Question

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

Answer 1

Answer:

Option (4)

Step-by-step 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 = $\frac{1676.48-1440.72}{\sqrt{266.52\times 274.56} }$

r = $\frac{235.76}{\sqrt{73175.73}}$

r = $\frac{235.76}{270.51}$

r = 0.87

r ≈ 0.9

Therefore, Option (4) is the answer.