homework1key-fa07

homework1key-fa07 - Stat 501 Homework 1 ANSWERS Fall 07 1 a...

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Stat 501 Homework 1 ANSWERS Fall 07 1. a . The slope is −0.269. For each one-hour increase in studying average (or, predicted) amount of sleep decreases by 0.269 hours. b. Intercept = 7.56 hours. It does have useful meaning for this problem. It’s the average hours of sleep for people who studied 0 hours. c. The estimated value of average hours of sleep the previous day is y ˆ = 7.022, calculated by substituting 2 hours into the regression equation. d. The value of the residual for that person is –1.022, calculated by finding the difference between the observed value of 6 hours and the predicted value found in part c. 2. a. X 70 75 80 80 85 90 Y 75 82 80 86 90 91 i y ˆ 76 80 84 84 88 92 i e −1 2 −4 2 2 −1 b. SSE = 30. SSE = ( 29 30 ) 1 ( ) 2 ( 2 ) 4 ( ) 2 ( ) 1 ( 2 2 2 2 2 2 = - + + + - + + - c. MSE = SSE/(n−2) = 30/(6-2) = 7.5 d. s = 5 . 7 =2.74. This is roughly the average absolute size of a residual (difference between actual and predicted value of y). e.
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