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Problem: Correlation Coefficient {{10,11,12,13,14},{3,12,18,12,3}} [ Calculator, Method and examples ]

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Your problem -> Correlation Coefficient {{10,11,12,13,14},{3,12,18,12,3}}

 x y x^2 y^2 x*y 10 3 100 9 30 11 12 121 144 132 12 18 144 324 216 13 12 169 144 156 14 3 196 9 42 --- --- --- --- --- sum x=60 sum y=48 sum x^2=730 sum y^2=630 sum xy=576

Correlation Coefficient r :
r = (n * sum xy - sum x * sum y)/(sqrt(n * sum x^2 - (sum x)^2) * sqrt(n * sum y^2 - (sum y)^2))

=(5 * 576 - 60 * 48 )/(sqrt(5 * 730 - (60)^2) * sqrt(5 * 630 - (48)^2)

=(2880 - 2880)/(sqrt(3650 - 3600) * sqrt(3150 - 2304))

=0/( sqrt(50) * sqrt(846))

=0/( 7.0711 * 29.0861)

=0/205.6696

=0

Correlation Coefficient r with Population Cov(x,y) :
Population Cov(x,y) = (sum xy - (sum x * sum y)/n)/(n)

=(576 - (60 xx 48)/5)/5

=(576 - (2880)/5)/5

=(576 - 576)/5

=(0)/5

=0

Population Standard deviation sigma_x = sqrt((sum x^2 - (sum x)^2/n)/(n))

=sqrt((730 - (60)^2/5)/5)

=sqrt((730 - 720)/5)

=sqrt(10/5)

=sqrt(2)

=1.4142

Population Standard deviation sigma_y = sqrt((sum y^2 - (sum y)^2/n)/(n))

=sqrt((630 - (48)^2/5)/5)

=sqrt((630 - 460.8)/5)

=sqrt(169.2/5)

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