Finite Math Examples

$\begin{array}{c} x & y \\ 1 & 12.5 \\ 2 & 13.9 \\ 3 & 14.7 \\ 4 & 15.2 \\ 5 & 15.3 \\ 6 & 15.5 \end{array}$

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.

$\sum_{}^{} x = 1 + 2 + 3 + 4 + 5 + 6$

Step 3

Simplify the expression.

$\sum_{}^{} x = 21$

Step 4

Sum up the

$y$ values.

$\sum_{}^{} y = 12.5 + 13.9 + 14.7 + 15.2 + 15.3 + 15.5$

Step 5

Simplify the expression.

$\sum_{}^{} y = 87.1$

Step 6

Sum up the values of

$x \cdot y$ .

$\sum_{}^{} x y = 1 \cdot 12.5 + 2 \cdot 13.9 + 3 \cdot 14.7 + 4 \cdot 15.2 + 5 \cdot 15.3 + 6 \cdot 15.5$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 314.7$

Step 8

Sum up the values of

$x^{2}$ .

$\sum_{}^{} x^{2} = {(1)}^{2} + {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2} + {(6)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 91$

Step 10

Sum up the values of

$y^{2}$ .

$\sum_{}^{} y^{2} = {(12.5)}^{2} + {(13.9)}^{2} + {(14.7)}^{2} + {(15.2)}^{2} + {(15.3)}^{2} + {(15.5)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 1270.92998382$

Step 12

Fill in the computed values.

$r = \frac{6 (314.7) - 21 \cdot 87.1}{\sqrt{6 (91) - {(21)}^{2}} \cdot \sqrt{6 (1270.9299) - {(87.1)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.92154715$