Finite Math Examples

$\begin{array}{c} x & y \\ 5 & 64 \\ 10 & 86 \\ 4 & 69 \\ 6 & 86 \\ 10 & 59 \\ 9 & 87 \end{array}$

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.

$\sum_{}^{} x = 5 + 10 + 4 + 6 + 10 + 9$

Step 3

Simplify the expression.

$\sum_{}^{} x = 44$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 64 + 86 + 69 + 86 + 59 + 87$

Step 5

Simplify the expression.

$\sum_{}^{} y = 451$

Step 6

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

$\sum_{}^{} x y = 5 \cdot 64 + 10 \cdot 86 + 4 \cdot 69 + 6 \cdot 86 + 10 \cdot 59 + 9 \cdot 87$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 3345$

Step 8

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

$\sum_{}^{} x^{2} = {(5)}^{2} + {(10)}^{2} + {(4)}^{2} + {(6)}^{2} + {(10)}^{2} + {(9)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 358$

Step 10

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

$\sum_{}^{} y^{2} = {(64)}^{2} + {(86)}^{2} + {(69)}^{2} + {(86)}^{2} + {(59)}^{2} + {(87)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 34699$

Step 12

Fill in the computed values.

$r = \frac{6 (3345) - 44 \cdot 451}{\sqrt{6 (358) - {(44)}^{2}} \cdot \sqrt{6 (34699) - {(451)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.22420061$