Finite Math Examples

$\begin{array}{c} x & y \\ 1985 & 2.5 \\ 1995 & 3.3 \\ 2010 & 3.9 \\ 2035 & 3.7 \end{array}$

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.

$\sum_{}^{} x = 1985 + 1995 + 2010 + 2035$

Step 3

Simplify the expression.

$\sum_{}^{} x = 8025$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 2.5 + 3.3 + 3.9 + 3.7$

Step 5

Simplify the expression.

$\sum_{}^{} y = 13.400001$

Step 6

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

$\sum_{}^{} x y = 1985 \cdot 2.5 + 1995 \cdot 3.3 + 2010 \cdot 3.9 + 2035 \cdot 3.7$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 26914.5$

Step 8

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

$\sum_{}^{} x^{2} = {(1985)}^{2} + {(1995)}^{2} + {(2010)}^{2} + {(2035)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 16101575$

Step 10

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

$\sum_{}^{} y^{2} = {(2.5)}^{2} + {(3.3)}^{2} + {(3.9)}^{2} + {(3.7)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 46.04000078$

Step 12

Fill in the computed values.

$r = \frac{4 (26914.5) - 8025 \cdot 13.400001}{\sqrt{4 (16101575) - {(8025)}^{2}} \cdot \sqrt{4 (46.04) - {(13.400001)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.76123058$