Question

Use the accompanying paired data consisting of registered boats? (tens of? thousands) and manatee fatalities from boat encounters. Let x represent the number of registered boats and let y represent the corresponding number of manatee deaths. Use the given number of registered boats and the given confidence level to construct a prediction interval estimate of manatee deaths. Use = 87 (for 87?0,000 registered? boats) with a 99?% confidence level.

Find the indicated prediction interval.

__ manatees < y < __ manatees

		Open in StatCrunch + Copy to Clipboard + Open in Excel +
Boats ?(tens of? thousands)	Manatees
65	51
70	38
66	36
72	51
69	41
70	58
75	55
82	65
85	83
87	80
92	82
95	96
91	73
97	69
98	80
100	90
97	72
99	92
95	97
88	84
89	89
85	81
90	71
88	70

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Manatees
Independent Variable: Boats
Manatees = -46.112894 + 1.3744301 Boats
Sample size: 24
R (correlation coefficient) = 0.85874173
R-sq = 0.73743737
Estimate of error standard deviation: 9.5288474

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-46.112894	15.025093	? 0	22	-3.0690589	0.0056
Slope	1.3744301	0.17484982	? 0	22	7.8606318	<0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	5610.4235	5610.4235	61.789532	<0.0001
Error	22	1997.5765	90.798932
Total	23	7608

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	99% C.I. for mean	99% P.I. for new
87	73.462521	1.9701341	(67.909193, 79.015848)	(46.034943, 100.8901)

Hence,

99% prediction interval will be:

46.035 < y < 100.890