Manatees are large gentle sea creatures that live along the

Manatees are large, gentle sea creatures that live along the Florida coast. Many manatees are killed or injured by powerboats. Below are data on powerboat registrations (in thousands) and the number of manatees killed by boats in Florida for four different years between 2001 and 2004: Assume the relationship between the number of boats and the number of manatee deaths is linear, and complete the following parts using hand calculations. (a) Find the estimated regression line and estimate the expected number of manatee deaths in a year with 550 (thousand) powerboat registrations. (b) Use (6.3.11) to compute the error sum of squares, and give the estimate of the intrinsic error variance. (c) Compute the four fitted values and the corresponding residuals. Verify that the sum of squared residuals equals the SSE obtained in part (b).

Solution

(a)

The estimated regression line is

Number of manatee deaths = -78.7381+ 0.1952*Number of Boats

The estimate the expected number is

-78.7381+ 0.1952*550 = 28.6219

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(b)

The error sum of squares = 24.8214

The estimate error varaince= 24.8214

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(c)

The sum of squared residuals equals to SSE obtained in part (b)

Regression output				confidence interval
variables	coefficients	std. error	t (df=2)	p-value	95% lower	95% upper
Intercept	-78.7381	22.4796	-3.503	.0727	-175.4602	17.9839
Number of Boats	0.1952	0.0408	4.785	.0410	0.0197	0.3708