Question

Ocean currents are important in the studies of climate change as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, new guinea, and other islands. X represent the number of days to recovery of a drift bottle after release and why represent the distance from point of release to point of recovery in km/100. The following data are taken from the reference by professor E.A. Kay, University of Hawaii.

x days 74 79 34 97 208

y km/100 14.6 19.5 5.3 11.6 35.7

Test slope in regression use significance level of 0.05

Find a confidence interval

Answer 1

x	y
74	14.6
79	19.5
34	5.3
97	11.6
208	35.7

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9385
R Square	0.8808
Adjusted R Square	0.8411
Standard Error	4.5759
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	464.3556	464.3556	22.1768	0.0181
Residual	3	62.8164	20.9388
Total	4	527.1720
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.1405	4.0026	0.2849	0.7942	-11.5976	13.8787
x	0.1646	0.0350	4.7092	0.0181	0.0534	0.2759

y^ = 1.1405 + 0.1646*x

p-value of slope = 0.0181

since p-value < alpha, we reject the null hypothesis

we conclude that slope is significant

95% confidence interval for slope is (0.0534,0.2759)

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