Question

Which is the best estimate of the correlation coefficient for the scatter plot ?

Answer 1

Option (4)

Explanation:

Table for the points from the graph attached,

x y
`x^(2)`
`y^(2)` 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

`\sum x=41.4`

`\sum y=34.8`

`\sum x^2=247.58`

`\sum y^2=185.7`

`\sum xy=209.56`

n = 8

Formula for the correlation coefficient
`r=\frac{n\sum xy-(\sum x)(\sum y)}{\sqrt{[{n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}}`

`r=\frac{8(209.56)-(41.4)(34.8)}{\sqrt{[{8(247.58)-(41.4)^2][8(185.7)-(34.8)^2]}}}`

r =
`(1676.48-1440.72)/(√(266.52* 274.56) )`

r =
`(235.76)/(√(73175.73))`

r =
`(235.76)/(270.51)`

r = 0.87

r ≈ 0.9

Therefore, Option (4) is the answer.