Finite Math Examples

$\begin{array}{c} x & y \\ 4 & 5 \\ 5 & 11 \\ 6 & 18 \\ 7 & 26 \\ 8 & 35 \end{array}$

Step 1

The slope of the best fit regression line can be found using the formula.

$m = \frac{n (\sum_{}^{} x y) - \sum_{}^{} x \sum_{}^{} y}{n (\sum_{}^{} x^{2}) - {(\sum_{}^{} x)}^{2}}$

Step 2

The y-intercept of the best fit regression line can be found using the formula.

$b = \frac{(\sum_{}^{} y) (\sum_{}^{} x^{2}) - \sum_{}^{} x \sum_{}^{} x y}{n (\sum_{}^{} x^{2}) - {(\sum_{}^{} x)}^{2}}$

Step 3

Sum up the $x$ values.

$\sum_{}^{} x = 4 + 5 + 6 + 7 + 8$

Step 4

Simplify the expression.

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

Step 5

Sum up the $y$ values.

$\sum_{}^{} y = 5 + 11 + 18 + 26 + 35$

Step 6

Simplify the expression.

$\sum_{}^{} y = 95$

Step 7

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

$\sum_{}^{} x y = 4 \cdot 5 + 5 \cdot 11 + 6 \cdot 18 + 7 \cdot 26 + 8 \cdot 35$

Step 8

Simplify the expression.

$\sum_{}^{} x y = 645$

Step 9

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

$\sum_{}^{} x^{2} = {(4)}^{2} + {(5)}^{2} + {(6)}^{2} + {(7)}^{2} + {(8)}^{2}$

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 190$

Step 11

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

$\sum_{}^{} y^{2} = {(5)}^{2} + {(11)}^{2} + {(18)}^{2} + {(26)}^{2} + {(35)}^{2}$

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 2371$

Step 13

Fill in the computed values.

$m = \frac{5 (645) - 30 \cdot 95}{5 (190) - {(30)}^{2}}$

Step 14

Simplify the expression.

$m = 7.5$

Step 15

Fill in the computed values.

$b = \frac{(95) (190) - 30 \cdot 645}{5 (190) - {(30)}^{2}}$

Step 16

Simplify the expression.

$b = - 26$

Step 17

Fill in the values of slope $m$ and y-intercept $b$ into the slope-intercept formula.

$y = 7.5 x - 26$