Finite Math Examples

$\begin{array}{c} x & R (x) \\ 0 & 21.8 \\ 10 & 26.9 \\ 14 & 35.3 \\ 15 & 39.8 \\ 16 & 40.1 \\ 17 & 40.6 \\ 18 & 50.3 \\ 19 & 48.1 \\ 20 & 49.5 \end{array}$

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.

$\sum_{}^{} x = 0 + 10 + 14 + 15 + 16 + 17 + 18 + 19 + 20$

Step 3

Simplify the expression.

$\sum_{}^{} x = 129$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 21.8 + 26.9 + 35.3 + 39.8 + 40.1 + 40.6 + 50.3 + 48.1 + 49.5$

Step 5

Simplify the expression.

$\sum_{}^{} y = 352.4$

Step 6

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

$\sum_{}^{} x y = 0 \cdot 21.8 + 10 \cdot 26.9 + 14 \cdot 35.3 + 15 \cdot 39.8 + 16 \cdot 40.1 + 17 \cdot 40.6 + 18 \cdot 50.3 + 19 \cdot 48.1 + 20 \cdot 49.5$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 5501.3$

Step 8

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

$\sum_{}^{} x^{2} = {(0)}^{2} + {(10)}^{2} + {(14)}^{2} + {(15)}^{2} + {(16)}^{2} + {(17)}^{2} + {(18)}^{2} + {(19)}^{2} + {(20)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 2151$

Step 10

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

$\sum_{}^{} y^{2} = {(21.8)}^{2} + {(26.9)}^{2} + {(35.3)}^{2} + {(39.8)}^{2} + {(40.1)}^{2} + {(40.6)}^{2} + {(50.3)}^{2} + {(48.1)}^{2} + {(49.5)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 14579.2993618$

Step 12

Fill in the computed values.

$r = \frac{9 (5501.3) - 129 \cdot 352.4}{\sqrt{9 (2151) - {(129)}^{2}} \cdot \sqrt{9 (14579.3) - {(352.4)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.92713151$