Finite Math Examples

\begin{array}{c} f (x) & y \\ - 3 & 0 \\ 3 & 1 \\ 9 & 2 \\ 15 & 3 \end{array}

$\begin{array}{c} f (x) & y \\ - 3 & 0 \\ 3 & 1 \\ 9 & 2 \\ 15 & 3 \end{array}$

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}}}

$r = \frac{n (\sum_{}^{} x y) - \sum_{}^{} x \sum_{}^{} y}{\sqrt{n (\sum_{}^{} x^{2}) - {(\sum_{}^{} x)}^{2}} \cdot \sqrt{n (\sum_{}^{} y^{2}) - {(\sum_{}^{} y)}^{2}}}$

Step 2

Sum up the

x

$x$ values.

\sum_{}^{} x = - 3 + 3 + 9 + 15

$\sum_{}^{} x = - 3 + 3 + 9 + 15$

Step 3

Simplify the expression.

\sum_{}^{} x = 24

$\sum_{}^{} x = 24$

Step 4

Sum up the

y

$y$ values.

\sum_{}^{} y = 0 + 1 + 2 + 3

$\sum_{}^{} y = 0 + 1 + 2 + 3$

Step 5

Simplify the expression.

\sum_{}^{} y = 6

$\sum_{}^{} y = 6$

Step 6

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum_{}^{} x y = - 3 \cdot 0 + 3 \cdot 1 + 9 \cdot 2 + 15 \cdot 3

$\sum_{}^{} x y = - 3 \cdot 0 + 3 \cdot 1 + 9 \cdot 2 + 15 \cdot 3$

Step 7

Simplify the expression.

\sum_{}^{} x y = 66

$\sum_{}^{} x y = 66$

Step 8

Sum up the values of

x^{2}

$x^{2}$ .

\sum_{}^{} x^{2} = {(- 3)}^{2} + {(3)}^{2} + {(9)}^{2} + {(15)}^{2}

$\sum_{}^{} x^{2} = {(- 3)}^{2} + {(3)}^{2} + {(9)}^{2} + {(15)}^{2}$

Step 9

Simplify the expression.

\sum_{}^{} x^{2} = 324

$\sum_{}^{} x^{2} = 324$

Step 10

Sum up the values of

y^{2}

$y^{2}$ .

\sum_{}^{} y^{2} = {(0)}^{2} + {(1)}^{2} + {(2)}^{2} + {(3)}^{2}

$\sum_{}^{} y^{2} = {(0)}^{2} + {(1)}^{2} + {(2)}^{2} + {(3)}^{2}$

Step 11

Simplify the expression.

\sum_{}^{} y^{2} = 14

$\sum_{}^{} y^{2} = 14$

Step 12

Fill in the computed values.

r = \frac{4 (66) - 24 \cdot 6}{\sqrt{4 (324) - {(24)}^{2}} \cdot \sqrt{4 (14) - {(6)}^{2}}}

$r = \frac{4 (66) - 24 \cdot 6}{\sqrt{4 (324) - {(24)}^{2}} \cdot \sqrt{4 (14) - {(6)}^{2}}}$

Step 13

Simplify the expression.

r = 1

$r = 1$