The correlation coefficient is calculated by the given formula
[tex] r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{(n\sum x^{2}-(\sum x)^{2})(n\sum y^{2}-(\sum y)^{2})}}} [/tex]
Here we have to find correlation coefficient for three ordered pairs, so n=3
[tex] \sum x = 2+3+5=10 [/tex]
[tex] \sum y = 26+2+16=44 [/tex]
[tex] \sum xy = 52+6+80 =138 [/tex]
[tex] \sum x^{2} = 4+9+25 =38 [/tex]
[tex] \sum y^{2} =676+4+256 =936 [/tex]
Substituting all the values in the above formula,
[tex] r=\frac{3(138)-440}{\sqrt{(38(3)-100)(3(936)-1936)}} [/tex]
[tex] r= \frac{-26}{\sqrt{14 \times 872}} [/tex]
r= -0.24
Answer:
Long answer short, its B: -0.24
Step-by-step explanation:
