The correlation coefficient is a way to determine the strength of the linear association between two variables, such as "X" and "Y." The correlation will always be between the numbers "-1" and "1." If the correlation is negative, then there is a negative relationship. If the correlation is "0," then there is a neutral relationship. If the correlation is positive, then there is a positive relationship.
Write out the numbers of the "X" and "Y" values you want the correlation coefficient of:
X Values Y Values
Count the total number of "X" and "Y" values; in this case, there are four, so "N"=4.
Multiply "X" by "Y," "X" by "X" and "Y" by "Y" for all four values with a calculator:
Add up the "X" values, the "Y" values and all of the multiplied "X" and "Y" values; find the square roots of the "X" and "Y" values and add them together:
XY=204.1=82 and XY=214.6=96.6 and 82+96.6=178.6
XX=2020=400 and XX=2121=441 and 400+441=841
YY=4.14.1=16.81 and YY=4.64.6=21.16 and 16.81+21.16=37.97
Plug the numbers into the formula (r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX^2 - (ΣX)^2][NΣY^2 - (ΣY)^2])] and make the calculations with the calculator:
Correlation(r)=((4)(178.6)-(41)(8.7)) / square-root ([4)(841)-(4141)][(4)(37.97)-(8.7*8.7)])
Correlation(r)=(714.4-356.7) / square-root ([3364-1681)*[151.88-75.69)
Correlation(r)=357.7 / square-root (1683*76.19)
Correlation(r)=357.7 / square-root (128227.77)
Correlation(r)=357.7 / 358.089
Tips & Warnings
- Use a square root calculator, such as Math.com's, to get the square roots of large numbers; simply enter the number and press "Calculate," and the square root will appear.
- Remember to plug the numbers you get from the calculator into their correct places within the formula; you won't get the proper correlation coefficient otherwise, and any number you get that is either below -1 or above 1 is an incorrect coefficient.
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