Question

Calculate Pearson's coefficient of correlation from the following data using 44 and 26 as the origin* of X and Y respectively.х 43 44 46 40 44 42 45 42 38 40 42 57y29 31 19 18 19 27 27 29 41 30 26 1pCQ Answers:​

Answer 1

Given : .

х  43 44 46 40 44 42 45 42 38 40 42 57

y  29 31  19 18  19  27 27 29  41 30 26 10

To Find : Pearson's coefficient of correlation

Solution:

$\overline{x}=\frac{523}{12}$

$\overline{y}=\frac{306}{12}=\frac{ 51}{2}$

x        y    $x-\overline{x}$      $y-\overline{y}$ ($x-\overline{x}$).($y-\overline{y}$)     $(x-\overline{x})^2$   $(y-\overline{y})^2$

43 29 -0.58 3.50 -2.04 0.34 12.25

44 31 0.42 5.50 2.29 0.17        30.25

46 19 2.42 -6.50 -15.71 5.84 42.25

40 18 -3.58 -7.50 26.88 12.84 56.25

44 19 0.42 -6.50 -2.71 0.17      42.25

42 27 -1.58 1.50  -2.38 2.51           2.25

45 27 1.42   1.50  2.13  2.01           2.25

42 29 -1.58 3.50 -5.54 2.51          12.25

38 41 -5.58 15.50 -86.54 31.17 240.25

40 30 -3.58 4.50 -16.13 12.84 20.25

42 26 -1.58 0.50 -0.79 2.51       0.25

57 10 13.42 -15.50 -207.96 180.01 240.25

                         -308.5 252.92  701

Pearson's coefficient of correlation = r

$r=\dfrac{\sum(x-\overline{x}).(y-\overline{y})}{\sqrt{\sum(x-\overline{x})^2.\sum(y-\overline{y})^2}}$

r =  -308.5 / √(259.92)(701)

=> r = -0.7327

Pearson's coefficient of correlation =  -0.7327

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