Finite Math Examples

$\begin{array}{c} x & y \\ 0 & 0 \\ 10 & 0.503 \\ 20 & 0.44 \\ 30 & 0.581 \\ 40 & 0.686 \\ 50 & 0.765 \end{array}$

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.

$\sum_{}^{} x = 0 + 10 + 20 + 30 + 40 + 50$

Step 3

Simplify the expression.

$\sum_{}^{} x = 150$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 0 + 0.503 + 0.44 + 0.581 + 0.686 + 0.765$

Step 5

Simplify the expression.

$\sum_{}^{} y = 2.975$

Step 6

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

$\sum_{}^{} x y = 0 \cdot 0 + 10 \cdot 0.503 + 20 \cdot 0.44 + 30 \cdot 0.581 + 40 \cdot 0.686 + 50 \cdot 0.765$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 96.95$

Step 8

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

$\sum_{}^{} x^{2} = {(0)}^{2} + {(10)}^{2} + {(20)}^{2} + {(30)}^{2} + {(40)}^{2} + {(50)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 5500$

Step 10

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

$\sum_{}^{} y^{2} = {(0)}^{2} + {(0.503)}^{2} + {(0.44)}^{2} + {(0.581)}^{2} + {(0.686)}^{2} + {(0.765)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 1.83999094$

Step 12

Fill in the computed values.

$r = \frac{6 (96.95) - 150 \cdot 2.975}{\sqrt{6 (5500) - {(150)}^{2}} \cdot \sqrt{6 (1.839991) - {(2.975)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.89336609$