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1. Pearson's Correlation Coefficient example ( Enter your problem )
  1. Formula & Example-1 (Class-X & Y)
  2. Example-2 (Class-X & Y)
  3. Example-3 (X & Y)
  4. Example-4 (X & Y)
Other related methods
  1. Correlation Coefficient r
  2. Covariance - Population Covariance, Sample Covariance

3. Example-3 (X & Y)
(Previous example)
2. Covariance - Population Covariance, Sample Covariance
(Next method)

4. Example-4 (X & Y)





Calculate Correlation Coefficient r without cov(x,y), Correlation Coefficient r with population cov(x,y), Correlation Coefficient r with sample cov(x,y) from the following data
XY
300800
350900
4001000
4501100
5001200
5501300
6001400
6501500
7001600


Solution:
Mean ˉx=xin

=300+350+400+450+500+550+600+650+7009

=45009

=500

Mean ˉy=yin

=800+900+1000+1100+1200+1300+1400+1500+16009

=108009

=1200

xyX=x-50050Y=y-1200100X2Y2XY
300800-4-4161616
350900-3-3999
4001000-2-2444
4501100-1-1111
500120000000
550130011111
600140022444
650150033999
700160044161616
---------------------
450010800X=0Y=0X2=60Y2=60XY=60


Correlation Coefficient r :
r=XYX2Y2

=606060

=607.7467.746

=1




Correlation Coefficient r with Population Cov(x,y) :

Population Cov(x,y)=(x-ˉx)(y-ˉy)n

=609

=6.6667


Population Standard deviation σ=(x-ˉx)2n

=609

=6.6667

=2.582

Population Standard deviation σ=(y-ˉy)2n

=609

=6.6667

=2.582

Now, r=cov(x,y)σxσy

=6.66672.5822.582

=1




Correlation Coefficient r with Sample Cov(x,y) :

Sample Cov(x,y)=(x-ˉx)(y-ˉy)n-1

=608

=7.5


Sample Standard deviation σ=(x-ˉx)2n-1

=608

=7.5

=2.7386

Sample Standard deviation σ=(y-ˉy)2n-1

=608

=7.5

=2.7386

Now, r=cov(x,y)σxσy

=7.52.73862.7386

=1




This material is intended as a summary. Use your textbook for detail explanation.
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3. Example-3 (X & Y)
(Previous example)
2. Covariance - Population Covariance, Sample Covariance
(Next method)





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