Finite Math Examples

$\begin{array}{c} x & y \\ 31831 & 7765 \\ 293089 & 8907 \\ 280043 & 11178 \\ 276548 & 14946 \\ 246923 & 20639 \\ 29373 & 26220 \\ 205730 & 32285 \end{array}$

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.

$\sum_{}^{} x = 31831 + 293089 + 280043 + 276548 + 246923 + 29373 + 205730$

Step 3

Simplify the expression.

$\sum_{}^{} x = 1363537$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 7765 + 8907 + 11178 + 14946 + 20639 + 26220 + 32285$

Step 5

Simplify the expression.

$\sum_{}^{} y = 121940$

Step 6

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

$\sum_{}^{} x y = 31831 \cdot 7765 + 293089 \cdot 8907 + 280043 \cdot 11178 + 276548 \cdot 14946 + 246923 \cdot 20639 + 29373 \cdot 26220 + 205730 \cdot 32285$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 2.2629714 E + 10$

Step 8

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

$\sum_{}^{} x^{2} = {(31831)}^{2} + {(293089)}^{2} + {(280043)}^{2} + {(276548)}^{2} + {(246923)}^{2} + {(29373)}^{2} + {(205730)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 345975826593$

Step 10

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

$\sum_{}^{} y^{2} = {(7765)}^{2} + {(8907)}^{2} + {(11178)}^{2} + {(14946)}^{2} + {(20639)}^{2} + {(26220)}^{2} + {(32285)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 2643738420$

Step 12

Fill in the computed values.

$r = \frac{7 (2.2629714 E + 10) - 1363537 \cdot 121940}{\sqrt{7 (3.459758 E + 11) - {(1363537)}^{2}} \cdot \sqrt{7 (2.6437384 E + 9) - {(121940)}^{2}}}$

Step 13

Simplify the expression.

$r = - 0.17380308$