AutoSave . Off ManateeDeathsInvTask - Compatibility Mode MarkedManx 96954 M X File Home Insert Design Layout References Mailings Review View Help Search Share Comments X Cut Arial AaBbCcI AaBbCcI AaBbC AaBbC AaBbC AaBbCcD AaBbCcl AaBbCcl AaBbCcl AaBbCc] AaBbCcl AaBbCc/ AABBCC. AABBCC Find 12 ~ A" A Aa Ap [B Copy Intense Q... Subtle Ref... Intense Re.. = Gc Replace Paste Dictate BI U ~ ab x x A LA~ Quote Format Painter 1 Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle Subtle Em... Emphasis Intense E... Strong Select Clipboard Font Paragraph Styles Editing Voice 1 . . . 1 . . . . . . 1 . . . 1 . . . 1 . . . 2 . . . 1 . . . 3 . . . 1 . . . 4 . . . 1 . . . 5 . . . 1 . . . 6 . . . . . . 7 . . . MANATEE DEATHS LINEAR REGRESSION Inv Task a) (2 points) What are you interested in modeling? Photo @ David R. Schlichte I'm in interested in modeling the relationship between powerboat registrations and manatees killed. Specifically, the effect of powerboat registrations on manatees. (b) (5 points) Make a scatter plot of your data. Describe the form and direction of the relationship. Is there a linear pattern? Do you see any unusual observations or outliers, if so, list them ? A moderately strong and positive linear relationship can be examined. There isn't an exact linear pattern as it doesn't form an exact straight line. There aren't any unusual observations or outliers. Manatees are passive, slow-moving animals. Most of their time is spent eating, resting, and traveling. They are often shy and reclusive. (c) (2 points) The following table gives data on powerboat registrations (in thousands) and the Explain, in general, what an influential observation is, include a sketch. number of manatees killed by boats in Florida in the years 1977 to 1990. Explain how you can check if an observation is influential? Boats (thousands) Manatees Killed An influential observation is best defined as a data point that is noticeably father 447 13 away from the rest of the data set and has a large impact on the slope of the 460 21 regression line. It can be called a "special type of outlier." You can check if an 481 24 observation is influential in two ways: calculate the coefficient of determination 498 16 and the slope of the regression line both with and It the point. If they differ 513 24 significantly, then the data point is an influential point. All influential points are 512 20 outliers, but not all outliers are influential points. 526 559 15 34 585 33 614 33 2. 645 39 (a) (5 points) 675 43 Fit the least squares regression line to your data. You may use you 711 50 calculator. Give the equation of your line, round answer to 2 decimal places. Be 719 47 sure to label your variables. The regression line equation is y = 358.59 + 7.10x (x is manatees killed and y is boats [thousands]). Page 1 of 3 523 words FocusAutoSave . Off ManateeDeathsInvTask - Compatibility Mode MarkedManx 96954 M X File Home Insert Design Layout References Mailings Review View Help Search Share Comments X Cut Arial 12 ~ A" A Aa A AaBbCcI AaBbCcI AaBbC AaBbC AaBbC AaBbCcD AaBbCcl AaBbCcl AaBbCcl AaBbCc] AaBbCcl AaBbCc/ AABBCC. AABBCC Find Paste [A Copy Replace Format Painter BI U ~ ab x x A LA 1 Normal 1 No Spac.. Heading 1 Heading 2 Title Subtitle Subtle Em... Emphasis Intense E... Strong Quote Intense Q... Subtle Ref... Intense Re.. = Select Dictate Clipboard Font Paragraph Styles Editing Voice 1 . . . 1 . . . x . . . 1 . . . 1 . . . 1 . . . 2 . . . 1 . . . 3 . . . 1 . . . 4 . . . 1 . . . 5 . . . 1 . . . 6 . . . 6 . . . 7 . . . b) (3 points) Explain what the criterion is that is used to find the equation of Least Squares Regression Line. (LSRL (c) (4 points) Explain what the slope of your equation tells you about the change in Manatees killed with respect to the change in number of boats. Give units of the slope. 3. (a) (2 points) Use your equation to predict the number of manatee deaths if the number of boats is 585,000. Compute the error you made by using the equation. Did you overestimate or underestimate by using your equation? (b) (2 points) Use your equation to predict the number of manatee deaths if the number of boats is 950,000. Clearly explain why this may not be a reasonable prediction. 4. a ) (2 points ) Compute correlation coefficient r (use calculator). Explain what r tells about the strength of linear relationship between the number of boats (in thousands) and number of manatee deaths. (b) (3 points) Determine the percentage of variation in the number of manatee deaths that is fits well? Explain. explained by the regression line you found in (2a)? Does it mean that the regression line Page 3 of 3 523 words Focus 80%