Finite Math Examples

$\begin{array}{c} x & y \\ 0.1 & 1 \\ 0.2 & 0.98 \\ 0.3 & 0.96 \\ 0.4 & 0.92 \\ 0.5 & 0.87 \\ 0.6 & 0.8 \\ 0.7 & 0.71 \\ 0.8 & 0.6 \\ 0.9 & 44 \end{array}$

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.

$\sum_{}^{} x = 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9$

Step 3

Simplify the expression.

$\sum_{}^{} x = 4.5$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 1 + 0.98 + 0.96 + 0.92 + 0.87 + 0.8 + 0.71 + 0.6 + 44$

Step 5

Simplify the expression.

$\sum_{}^{} y = 50.84$

Step 6

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

$\sum_{}^{} x y = 0.1 \cdot 1 + 0.2 \cdot 0.98 + 0.3 \cdot 0.96 + 0.4 \cdot 0.92 + 0.5 \cdot 0.87 + 0.6 \cdot 0.8 + 0.7 \cdot 0.71 + 0.8 \cdot 0.6 + 0.9 \cdot 44$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 42.444$

Step 8

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

$\sum_{}^{} x^{2} = {(0.1)}^{2} + {(0.2)}^{2} + {(0.3)}^{2} + {(0.4)}^{2} + {(0.5)}^{2} + {(0.6)}^{2} + {(0.7)}^{2} + {(0.8)}^{2} + {(0.9)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 2.85$

Step 10

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

$\sum_{}^{} y^{2} = {(1)}^{2} + {(0.98)}^{2} + {(0.96)}^{2} + {(0.92)}^{2} + {(0.87)}^{2} + {(0.8)}^{2} + {(0.71)}^{2} + {(0.6)}^{2} + {(44)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 1941.98940005$

Step 12

Fill in the computed values.

$r = \frac{9 (42.444) - 4.5 \cdot 50.84}{\sqrt{9 (2.85) - {(4.5)}^{2}} \cdot \sqrt{9 (1941.9894) - {(50.84)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.54027301$

Step 14

Find the critical value for a confidence level of $0$ and $9$ degrees of freedom.

$t = 2.36462424$