Find the Linear Correlation Coefficient table[[x,y],[2,15],[6,13],[7,9]]

$\begin{array}{c} x & y \\ 2 & 15 \\ 6 & 13 \\ 7 & 9 \end{array}$

Step 1

The linear correlation coefficient measures the relationship between the paired values in a sample.

$r = \frac{n (\sum_{}^{} x y) - \sum_{}^{} x \sum_{}^{} y}{\sqrt{n (\sum_{}^{} x^{2}) - {(\sum_{}^{} x)}^{2}} \cdot \sqrt{n (\sum_{}^{} y^{2}) - {(\sum_{}^{} y)}^{2}}}$

Step 2

Sum up the $x$ values.

$\sum_{}^{} x = 2 + 6 + 7$

Step 3

Simplify the expression.

$\sum_{}^{} x = 15$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 15 + 13 + 9$

Step 5

Simplify the expression.

$\sum_{}^{} y = 37$

Step 6

Sum up the values of $x \cdot y$ .

$\sum_{}^{} x y = 2 \cdot 15 + 6 \cdot 13 + 7 \cdot 9$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 171$

Step 8

Sum up the values of $x^{2}$ .

$\sum_{}^{} x^{2} = {(2)}^{2} + {(6)}^{2} + {(7)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 89$

Step 10

Sum up the values of $y^{2}$ .

$\sum_{}^{} y^{2} = {(15)}^{2} + {(13)}^{2} + {(9)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 475$

Step 12

Fill in the computed values.

$r = \frac{3 (171) - 15 \cdot 37}{\sqrt{3 (89) - {(15)}^{2}} \cdot \sqrt{3 (475) - {(37)}^{2}}}$

Step 13

Simplify the expression.

$r = - 0.8660254$

Find the Linear Correlation Coefficient table[[x,y],[2,15],[6,13],[7,9]]

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