Answer:
Option (4)
Step-by-step explanation:
Table for the points from the graph attached,
x y [tex]x^{2}[/tex] [tex]y^{2}[/tex] xy
2.2 1.8 4.84 3.24 3.96
3.2 1.8 10.24 3.24 5.76
3.6 3 12.96 9 10.8
4.8 3.5 23.04 12.25 16.8
5.2 6.2 27.04 38.44 32.24
6.4 4.5 40.96 20.25 28.8
7.5 7.8 56.25 60.84 58.5
8.5 6.2 72.25 38.44 52.7
[tex]\sum x=41.4[/tex]
[tex]\sum y=34.8[/tex]
[tex]\sum x^2=247.58[/tex]
[tex]\sum y^2=185.7[/tex]
[tex]\sum xy=209.56[/tex]
n = 8
Formula for the correlation coefficient [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]
[tex]r=\frac{8(209.56)-(41.4)(34.8)}{\sqrt{[{8(247.58)-(41.4)^2][8(185.7)-(34.8)^2]}}}[/tex]
r = [tex]\frac{1676.48-1440.72}{\sqrt{266.52\times 274.56} }[/tex]
r = [tex]\frac{235.76}{\sqrt{73175.73}}[/tex]
r = [tex]\frac{235.76}{270.51}[/tex]
r = 0.87
r ≈ 0.9
Therefore, Option (4) is the answer.
