Finite Math Examples

$\begin{array}{c} x & y \\ 1 & - 1 \\ 2 & 1 \\ 3 & 11 \\ 4 & 35 \\ 5 & 79 \end{array}$

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.

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

Step 4

Simplify the expression.

$\sum_{}^{} x = 15$

Step 5

Sum up the $y$ values.

$\sum_{}^{} y = - 1 + 1 + 11 + 35 + 79$

Step 6

Simplify the expression.

$\sum_{}^{} y = 125$

Step 7

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

$\sum_{}^{} x y = 1 \cdot - 1 + 2 \cdot 1 + 3 \cdot 11 + 4 \cdot 35 + 5 \cdot 79$

Step 8

Simplify the expression.

$\sum_{}^{} x y = 569$

Step 9

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

$\sum_{}^{} x^{2} = {(1)}^{2} + {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2}$

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 55$

Step 11

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

$\sum_{}^{} y^{2} = {(- 1)}^{2} + {(1)}^{2} + {(11)}^{2} + {(35)}^{2} + {(79)}^{2}$

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 7589$

Step 13

Fill in the computed values.

$m = \frac{5 (569) - 15 \cdot 125}{5 (55) - {(15)}^{2}}$

Step 14

Simplify the expression.

$m = 19.4$

Step 15

Fill in the computed values.

$b = \frac{(125) (55) - 15 \cdot 569}{5 (55) - {(15)}^{2}}$

Step 16

Simplify the expression.

$b = - 33.2$

Step 17

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

$y = 19.4 x - 33.2$