What is the r-value of the following data, to three decimal places

Question

asked Aug 26, 2020 183k views

2 Answers

Greg McNulty · Answer 1 · 2020-08-31T08:16:39+0000

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:

$r=\frac{n\sum{xy}-(\sum x)(\sum y)}{√((n\sum x^2-(\sum x)^2)(n\sum y^2-(\sum y)^2))}$

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:

$r=(5* 294-(39)\cdot (53))/(√((5* \sum 355-(39)^2)(5* 971-(53)^2)))$

$r=(1470-2067)/(√((1775-1521)\cdot (4855-2809)))\\\\\\r=(-597)/(√(254* 2046))\\\\\\r=(-597)/(√(519684))\\\\\\r=(-597)/(720.89111)\\\\\\r=-0.828141$

Hence, the r-value is:

r= -0.828