Find the Linear Correlation Coefficient table[[x,y],[1,20],[3,14],[5,10]]

$\begin{array}{c} x & y \\ 1 & 20 \\ 3 & 14 \\ 5 & 10 \end{array}$

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.

$\sum_{}^{} x = 1 + 3 + 5$

Step 3

Simplify the expression.

$\sum_{}^{} x = 9$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 20 + 14 + 10$

Step 5

Simplify the expression.

$\sum_{}^{} y = 44$

Step 6

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

$\sum_{}^{} x y = 1 \cdot 20 + 3 \cdot 14 + 5 \cdot 10$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 112$

Step 8

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

$\sum_{}^{} x^{2} = {(1)}^{2} + {(3)}^{2} + {(5)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 35$

Step 10

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

$\sum_{}^{} y^{2} = {(20)}^{2} + {(14)}^{2} + {(10)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 696$

Step 12

Fill in the computed values.

$r = \frac{3 (112) - 9 \cdot 44}{\sqrt{3 (35) - {(9)}^{2}} \cdot \sqrt{3 (696) - {(44)}^{2}}}$

Step 13

Simplify the expression.

$r = - 0.99339926$

Find the Linear Correlation Coefficient table[[x,y],[1,20],[3,14],[5,10]]

Related Questions

Support LCMGCF.com by disabling your adblocker.