Ten major college football bowl games were played in January 2010 with the University of Alabama beating the University of Texas 37 to 21 to become the national champion of college football. The results of the 10 bowl games are shown in the following table (USA Today, January 8, 2010). The predicted winning point margin was based on Las Vegas betting odds approximately one week before the bowl games were played. For example, Auburn was predicted to beat Northwestern in the Outback Bowl by 5 points. The actual winning point margin for Auburn was 3 points. A negative predicted winning point margin means that the team that won the bowl game was an underdog and expected to lose. For example, in the Rose Bowl, Ohio State was a 2-point underdog to Oregon and ended up wining by 9 points.
a. Develop a scatter diagram with the predicted point margin on the horizontal axis.
b. What is the relationship between the predicted and actual point margins?
c. Compute and interpret the sample covariance.
d. Compute the sample correlation coefficient. What does this value tell us about the relationship between the Las Vegas predicted point margin ad the actual point margin in college football bowl games?
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Bowl Game
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Score
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Predicted Point Margin
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Actual Point Margin
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| |
|
|
|
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Outback
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Auburn 38 Northwestern 35
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5
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3
|
|
Gator
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Florida State 33 West Virginia 21
|
1
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12
|
|
Capital One
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Penn State 19 LSU 17
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3
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2
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|
Rose
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Ohio State 26 Oregon 17
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-2
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9
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|
Sugar
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Florida 51 Cincinnati 24
|
14
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27
|
|
Cotton
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Mississippi State 21 Oklahoma State 7
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3
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14
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|
Alamo
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Texas Tech 41 Michigan State 31
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9
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10
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Fiesta
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Boise State 17 TCU 10
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-4
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7
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Orange
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Iowa 24 Georgia Tech 14
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-3
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10
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Championship
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Alabama 37 Texas 21
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4
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16
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