Finite Math Examples

$\begin{array}{c} x & y \\ 0 & 181 \\ 5 & 194 \\ 10 & 205 \\ 15 & 216 \\ 20 & 228 \\ 25 & 238 \\ 30 & 250 \\ 35 & 263 \\ 38 & 271 \\ 40 & 281 \\ 43 & 291 \\ 45 & 296 \\ 65 & 348 \\ 90 & 420 \end{array}$

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.

$\sum_{}^{} x = 0 + 5 + 10 + 15 + 20 + 25 + 30 + 35 + 38 + 40 + 43 + 45 + 65 + 90$

Step 3

Simplify the expression.

$\sum_{}^{} x = 461$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 181 + 194 + 205 + 216 + 228 + 238 + 250 + 263 + 271 + 281 + 291 + 296 + 348 + 420$

Step 5

Simplify the expression.

$\sum_{}^{} y = 3682$

Step 6

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

$\sum_{}^{} x y = 0 \cdot 181 + 5 \cdot 194 + 10 \cdot 205 + 15 \cdot 216 + 20 \cdot 228 + 25 \cdot 238 + 30 \cdot 250 + 35 \cdot 263 + 38 \cdot 271 + 40 \cdot 281 + 43 \cdot 291 + 45 \cdot 296 + 65 \cdot 348 + 90 \cdot 420$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 141266$

Step 8

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

$\sum_{}^{} x^{2} = {(0)}^{2} + {(5)}^{2} + {(10)}^{2} + {(15)}^{2} + {(20)}^{2} + {(25)}^{2} + {(30)}^{2} + {(35)}^{2} + {(38)}^{2} + {(40)}^{2} + {(43)}^{2} + {(45)}^{2} + {(65)}^{2} + {(90)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 22743$

Step 10

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

$\sum_{}^{} y^{2} = {(181)}^{2} + {(194)}^{2} + {(205)}^{2} + {(216)}^{2} + {(228)}^{2} + {(238)}^{2} + {(250)}^{2} + {(263)}^{2} + {(271)}^{2} + {(281)}^{2} + {(291)}^{2} + {(296)}^{2} + {(348)}^{2} + {(420)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 1021578$

Step 12

Fill in the computed values.

$r = \frac{14 (141266) - 461 \cdot 3682}{\sqrt{14 (22743) - {(461)}^{2}} \cdot \sqrt{14 (1021578) - {(3682)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.99811218$