Q5. Colorado Rockies owners want to know if success on the field and attendance
ID: 2930097 • Letter: Q
Question
Q5. Colorado Rockies owners want to know if success on the field and attendance are related. A consultant recorded the number of wins and the average attendance for each season since 2008 for the Colorado Rockies. The data is as follows:
Year
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2004
2003
2002
2001
2000
Attendance
2,953,650
2,602,524
2,506,789
2,680,329
2,793,828
2,630,458
2,909,777
2,875,245
2,665,080
2,650,218
2,338,069
2,334,085
2,737,838
3,166,821
3,295,129
Wins
87
75
68
66
74
64
73
83
92
74
68
74
73
73
82
Year
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2004
2003
2002
2001
2000
Attendance
2,953,650
2,602,524
2,506,789
2,680,329
2,793,828
2,630,458
2,909,777
2,875,245
2,665,080
2,650,218
2,338,069
2,334,085
2,737,838
3,166,821
3,295,129
Wins
87
75
68
66
74
64
73
83
92
74
68
74
73
73
82
Explanation / Answer
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
=10* 2066975348-( 27267898*756)/10* 74550261168864-(27267898*27267898)
=0.000028
b0=Ey-b1Ex/n
=756*10-27267898/10
=-1.05659
y=b0+b1x
y=-1.05659+0.000028x
r (correlation)=n(Exy)-(Ex)(Ey)/(nEx2-(Ex)2)(nEY2-(Ey)2)
=10(2066975348)-(27267898)(756)/ (10*74550261168864-27267898^2)(10*57904-756^2)
=0.4548
Therefore, r^2=0.20688
Year Attendance (x) Wins (y) x^2 y^2 xy 2017 2953650 87 87,24,04,83,22,500 7,569 25,69,67,550 2016 2602524 75 67,73,13,11,70,576 5,625 19,51,89,300 2015 2506789 68 62,83,99,10,90,521 4,624 17,04,61,652 2014 2680329 66 71,84,16,35,48,241 4,356 17,69,01,714 2013 2793828 74 78,05,47,48,93,584 5,476 20,67,43,272 2012 2630458 64 69,19,30,92,89,764 4,096 16,83,49,312 2011 2909777 73 84,66,80,21,89,729 5,329 21,24,13,721 2010 2875245 83 82,67,03,38,10,025 6,889 23,86,45,335 2009 2665080 92 71,02,65,14,06,400 8,464 24,51,87,360 2008 2650218 74 70,23,65,54,47,524 5,476 19,61,16,132 Sum Sum Sum Sum Sum 27267898 756 7,45,50,26,11,68,864 57,904 2,06,69,75,348Related Questions
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