The r-value of the following data to three decimal places is:
r= -0.828
The correlation coefficient i.e. r is calculated by the formula:
[tex]r=\dfrac{n\sum{xy}-(\sum x)(\sum y)}{\sqrt{(n\sum x^2-(\sum x)^2)(n\sum y^2-(\sum y)^2)}}[/tex]
where n is the sample size.
i.e. here n=5
x y x² y² xy
4 26 16 676 104
5 11 25 121 55
8 13 64 169 104
9 2 81 4 18
13 1 169 1 13
∑ 39 53 355 971 294
Hence, the correlation coefficient is calculated as follows:
[tex]r=\dfrac{5\times 294-(39)\cdot (53)}{\sqrt{(5\times \sum 355-(39)^2)(5\times 971-(53)^2)}}[/tex]
[tex]r=\dfrac{1470-2067}{\sqrt{(1775-1521)\cdot (4855-2809)}}\\\\\\r=\dfrac{-597}{\sqrt{254\times 2046}}\\\\\\r=\dfrac{-597}{\sqrt{519684}}\\\\\\r=\dfrac{-597}{720.89111}\\\\\\r=-0.828141[/tex]
Hence, the r-value is:
r= -0.828
