Question

What is the r-value of the following data, to three decimal places

Answer 1

Answer:

Option: A is the correct answer.

              A.  -0.903

Step-by-step explanation:

The formula to calculate correlation coefficient r is given by:

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

        x          y         xy          x²            y²        

        4         23        92        16           529

        5          12        60        25          144

        8          10        80        64          100

        9          9          81         81            81

        13         2          26       169           4

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∑     39       56        339      355         858

Also n=5 ( as there are 5 data points )

Hence, we get:

$r=\dfrac{5\times 339-39\times 56}{\sqrt{5\times 355-(39)^2}\times \sqrt{5\times 858-(56)^2}}\\\\\\r=\dfrac{-489}{\sqrt{254}\times \sqrt{1154}}$

$r=-\dfrac{489}{541.40188}=-0.9032$

     Hence,  the r-value of the following data, to three decimal places is:

                               A.  -0.932