Finite Math Examples

$\begin{array}{c} x & y \\ 5.7 & 5.2 \\ 5.8 & 5.4 \\ 6.2 & 6.7 \\ 7.3 & 7.7 \\ 8.5 & 8.5 \end{array}$

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.

$\sum_{}^{} x = 5.7 + 5.8 + 6.2 + 7.3 + 8.5$

Step 3

Simplify the expression.

$\sum_{}^{} x = 33.5$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 5.2 + 5.4 + 6.7 + 7.7 + 8.5$

Step 5

Simplify the expression.

$\sum_{}^{} y = 33.5$

Step 6

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

$\sum_{}^{} x y = 5.7 \cdot 5.2 + 5.8 \cdot 5.4 + 6.2 \cdot 6.7 + 7.3 \cdot 7.7 + 8.5 \cdot 8.5$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 230.95999$

Step 8

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

$\sum_{}^{} x^{2} = {(5.7)}^{2} + {(5.8)}^{2} + {(6.2)}^{2} + {(7.3)}^{2} + {(8.5)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 230.11000045$

Step 10

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

$\sum_{}^{} y^{2} = {(5.2)}^{2} + {(5.4)}^{2} + {(6.7)}^{2} + {(7.7)}^{2} + {(8.5)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 232.62999355$

Step 12

Fill in the computed values.

$r = \frac{5 (230.95999) - 33.5 \cdot 33.5}{\sqrt{5 (230.11) - {(33.5)}^{2}} \cdot \sqrt{5 (232.62999) - {(33.5)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.95674298$