Finite Math Examples

$\begin{array}{c} x & y \\ 1 & 153.2 \\ 11 & 150.7 \\ 21 & 147.9 \\ 31 & 206.1 \\ 38 & 151.2 \end{array}$

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.

$\sum_{}^{} x = 1 + 11 + 21 + 31 + 38$

Step 3

Simplify the expression.

$\sum_{}^{} x = 102$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 153.2 + 150.7 + 147.9 + 206.1 + 151.2$

Step 5

Simplify the expression.

$\sum_{}^{} y = 809.10004$

Step 6

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

$\sum_{}^{} x y = 1 \cdot 153.2 + 11 \cdot 150.7 + 21 \cdot 147.9 + 31 \cdot 206.1 + 38 \cdot 151.2$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 17051.5$

Step 8

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

$\sum_{}^{} x^{2} = {(1)}^{2} + {(11)}^{2} + {(21)}^{2} + {(31)}^{2} + {(38)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 2968$

Step 10

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

$\sum_{}^{} y^{2} = {(153.2)}^{2} + {(150.7)}^{2} + {(147.9)}^{2} + {(206.1)}^{2} + {(151.2)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 133393.78793273$

Step 12

Fill in the computed values.

$r = \frac{5 (17051.5) - 102 \cdot 809.10004}{\sqrt{5 (2968) - {(102)}^{2}} \cdot \sqrt{5 (133393.78) - {(809.10004)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.36909981$