Finite Math Examples

$\begin{array}{c} x & y \\ 1995 & 135 \\ 1999 & 156 \\ 2003 & 154 \end{array}$

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.

$\sum_{}^{} x = 1995 + 1999 + 2003$

Step 3

Simplify the expression.

$\sum_{}^{} x = 5997$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 135 + 156 + 154$

Step 5

Simplify the expression.

$\sum_{}^{} y = 445$

Step 6

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

$\sum_{}^{} x y = 1995 \cdot 135 + 1999 \cdot 156 + 2003 \cdot 154$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 889631$

Step 8

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

$\sum_{}^{} x^{2} = {(1995)}^{2} + {(1999)}^{2} + {(2003)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 11988035$

Step 10

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

$\sum_{}^{} y^{2} = {(135)}^{2} + {(156)}^{2} + {(154)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 66277$

Step 12

Fill in the computed values.

$r = \frac{3 (889631) - 5997 \cdot 445}{\sqrt{3 (11988035) - {(5997)}^{2}} \cdot \sqrt{3 (66277) - {(445)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.82395885$