Finite Math Examples

$\begin{array}{c} x & y \\ 1 & 1.3 \\ 4 & 1.8 \\ 8 & 2.4 \\ 8 & 2.3 \\ 9 & 2.7 \end{array}$

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.

$\sum_{}^{} x = 1 + 4 + 8 + 8 + 9$

Step 3

Simplify the expression.

$\sum_{}^{} x = 30$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 1.3 + 1.8 + 2.4 + 2.3 + 2.7$

Step 5

Simplify the expression.

$\sum_{}^{} y = 10.5$

Step 6

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

$\sum_{}^{} x y = 1 \cdot 1.3 + 4 \cdot 1.8 + 8 \cdot 2.4 + 8 \cdot 2.3 + 9 \cdot 2.7$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 70.4$

Step 8

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

$\sum_{}^{} x^{2} = {(1)}^{2} + {(4)}^{2} + {(8)}^{2} + {(8)}^{2} + {(9)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 226$

Step 10

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

$\sum_{}^{} y^{2} = {(1.3)}^{2} + {(1.8)}^{2} + {(2.4)}^{2} + {(2.3)}^{2} + {(2.7)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 23.2700002$

Step 12

Fill in the computed values.

$r = \frac{5 (70.4) - 30 \cdot 10.5}{\sqrt{5 (226) - {(30)}^{2}} \cdot \sqrt{5 (23.27) - {(10.5)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.9878083$