mid2soln - Midterm Two Solutions General Comments The...

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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 ------------------------------------------------------------------------------ Part a (3 points) 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. Solution: Yes, the p-value for the F test (or the t-test for the Milk variable) is 0.0000 which is certainly much less than α = . 05 so we reject the null hypothesis that β 1 = 0 and conclude that there is a significant relationship between amount of milk drunk and length of time slept.
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