
SD(Y)	40.0236
b	-1.4898
a	1539.7295

r = -0.983