The table below gives 37 years of data on boats (in thousands) registered in Florida and manatees killed by boats. (Data set may be found here.) (a) Find the equation of the least-squares line for predicting manatees killed from thousands of boats registered. Because the linear pattern is so strong, we expect predictions from this line to be quite accurate—but only if conditions in Florida remain similar to those of the past 37 years. (Round your intercept to two decimal places, and your slope to four decimal places.) y = ? + ? x (b) Suppose we expect that the number of boats registered in Florida will be 898,000 in 2014. Predict the number of manatees killed by boats in 2014. (Round your answer to the nearest whole number.) ? manatees killed Explain why we can trust this prediction. (Select all that apply.) –The prediction is reliable because of the strong linear association visible in the scatterplot. –The regression line always gives a good prediction. –The value of r2 is very close to 1, thus ensuring a high prediction accuracy. –The prediction is reliable because the regression line explains 95.3% of the variations in y. (c) Predict manatee deaths if there were no boats registered in Florida. (Round your answer to two decimal places.) ? manatees killed Explain why the predicted count of deaths is impossible. (We use x = 0 to find the intercept of the regression line, but unless the explanatory variable x actually takes values near 0, prediction for x = 0 is an example of extrapolation. (Select all that apply.) –Because x = 0 is far outside the range of values of the explanatory variable. –Because a negative number of deaths makes no sense. –Because the intercept is usually a non-accurate prediction.
Powerboat registrations (x) Manatees killed (y) 447 13 460 21 481 24 498 16 513 24 512 20 526 15 559 34 585 33 614 33 645 39 675 43 711 50 719 47
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