Finite Math Examples

$\begin{array}{c} x & y \\ 1 & 5.8 \\ 2 & 6.1 \\ 3 & 7.2 \\ 4 & 8.3 \\ 5 & 9 \end{array}$

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.

$\sum_{}^{} x = 1 + 2 + 3 + 4 + 5$

Step 3

Simplify the expression.

$\sum_{}^{} x = 15$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 5.8 + 6.1 + 7.2 + 8.3 + 9$

Step 5

Simplify the expression.

$\sum_{}^{} y = 36.399998$

Step 6

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

$\sum_{}^{} x y = 1 \cdot 5.8 + 2 \cdot 6.1 + 3 \cdot 7.2 + 4 \cdot 8.3 + 5 \cdot 9$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 117.8$

Step 8

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

$\sum_{}^{} x^{2} = {(1)}^{2} + {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 55$

Step 10

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

$\sum_{}^{} y^{2} = {(5.8)}^{2} + {(6.1)}^{2} + {(7.2)}^{2} + {(8.3)}^{2} + {(9)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 272.58000146$

Step 12

Fill in the computed values.

$r = \frac{5 (117.8) - 15 \cdot 36.399998}{\sqrt{5 (55) - {(15)}^{2}} \cdot \sqrt{5 (272.58) - {(36.399998)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.98726788$