Finite Math Examples

$\begin{array}{c} x & y \\ 1997 & 9.5 \\ 1998 & 9.9 \\ 1999 & 10.3 \\ 2000 & 10.7 \\ 2001 & 10.9 \\ 2002 & 11.7 \\ 2003 & 11.8 \\ 2004 & 11.9 \\ 2005 & 12 \\ 2006 & 12.1 \end{array}$

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.

$\sum_{}^{} x = 1997 + 1998 + 1999 + 2000 + 2001 + 2002 + 2003 + 2004 + 2005 + 2006$

Step 3

Simplify the expression.

$\sum_{}^{} x = 20015$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 9.5 + 9.9 + 10.3 + 10.7 + 10.9 + 11.7 + 11.8 + 11.9 + 12 + 12.1$

Step 5

Simplify the expression.

$\sum_{}^{} y = 110.8$

Step 6

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

$\sum_{}^{} x y = 1997 \cdot 9.5 + 1998 \cdot 9.9 + 1999 \cdot 10.3 + 2000 \cdot 10.7 + 2001 \cdot 10.9 + 2002 \cdot 11.7 + 2003 \cdot 11.8 + 2004 \cdot 11.9 + 2005 \cdot 12 + 2006 \cdot 12.1$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 221791.28$

Step 8

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

$\sum_{}^{} x^{2} = {(1997)}^{2} + {(1998)}^{2} + {(1999)}^{2} + {(2000)}^{2} + {(2001)}^{2} + {(2002)}^{2} + {(2003)}^{2} + {(2004)}^{2} + {(2005)}^{2} + {(2006)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 40060105$

Step 10

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

$\sum_{}^{} y^{2} = {(9.5)}^{2} + {(9.9)}^{2} + {(10.3)}^{2} + {(10.7)}^{2} + {(10.9)}^{2} + {(11.7)}^{2} + {(11.8)}^{2} + {(11.9)}^{2} + {(12)}^{2} + {(12.1)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 1235.79998416$

Step 12

Fill in the computed values.

$r = \frac{10 (221791.28) - 20015 \cdot 110.8}{\sqrt{10 (40060104) - {(20015)}^{2}} \cdot \sqrt{10 (1235.7999) - {(110.8)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.98348217$