Finite Math Examples

$\begin{array}{c} x & y \\ 8 & 23 \\ 2 & 5 \\ - 3 & - 10 \\ 9 & 26 \end{array}$

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.

$\sum_{}^{} x = 8 + 2 - 3 + 9$

Step 3

Simplify the expression.

$\sum_{}^{} x = 16$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 23 + 5 - 10 + 26$

Step 5

Simplify the expression.

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

Step 6

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

$\sum_{}^{} x y = 8 \cdot 23 + 2 \cdot 5 - 3 \cdot - 10 + 9 \cdot 26$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 458$

Step 8

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

$\sum_{}^{} x^{2} = {(8)}^{2} + {(2)}^{2} + {(- 3)}^{2} + {(9)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 158$

Step 10

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

$\sum_{}^{} y^{2} = {(23)}^{2} + {(5)}^{2} + {(- 10)}^{2} + {(26)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 1330$

Step 12

Fill in the computed values.

$r = \frac{4 (458) - 16 \cdot 44}{\sqrt{4 (158) - {(16)}^{2}} \cdot \sqrt{4 (1330) - {(44)}^{2}}}$

Step 13

Simplify the expression.

$r = 1$