Finite Math Examples

\begin{array}{c} x & y \\ 1 & 2 \\ 2 & 5 \\ 3 & 5 \\ 4 & 8 \\ 5 & 9 \end{array}

$\begin{array}{c} x & y \\ 1 & 2 \\ 2 & 5 \\ 3 & 5 \\ 4 & 8 \\ 5 & 9 \end{array}$

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 + 2 + 3 + 4 + 5

$\sum_{}^{} x = 1 + 2 + 3 + 4 + 5$

Step 3

Simplify the expression.

\sum_{}^{} x = 15

$\sum_{}^{} x = 15$

Step 4

Sum up the

y

$y$ values.

\sum_{}^{} y = 2 + 5 + 5 + 8 + 9

$\sum_{}^{} y = 2 + 5 + 5 + 8 + 9$

Step 5

Simplify the expression.

\sum_{}^{} y = 29

$\sum_{}^{} y = 29$

Step 6

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum_{}^{} x y = 1 \cdot 2 + 2 \cdot 5 + 3 \cdot 5 + 4 \cdot 8 + 5 \cdot 9

$\sum_{}^{} x y = 1 \cdot 2 + 2 \cdot 5 + 3 \cdot 5 + 4 \cdot 8 + 5 \cdot 9$

Step 7

Simplify the expression.

\sum_{}^{} x y = 104

$\sum_{}^{} x y = 104$

Step 8

Sum up the values of

x^{2}

$x^{2}$ .

\sum_{}^{} x^{2} = {(1)}^{2} + {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2}

$\sum_{}^{} x^{2} = {(1)}^{2} + {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2}$

Step 9

Simplify the expression.

\sum_{}^{} x^{2} = 55

$\sum_{}^{} x^{2} = 55$

Step 10

Sum up the values of

y^{2}

$y^{2}$ .

\sum_{}^{} y^{2} = {(2)}^{2} + {(5)}^{2} + {(5)}^{2} + {(8)}^{2} + {(9)}^{2}

$\sum_{}^{} y^{2} = {(2)}^{2} + {(5)}^{2} + {(5)}^{2} + {(8)}^{2} + {(9)}^{2}$

Step 11

Simplify the expression.

\sum_{}^{} y^{2} = 199

$\sum_{}^{} y^{2} = 199$

Step 12

Fill in the computed values.

r = \frac{5 (104) - 15 \cdot 29}{\sqrt{5 (55) - {(15)}^{2}} \cdot \sqrt{5 (199) - {(29)}^{2}}}

$r = \frac{5 (104) - 15 \cdot 29}{\sqrt{5 (55) - {(15)}^{2}} \cdot \sqrt{5 (199) - {(29)}^{2}}}$

Step 13

Simplify the expression.

r = 0.96866489

$r = 0.96866489$