Finite Math Examples

$\begin{array}{c} x & y \\ 0 & 20444 \\ 2 & 24981 \\ 5 & 17980 \\ 6 & 16906 \\ 7 & 21292 \\ 8 & 26660 \\ 11 & 39788 \\ 12 & 51149 \\ 13 & 27841 \\ 14 & 37442 \\ 15 & 30995 \end{array}$

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.

$\sum_{}^{} x = 0 + 2 + 5 + 6 + 7 + 8 + 11 + 12 + 13 + 14 + 15$

Step 3

Simplify the expression.

$\sum_{}^{} x = 93$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 20444 + 24981 + 17980 + 16906 + 21292 + 26660 + 39788 + 51149 + 27841 + 37442 + 30995$

Step 5

Simplify the expression.

$\sum_{}^{} y = 315478$

Step 6

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

$\sum_{}^{} x y = 0 \cdot 20444 + 2 \cdot 24981 + 5 \cdot 17980 + 6 \cdot 16906 + 7 \cdot 21292 + 8 \cdot 26660 + 11 \cdot 39788 + 12 \cdot 51149 + 13 \cdot 27841 + 14 \cdot 37442 + 15 \cdot 30995$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 3006124$

Step 8

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

$\sum_{}^{} x^{2} = {(0)}^{2} + {(2)}^{2} + {(5)}^{2} + {(6)}^{2} + {(7)}^{2} + {(8)}^{2} + {(11)}^{2} + {(12)}^{2} + {(13)}^{2} + {(14)}^{2} + {(15)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 1033$

Step 10

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

$\sum_{}^{} y^{2} = {(20444)}^{2} + {(24981)}^{2} + {(17980)}^{2} + {(16906)}^{2} + {(21292)}^{2} + {(26660)}^{2} + {(39788)}^{2} + {(51149)}^{2} + {(27841)}^{2} + {(37442)}^{2} + {(30995)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 10152225412$

Step 12

Fill in the computed values.

$r = \frac{11 (3006124) - 93 \cdot 315478}{\sqrt{11 (1033) - {(93)}^{2}} \cdot \sqrt{11 (1.0152226 E + 10) - {(315478)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.64924118$