reg1-0459 - STA 3024 Section 7454/7459 Name: Homework 1 for...

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Homework 1 for Regression Section 7454/7459 Form B Name: UFID: This form is only for students whose UFID number begins with 0, 4, 5, or 9. Answer all problems neatly . If you turn in more than one piece of paper, they must be stapled . Work that isn’t neat or stapled may lose points. You don’t need to turn in this problem listing, but you do need to include your name , UF-ID number , and form code on your homework. 1. When paleontologists identify a new species of dinosaur, it’s often the case that they find only a few bones, rather than an entire skeleton. Still, they are usually able to figure out some basic facts, such as how big their new species of dinosaur was. They do this by comparing their new bones to the corresponding bones of related species whose sizes are already known. Suppose paleontologists discover a femur (thigh bone) for a new species of dinosaur. This femur is 0.54 m long. Shown below are the femur lengths and overall lengths of ten species that the paleontologists believe are closely related to their new species. ( X ) ( Y ) Species Femur (m) Overall (m) 1 0.29 3.8 2 0.34 4.8 3 0.51 6.6 4 0.31 5.2 5 0.60 8.0 6 0.45 7.3 7 0.57 8.4 8 0.27 4.1 9 0.55 8.5 10 0.35 6.2 0.30 0.40 0.50 0.60 5 6 7 8 Femur Length (m) Overall Length (m) (a) i. Calculate the regression equation using the following information: ¯ X = 0 . 424 , S X = 0 . 1262 , ¯ Y = 6 . 29 , S Y = 1 . 76 , r = 0 . 935 . (So that you can check your work, part of your answer should be that a = 0 . 77 . ) ii. Calculate the predicted overall length for Species 4 in the data set. iii. Calculate the residual for Species 4 in the data set. iv. Calculate the predicted overall length for the paleontologists’ new species. (Recall that its femur is 0.54 m long.) v. Suppose that some other paleontologists discover another femur with a length of 1.10 m from another new species that is also related to the species in this data set. Explain why it would be inappropriate to use the results of our regression to predict the length of this other new species. (b) i. We can calculate that SS Regr = 24 . 31 and SS Res = 3 . 48 . (You don’t have to check this.) Use this information to construct the regression ANOVA table. 1
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reg1-0459 - STA 3024 Section 7454/7459 Name: Homework 1 for...

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