Finite Math Examples

$\begin{array}{c} x & y \\ 1997 & 9846 \\ 1998 & 10466 \\ 1999 & 10928 \\ 2000 & 11456 \\ 2001 & 12069 \end{array}$

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.

$\sum_{}^{} x = 1997 + 1998 + 1999 + 2000 + 2001$

Step 3

Simplify the expression.

$\sum_{}^{} x = 9995$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 9846 + 10466 + 10928 + 11456 + 12069$

Step 5

Simplify the expression.

$\sum_{}^{} y = 54765$

Step 6

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

$\sum_{}^{} x y = 1997 \cdot 9846 + 1998 \cdot 10466 + 1999 \cdot 10928 + 2000 \cdot 11456 + 2001 \cdot 12069$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 109480670$

Step 8

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

$\sum_{}^{} x^{2} = {(1997)}^{2} + {(1998)}^{2} + {(1999)}^{2} + {(2000)}^{2} + {(2001)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 19980015$

Step 10

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

$\sum_{}^{} y^{2} = {(9846)}^{2} + {(10466)}^{2} + {(10928)}^{2} + {(11456)}^{2} + {(12069)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 602802753$

Step 12

Fill in the computed values.

$r = \frac{5 (109480670) - 9995 \cdot 54765}{\sqrt{5 (19980016) - {(9995)}^{2}} \cdot \sqrt{5 (602802750) - {(54765)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.95308678$