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

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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
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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• Winter '07
• Sugar
• Regression Analysis, SS df MS, Coef, Adj R-squared Root, R-squared Root MSE

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