Finite Math Examples

$\begin{array}{c} x & y \\ 1 & 1.11 \\ 1.5 & 1.36 \\ 2 & 1.57 \\ 2.5 & 1.76 \\ 3 & 1.92 \\ 3.5 & 2.08 \\ 4 & 2.22 \end{array}$

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.

$\sum_{}^{} x = 1 + 1.5 + 2 + 2.5 + 3 + 3.5 + 4$

Step 3

Simplify the expression.

$\sum_{}^{} x = 17.5$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 1.11 + 1.36 + 1.57 + 1.76 + 1.92 + 2.08 + 2.22$

Step 5

Simplify the expression.

$\sum_{}^{} y = 12.02$

Step 6

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

$\sum_{}^{} x y = 1 \cdot 1.11 + 1.5 \cdot 1.36 + 2 \cdot 1.57 + 2.5 \cdot 1.76 + 3 \cdot 1.92 + 3.5 \cdot 2.08 + 4 \cdot 2.22$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 32.61$

Step 8

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

$\sum_{}^{} x^{2} = {(1)}^{2} + {(1.5)}^{2} + {(2)}^{2} + {(2.5)}^{2} + {(3)}^{2} + {(3.5)}^{2} + {(4)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 50.75$

Step 10

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

$\sum_{}^{} y^{2} = {(1.11)}^{2} + {(1.36)}^{2} + {(1.57)}^{2} + {(1.76)}^{2} + {(1.92)}^{2} + {(2.08)}^{2} + {(2.22)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 21.58539984$

Step 12

Fill in the computed values.

$r = \frac{7 (32.61) - 17.5 \cdot 12.02}{\sqrt{7 (50.75) - {(17.5)}^{2}} \cdot \sqrt{7 (21.5854) - {(12.02)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.9951689$