Finite Math Examples

\begin{matrix} x & y 0 & 5000 2 & 3750 4 & 2500 6 & 1250 8 & 0 \end{matrix}

$\begin{array}{c} x & y \\ 0 & 5000 \\ 2 & 3750 \\ 4 & 2500 \\ 6 & 1250 \\ 8 & 0 \end{array}$

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}}}

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

Step 2

Sum up the

x

$x$ values.

\sum x = 0 + 2 + 4 + 6 + 8

$\sum_{}^{} x = 0 + 2 + 4 + 6 + 8$

Step 3

Simplify the expression.

\sum x = 20

$\sum_{}^{} x = 20$

Step 4

Sum up the

y

$y$ values.

\sum y = 5000 + 3750 + 2500 + 1250 + 0

$\sum_{}^{} y = 5000 + 3750 + 2500 + 1250 + 0$

Step 5

Simplify the expression.

\sum y = 12500

$\sum_{}^{} y = 12500$

Step 6

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum x y = 0 \cdot 5000 + 2 \cdot 3750 + 4 \cdot 2500 + 6 \cdot 1250 + 8 \cdot 0

$\sum_{}^{} x y = 0 \cdot 5000 + 2 \cdot 3750 + 4 \cdot 2500 + 6 \cdot 1250 + 8 \cdot 0$

Step 7

Simplify the expression.

\sum x y = 25000

$\sum_{}^{} x y = 25000$

Step 8

Sum up the values of

x^{2}

$x^{2}$ .

\sum x^{2} = {(0)}^{2} + {(2)}^{2} + {(4)}^{2} + {(6)}^{2} + {(8)}^{2}

$\sum_{}^{} x^{2} = {(0)}^{2} + {(2)}^{2} + {(4)}^{2} + {(6)}^{2} + {(8)}^{2}$

Step 9

Simplify the expression.

\sum x^{2} = 120

$\sum_{}^{} x^{2} = 120$

Step 10

Sum up the values of

y^{2}

$y^{2}$ .

\sum y^{2} = {(5000)}^{2} + {(3750)}^{2} + {(2500)}^{2} + {(1250)}^{2} + {(0)}^{2}

$\sum_{}^{} y^{2} = {(5000)}^{2} + {(3750)}^{2} + {(2500)}^{2} + {(1250)}^{2} + {(0)}^{2}$

Step 11

Simplify the expression.

\sum y^{2} = 46875000

$\sum_{}^{} y^{2} = 46875000$

Step 12

Fill in the computed values.

r = \frac{5 (25000) - 20 \cdot 12500}{\sqrt{5 (120) - {(20)}^{2}} \cdot \sqrt{5 (46875000) - {(12500)}^{2}}}

$r = \frac{5 (25000) - 20 \cdot 12500}{\sqrt{5 (120) - {(20)}^{2}} \cdot \sqrt{5 (46875000) - {(12500)}^{2}}}$

Step 13

Simplify the expression.

r = - 0.99999994

$r = - 0.99999994$