Finite Math Examples

$\begin{array}{c} x & y \\ - 2 & 6 \\ 2 & 7 \\ 5 & 15 \\ 8 & 24 \\ 11 & 33 \end{array}$

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.

$\sum_{}^{} x = - 2 + 2 + 5 + 8 + 11$

Step 3

Simplify the expression.

$\sum_{}^{} x = 24$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 6 + 7 + 15 + 24 + 33$

Step 5

Simplify the expression.

$\sum_{}^{} y = 85$

Step 6

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

$\sum_{}^{} x y = - 2 \cdot 6 + 2 \cdot 7 + 5 \cdot 15 + 8 \cdot 24 + 11 \cdot 33$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 632$

Step 8

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

$\sum_{}^{} x^{2} = {(- 2)}^{2} + {(2)}^{2} + {(5)}^{2} + {(8)}^{2} + {(11)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 218$

Step 10

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

$\sum_{}^{} y^{2} = {(6)}^{2} + {(7)}^{2} + {(15)}^{2} + {(24)}^{2} + {(33)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 1975$

Step 12

Fill in the computed values.

$r = \frac{5 (632) - 24 \cdot 85}{\sqrt{5 (218) - {(24)}^{2}} \cdot \sqrt{5 (1975) - {(85)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.95965145$