Math, asked by prinkle3614, 7 hours ago

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:​

Answers

Answered by amitnrw
9

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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