Question

Hurricanes The data below represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.

Atmospheric Pressure (mb)	Wind Speed (knots)
993	50
995	60
994	60
997	45
1003	45
1004	40
1000	55
994	55
942	105
1006	30
1006	40
942	120
1002	40
986	50
983	70
994	65
940	120
976	80
966	100
982	55

Source: National Hurricane Center

• (a) Draw a scatter diagram treating atmospheric pressure as the explanatory variable.

• (b) determine the linear correlation coefficient between atmospheric pressure and wind speed.

• (c) Does a linear relation exist between atmospheric pressure and wind speed?

• D. Make sure that your scatter diagram includes a title and the axes are labeled.

Answer 1

Part a

Required scatter diagram and regression model for the prediction of the response variable wind speed (knots) and explanatory variable atmospheric Pressure (mb) is given as below:

Regression Statistics
Multiple R	0.957818661
R Square	0.917416586
Adjusted R Square	0.912828619
Standard Error	7.960969471
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	12672.96337	12672.96337	199.9614433	3.44423E-11
Residual	18	1140.786628	63.37703491
Total	19	13813.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1245.940492	83.58514949	14.90624231	1.43155E-11	1070.33461	1421.546375
Atmospheric Pressure (mb)	-1.199381367	0.084817246	-14.14077237	3.44423E-11	-1.377575788	-1.021186946

Part b

The linear correlation coefficient between the given two variables wind speed and atmospheric pressure is given as -0.9578, which means there is a very strong negative linear relationship exists between the given two variables.

Part c

From given scatter plot and above linear correlation coefficient, it is observed that there is a linear relationship exists between atmospheric pressure and wind speed.

Part d

Required scatter diagram is given as below: