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Calculate the coefficient of correlation using Pearson's product-moment correlation coefficient formula with the given data.

Mathematics

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Answer

0.9791

Step-by-step solution

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गुणांक सहसंबंध (coefficient of correlation) की गणना करने के लिए, हम पियर्सन के उत्पाद-क्षण सहसंबंध गुणांक (Pearson product-moment correlation coefficient) सूत्र का उपयोग करेंगे:

r=n∑(XY)−(∑X)(∑Y)[n∑X2−(∑X)2][n∑Y2−(∑Y)2]r = \frac{n \sum (XY) - (\sum X)(\sum Y)}{\sqrt{[n \sum X^2 - (\sum X)^2][n \sum Y^2 - (\sum Y)^2]}}

जहाँ nn डेटा बिंदुओं की संख्या है।

  1. आवश्यक योगों की गणना करें।

    यहाँ n=5n=5 डेटा बिंदु हैं।

    XYXYX^2Y^2
    2714449
    3927981
    4104016100
    5147025196
    6159036225
    --------------------
    ∑X=20\sum X = 20∑Y=55\sum Y = 55∑XY=241\sum XY = 241∑X2=90\sum X^2 = 90∑Y2=651\sum Y^2 = 651

  2. सूत्र में मानों को प्रतिस्थापित करें।

    r=5(241)−(20)(55)[5(90)−(20)2][5(651)−(55)2]r = \frac{5(241) - (20)(55)}{\sqrt{[5(90) - (20)^2][5(651) - (55)^2]}}

  3. अंश (numerator) की गणना करें।

    5(241)−(20)(55)=1205−1100=1055(241) - (20)(55) = 1205 - 1100 = 105

  4. हर (denominator) के पहले भाग की गणना करें।

    5(90)−(20)2=450−400=505(90) - (20)^2 = 450 - 400 = 50

  5. हर के दूसरे भाग की गणना करें।

    5(651)−(55)2=3255−3025=2305(651) - (55)^2 = 3255 - 3025 = 230

  6. हर की गणना करें।

    (50)(230)=11500≈107.23805\sqrt{(50)(230)} = \sqrt{11500} \approx 107.23805

  7. गुणांक सहसंबंध (rr) की गणना करें।

    r=105107.23805r = \frac{105}{107.23805} r≈0.97914r \approx 0.97914

    गुणांक सहसंबंध है:

    0.97910.9791
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