Finite Math Examples

$\begin{array}{c} x & y \\ 2000 & 152.9 \\ 2001 & 141.2 \\ 2002 & 131.6 \\ 2003 & 125.3 \\ 2004 & 122.5 \\ 2005 & 118.9 \\ 2006 & 121.6 \\ 2007 & 119.1 \\ 2008 & 117 \end{array}$

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.

$\sum_{}^{} x = 2000 + 2001 + 2002 + 2003 + 2004 + 2005 + 2006 + 2007 + 2008$

Step 3

Simplify the expression.

$\sum_{}^{} x = 18036$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 152.9 + 141.2 + 131.6 + 125.3 + 122.5 + 118.9 + 121.6 + 119.1 + 117$

Step 5

Simplify the expression.

$\sum_{}^{} y = 1150.1$

Step 6

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

$\sum_{}^{} x y = 2000 \cdot 152.9 + 2001 \cdot 141.2 + 2002 \cdot 131.6 + 2003 \cdot 125.3 + 2004 \cdot 122.5 + 2005 \cdot 118.9 + 2006 \cdot 121.6 + 2007 \cdot 119.1 + 2008 \cdot 117$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 2304564$

Step 8

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

$\sum_{}^{} x^{2} = {(2000)}^{2} + {(2001)}^{2} + {(2002)}^{2} + {(2003)}^{2} + {(2004)}^{2} + {(2005)}^{2} + {(2006)}^{2} + {(2007)}^{2} + {(2008)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 36144204$

Step 10

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

$\sum_{}^{} y^{2} = {(152.9)}^{2} + {(141.2)}^{2} + {(131.6)}^{2} + {(125.3)}^{2} + {(122.5)}^{2} + {(118.9)}^{2} + {(121.6)}^{2} + {(119.1)}^{2} + {(117)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 148138.32927124$

Step 12

Fill in the computed values.

$r = \frac{9 (2304564) - 18036 \cdot 1150.1}{\sqrt{9 (36144204) - {(18036)}^{2}} \cdot \sqrt{9 (148138.33) - {(1150.1)}^{2}}}$

Step 13

Simplify the expression.

$r = - 0.9031275$