Finite Math Examples

$\begin{array}{c} x & y \\ 1 & 2 \\ 2 & 3 \\ 3 & 4 \\ 4 & 5 \end{array}$

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.

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

Step 3

Simplify the expression.

$\sum_{}^{} x = 10$

Step 4

Sum up the

$y$ values.

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

Step 5

Simplify the expression.

$\sum_{}^{} y = 14$

Step 6

Sum up the values of

$x \cdot y$ .

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

Step 7

Simplify the expression.

$\sum_{}^{} x y = 40$

Step 8

Sum up the values of

$x^{2}$ .

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

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 30$

Step 10

Sum up the values of

$y^{2}$ .

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

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 54$

Step 12

Fill in the computed values.

$r = \frac{4 (40) - 10 \cdot 14}{\sqrt{4 (30) - {(10)}^{2}} \cdot \sqrt{4 (54) - {(14)}^{2}}}$

Step 13

Simplify the expression.

$r = 1$

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