Finite Math Examples

$\begin{array}{c} t & u \\ 2 & 220 \\ 3 & 290 \\ 4 & 360 \\ 5 & 430 \end{array}$

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.

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

Step 3

Simplify the expression.

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

Step 4

Sum up the

$y$ values.

$\sum_{}^{} y = 220 + 290 + 360 + 430$

Step 5

Simplify the expression.

$\sum_{}^{} y = 1300$

Step 6

Sum up the values of

$x \cdot y$ .

$\sum_{}^{} x y = 2 \cdot 220 + 3 \cdot 290 + 4 \cdot 360 + 5 \cdot 430$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 4900$

Step 8

Sum up the values of

$x^{2}$ .

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

Step 9

Simplify the expression.

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

Step 10

Sum up the values of

$y^{2}$ .

$\sum_{}^{} y^{2} = {(220)}^{2} + {(290)}^{2} + {(360)}^{2} + {(430)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 447000$

Step 12

Fill in the computed values.

$r = \frac{4 (4900) - 14 \cdot 1300}{\sqrt{4 (54) - {(14)}^{2}} \cdot \sqrt{4 (447000) - {(1300)}^{2}}}$

Step 13

Simplify the expression.

$r = 1$