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# tutorial 8 - Solution to Tutorial 8 1(a Hard hat E(Y = 0 2...

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Tutorial 8 1. In regression analysis of on-the-job head injuries of warehouse laborers caused by falling objects. Y is a measure of severity of the injury, X 1 is an index reﬂecting both the weight of the object and the distance it fell, and D 1 and D 2 are indicator variables for nature of head protection worn at the time of the accident, coded as follows type of protection D 1 D 2 Hard hat 1 0 Bump cap 0 1 None 0 0 the response function to be used in the study is E ( Y ) = β 0 + β 1 X 1 + β 2 D 1 + β 3 D 2 (a) Develop the response function for each type of the protection category (b) For each of the following questions, specify H 0 and H a for each appropriate test (1) with X 1 fixed, does wearing a bump cap reduce the expected severity of injury as compared with wearing no protection? (2) with X 1 fixed, is the expected severity of injury the same when wearing a hard hat as when wearing a bump cap? 2. Refer to the toll wear example (in the lecture notes, part 5 of Chapter 2), consider model Y = β 0 + β 1 X 1 + β 2 D 1 + β 3 D 2 + β 4 D 3 + β 5 X 1 D 1 + β 6 X 1 D 2 + β 7 X 1 D 3 + ε . Indicating the meaning of (1) β 3 , (2) β 4 - β 3 , (3) β 1 , (4) β 7 = 0, (5) β 5 - β 6 3. Steroid level. (Data) An endocrinologist was interested in exploring the relation- ship between the level of a steroid ( Y ) and age ( X ) in healthy female subjects whose ages ranged from 8 to 25 years. She collected a sample of 27 healthy females in this age range. a. Fit regression model Y = β 0 + β 1 X + β 2 X 2 + ε . Plot the fitted regression function and the data. Does the quadratic regression function appear to be a good fit here? Find R 2 .

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tutorial 8 - Solution to Tutorial 8 1(a Hard hat E(Y = 0 2...

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