mid1practice2 - Biostatistics 100B Midterm 1 Practice Set 2...

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Biostatistics 100B, Midterm 1, Practice Set 2 General Comments: These problems are taken from old exams from some of my past classes. I have picked a selection of problems that I think will be useful. I do not guarantee that I have here a problem on every subject that is fair game for the exam or that the balance is exactly right. A few of the regression problems contain questions about confidence intervals and hypothesis tests that may not be fair game for our exam depending on how far I get on Monday. I have left these pieces in (a) in case they are fair game and (b) so you can see the original structure of the questions. At the moment this list does not incllude examples of Fisher’s exact test and McNemar’s test. I will add a problem or two on these topics later but this should get you well started. In addition to practice problems it is worth reviewing the problems from HW1-3 as the assignments more accurately reflect what I think are the key topics we have covered so far. The exam will be closed book. However, you may use two pages, front and back, of notes and formulas. Write your answers on the exam sheets. If you need more space, continue your answer on the back of the pages. Normal and chi-squared tables will be provided for you at the end of the exam and I will have scratch paper available if you want it. You must show your work on the exam to obtain full credit. If you use a result from class, state what result you are using. If you can’t complete a problem for any reason, explain what concepts are at issue, and how you would attack the problem. If you can’t work out a number you need for a later part of a problem give it a symbol and show how you would do the calculations with a symbol in place of the missing number. It is, in any case, a good idea to explain briefly what your reasoning is in English. If I can’t tell that you understood what you were doing, I can’t give you credit, particularly if you get the wrong numerical answer. HAPPY STUDYING! (1) Regress a Wreck A statistician is trying to learn what factors affect the price of a used car. Her Y variable is the price of the car. She is considering several possible predictor variables. They are X 1 , the original value of the car, X 2 , the mileage on the car, X 3 , the number of repairs that have been done on the car, and X 4 , the number of seat belts in the car. (a) For each of the four possible predictor variables the statistician has obtained the covariance and correlation. Cor ( Y, X 1 ) = . 795 Cov ( Y, X 1 ) = 3 , 688 , 147 Cor ( Y, X 2 ) = - . 789 Cov ( Y, X 2 ) = - 149 . 155 Cor ( Y, X 3 ) = - . 539 Cov ( Y, X 3 ) = - 1186 . 4 Cor ( Y, X 4 ) = - . 004 Cov ( Y, X 4 ) = - 7 . 6 Note: For each variable described what a plot of X versus Y would look like and why. (b) Rank the variables X 1 , X 2 , X 3 , X 4 in terms of how good a job you expect them to do of pre- dicting Y based on the values given in part (a) (NOT on your common sense opinion!) Order them 1
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from best predictor to worst predictor and briefly explain your reasoning.
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