Boats and Manatees? The table below lists the numbers of registered pleasure boats (thousands) in Florida and the numbers of watercraft-related manatee deaths for each year of the past decade. B o a t s M a n a t e e D e a t h s a. Test for a linear correlation between the numbers of boats and the numbers of manatee deaths. b. Find the equation of the regression line. Use the numbers of boats for the independent x? ?variable. c. What is the best predicted number of manatee deaths for the year preceding those included in the table? For that year, there were 84 (thousand) registered pleasure boats in Florida. How accurate is that predicted value, given that there were actually 78 manatee deaths in that year?

Solution 5CRE Step1: From the given problem we have the numbers of registered pleasure boats (thousands) in Florida and the numbers of watercraft-related manatee deaths for each year of the past decade. boats 90 92 94 95 97 99 99 97 95 Manatee deaths 91 95 73 69 79 92 73 90 97 Step2: Our aim is to find a).Test for a linear correlation between the numbers of boats and the numbers of manatee deaths. b). Find the equation of the regression line. Use the numbers of boats for the independent x variable. c).What is the best predicted number of manatee deaths for the year preceding those included in the table For that year, there were 84 (thousand) registered pleasure boats in Florida. How accurate is that predicted value, given that there were actually 78 manatee deaths in that year Step3: a).By using SPSS we can find the correlation between number of boats and manatee deaths In SPSS just enter the all data after entering data go to analyze select correlation and then select bivariate therefore the correlation coefficient is -0.046 Correlations Boats Deaths Boats Pearson Correlation 1 -.046 Sig. (2-tailed) .900 N 10 10 Deaths Pearson Correlation -.046 1 Sig. (2-tailed) .900 N 10 10 Conclusion: The P value i.e, p = 0.900 which is greater than = 0.05. Hence we fail to reject the claim that there is a linear correlation between number of boats and number of deaths. b). X Y XY X 2 Y2 90 81 7290 8100 6561 92 95 8740 8464 9025 94 73 6862 8836 5329 95 69 6555 9025 4761 97 79 7663 9409 6241 99 92 9108 9801 8464 99 73 7227 9801 5329 97 90 8730 9409 8100 95 97 9215 9025 9409 90 83 7470 8100 6889 2 2 X XY X Y Y =832 =948 =78860 =89970 =70108 The least square line is represented as: y = a+ bx. Where, N( XY ) X Y a = 2 N( X ) ( X) 10(78860)948(832) = 10(89970)(948) = -0.137 It yields to a = 96.1 similarly, N( XY ) XY b = 2 2 N( Y ) ( Y ) = 10(78860)942(832) 10(70108)(832) = -0.137 Therefore, y = a + bx is y = -0.1370x+96.1 ………(1) c).For the registered boats 84, using equation 1, the predicted number of deaths comes 84.6. This value is not accurate because it is significantly different from actual value of 78 deaths.