Finite Math Examples

\begin{matrix} x & y 0 & 7 5 & 1 6 & 0 7 & 6 7 & 9 8 & 5 9 & 8 \end{matrix}

$\begin{array}{c} x & y \\ 0 & 7 \\ 5 & 1 \\ 6 & 0 \\ 7 & 6 \\ 7 & 9 \\ 8 & 5 \\ 9 & 8 \end{array}$

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 + 5 + 6 + 7 + 7 + 8 + 9

$\sum_{}^{} x = 0 + 5 + 6 + 7 + 7 + 8 + 9$

Step 3

Simplify the expression.

\sum x = 42

$\sum_{}^{} x = 42$

Step 4

Sum up the

$y$ values.

$\sum_{}^{} y = 7 + 1 + 0 + 6 + 9 + 5 + 8$

Step 5

Simplify the expression.

$\sum_{}^{} y = 36$

Step 6

Sum up the values of

$x \cdot y$ .

$\sum_{}^{} x y = 0 \cdot 7 + 5 \cdot 1 + 6 \cdot 0 + 7 \cdot 6 + 7 \cdot 9 + 8 \cdot 5 + 9 \cdot 8$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 222$

Step 8

Sum up the values of

$x^{2}$ .

$\sum_{}^{} x^{2} = {(0)}^{2} + {(5)}^{2} + {(6)}^{2} + {(7)}^{2} + {(7)}^{2} + {(8)}^{2} + {(9)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 304$

Step 10

Sum up the values of

$y^{2}$ .

$\sum_{}^{} y^{2} = {(7)}^{2} + {(1)}^{2} + {(0)}^{2} + {(6)}^{2} + {(9)}^{2} + {(5)}^{2} + {(8)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 256$

Step 12

Fill in the computed values.

$r = \frac{7 (222) - 42 \cdot 36}{\sqrt{7 (304) - {(42)}^{2}} \cdot \sqrt{7 (256) - {(36)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.09884569$

Enter YOUR Problem