Finite Math Examples

$\begin{array}{c} x & y \\ 1975 & 14.2 \\ 1980 & 16.9 \\ 1985 & 19.6 \\ 1990 & 21.4 \\ 1995 & 23.1 \\ 2000 & 25.6 \end{array}$

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.

$\sum_{}^{} x = 1975 + 1980 + 1985 + 1990 + 1995 + 2000$

Step 3

Simplify the expression.

$\sum_{}^{} x = 11925$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 14.2 + 16.9 + 19.6 + 21.4 + 23.1 + 25.6$

Step 5

Simplify the expression.

$\sum_{}^{} y = 120.799995$

Step 6

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

$\sum_{}^{} x y = 1975 \cdot 14.2 + 1980 \cdot 16.9 + 1985 \cdot 19.6 + 1990 \cdot 21.4 + 1995 \cdot 23.1 + 2000 \cdot 25.6$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 240283.5$

Step 8

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

$\sum_{}^{} x^{2} = {(1975)}^{2} + {(1980)}^{2} + {(1985)}^{2} + {(1990)}^{2} + {(1995)}^{2} + {(2000)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 23701375$

Step 10

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

$\sum_{}^{} y^{2} = {(14.2)}^{2} + {(16.9)}^{2} + {(19.6)}^{2} + {(21.4)}^{2} + {(23.1)}^{2} + {(25.6)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 2518.34001747$

Step 12

Fill in the computed values.

$r = \frac{6 (240283.5) - 11925 \cdot 120.799995}{\sqrt{6 (23701376) - {(11925)}^{2}} \cdot \sqrt{6 (2518.34) - {(120.799995)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.9950793$