Dr. Pendergrass
Spring 2009
Offline Quiz2
Statistics
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1. Is the number of gameswon in a seasonby a major leaguebaseballteam predicted by the averagebatting
averageof the team's members? Here is data from 14 teams in the American Leaguefrom the 2000 Major
LeagueBaseballseason:
Games
87
won
Batting
Avg.
83
74
85
69
90
79
77
95
69
82
71
91
91
0.277 0.275 0.272 0.267 0.257 0.288 0.275 0.286 0.288 o.270 0.280 0.283 0.269 o.270
a) (10 points) Find the equation of the least-squaresregressionline for predicting number of gameswon
(response)versusteam batting average(explanatory).
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b) (5 points) What fraction of the variation in number of games won is "explained by" team batting average?
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c) (5 points) How good a predictor is team batting averagefor number of gameswon? Explain in a clear
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2. How does aggressivebehavior in blackbream fish vary with age? Zoologists at the University of Western
Australia recordedthe number of aggressivestrikes of two blackbreamfish feeding at the bottom of an
aquarium in the 10-minuteperiod following the addition of food. The number of strikes and age of the fish
(in days) was recordedapproximately once a week for 9 weeks. The summary statisticsof the data are
given in the table below:
mean
standarddeviation
44.2
23.7
1 60.4
22.9
numberof strikes
age (in days)
correlation
-0.792
a) (10 points) Find the equationof the least squaresregressionline for predicting number of strikes (response)
versusage(explanatory).
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b) (5 points) According to the least-squaresmodel, how much doesnumber of strikes changeon averagefor
each day that a fish ages?
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