mid2 - Midterm Two Friday the 2nd of March 2007 Name...

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Midterm Two Friday the 2nd of March, 2007 Name: General Comments: This exam is 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 page. A normal table and a t table table are attached at the end. Make sure you have all 17 pages! The exam is 110 minutes long. There are 3 questions, worth a total of 100 points. They are not equally weighted, nor are they of equal difficulty. The number of points each question is worth is printed with the problem. Read the questions carefully. If you are unsure of the interpretation, come ask. You must show your work to obtain full credit. 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 a good idea to explain your reasoning briefly 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. GOOD LUCK! Question Total Points Score Number Possible Received 1 45 2 40 3 15 Total 100 THE STORY BEHIND THE EXAM: As we all know from class my baby has not been sleep- ing well...perhaps that has something to do with the exam theme! A professor of pediatrics at the University of Calculationally Learned Adults is interested in knowing what factors affect how well an infant sleeps at night. During the course of the exam you will help her analyze the data from a study she has conducted. 1
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Question 1: Drinking the Milk of Paradise (45 points, 45 minutes) A common story among parents of young babies is that if you can get them to drink a lot of milk before going to bed they will sleep longer. Our pediatric researcher decides to test this. She has collected information on Y, the number of minutes a baby sleeps and X, the number of ounces of milk the baby has consumed. Some summary statistics, a simple linear regression printout and sev- eral corresponding plots are shown below. Use them to answer the questions on the following pages. ¯ Y = 562 ¯ X = 4 . 75 SSX = 755 n = 100 . reg Sleep Milk Source | SS df MS Number of obs = 100 -------------+------------------------------ F( 1, 98) = 28.98 Model | 1034501.63 1 1034501.63 Prob > F = 0.0000 Residual | 3497999.72 98 35693.8747 R-squared = 0.2282 -------------+------------------------------ Adj R-squared = 0.2204 Total | 4532501.35 99 45782.8419 Root MSE = 188.93 ------------------------------------------------------------------------------ Sleep | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- Milk | 37.02467 6.877371 5.38 0.000 23.37675 50.67259 _cons | 385.8047 37.77206 10.21 0.000 310.8473 460.7621 ------------------------------------------------------------------------------ 2
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Part a Is there a significant linear relationship between sleeping time and amount of milk drunk? Justify your answer with an appropriate test using α = . 05. You do not need to write out all the details. Just give your basic reasoning. Part b List the four assumptions we make about the errors in a regression model and explain whether each of these assumptions is reasonable and why based on the plots given at the start of the problem.
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