Finite Math Examples

$\begin{array}{c} x & y \\ 8 & 14 \\ 9 & 11 \\ 10 & 15 \\ 12 & 14 \\ 12 & 15 \end{array}$

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.

$\sum_{}^{} x = 8 + 9 + 10 + 12 + 12$

Step 3

Simplify the expression.

$\sum_{}^{} x = 51$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 14 + 11 + 15 + 14 + 15$

Step 5

Simplify the expression.

$\sum_{}^{} y = 69$

Step 6

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

$\sum_{}^{} x y = 8 \cdot 14 + 9 \cdot 11 + 10 \cdot 15 + 12 \cdot 14 + 12 \cdot 15$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 709$

Step 8

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

$\sum_{}^{} x^{2} = {(8)}^{2} + {(9)}^{2} + {(10)}^{2} + {(12)}^{2} + {(12)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 533$

Step 10

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

$\sum_{}^{} y^{2} = {(14)}^{2} + {(11)}^{2} + {(15)}^{2} + {(14)}^{2} + {(15)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 963$

Step 12

Fill in the computed values.

$r = \frac{5 (709) - 51 \cdot 69}{\sqrt{5 (533) - {(51)}^{2}} \cdot \sqrt{5 (963) - {(69)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.44226898$

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