Finite Math Examples

\begin{matrix} x & y - 1 & 1.3 0 & 1 1 & 3 \end{matrix}

$\begin{array}{c} x & y \\ - 1 & 1.3 \\ 0 & 1 \\ 1 & 3 \end{array}$

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 = - 1 + 0 + 1

$\sum_{}^{} x = - 1 + 0 + 1$

Step 3

Simplify the expression.

\sum x = 0

$\sum_{}^{} x = 0$

Step 4

Sum up the

y

$y$ values.

\sum y = 1.3 + 1 + 3

$\sum_{}^{} y = 1.3 + 1 + 3$

Step 5

Simplify the expression.

\sum y = 5.3

$\sum_{}^{} y = 5.3$

Step 6

Sum up the values of

$x \cdot y$ .

$\sum_{}^{} x y = - 1 \cdot 1.3 + 0 \cdot 1 + 1 \cdot 3$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 1.7$

Step 8

Sum up the values of

$x^{2}$ .

$\sum_{}^{} x^{2} = {(- 1)}^{2} + {(0)}^{2} + {(1)}^{2}$

Step 9

Simplify the expression.

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

Step 10

Sum up the values of

$y^{2}$ .

$\sum_{}^{} y^{2} = {(1.3)}^{2} + {(1)}^{2} + {(3)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 11.68999987$

Step 12

Fill in the computed values.

$r = \frac{3 (1.7) + 0 \cdot 5.3}{\sqrt{3 (2) - {(0)}^{2}} \cdot \sqrt{3 (11.69) - {(5.3)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.7880739$