Find the correlatin coefficient r using bivariate data.

sodni3 2021-01-07 Answered
Find the correlatin coefficient r using bivariate data.
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Expert Answer

saiyansruleA
Answered 2021-01-08 Author has 110 answers

Given:
The given bivariate data is(1,6),(3,2), and (2,4).
Calculation:
First determine xiyi,xiandyi.
xi first coordinates of the ordered pairs.
yi second coordinates of the ordered pairs.
xiyi=16+32+24=20
xi=1+3+2=6
xi2=12+32+22=14
yi=6+2+4=12
yi2=62+22+42=56
Find the sample variance s2 using the formula s2=xi2xi2nn1
sx2=1462331=14122=1
sy2=56122331=56482=4
Find sample standard deviation.
sx=1=1
sy=4=2
For covariance sxyusing forμ  sxy=xiyixiyinn1.
Where n = number of ordered pairs.
n=3
sxy=20612331
=2072331
=20242
=42=2
Find the correlation coefficient r using the formula r=sxysxsy.
r=212=1
Hence the value of correlation coefficient r = -1.

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