Finite Math Examples

$\begin{array}{c} x & y \\ - 2 & 4.2 \\ - 1 & 4.3 \\ 0 & 4.4 \\ 1 & 4.5 \\ 2 & 4.6 \end{array}$

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.

$\sum_{}^{} x = - 2 - 1 + 0 + 1 + 2$

Step 4

Simplify the expression.

$\sum_{}^{} x = 0$

Step 5

Sum up the $y$ values.

$\sum_{}^{} y = 4.2 + 4.3 + 4.4 + 4.5 + 4.6$

Step 6

Simplify the expression.

$\sum_{}^{} y = 22$

Step 7

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

$\sum_{}^{} x y = - 2 \cdot 4.2 - 1 \cdot 4.3 + 0 \cdot 4.4 + 1 \cdot 4.5 + 2 \cdot 4.6$

Step 8

Simplify the expression.

$\sum_{}^{} x y = 1$

Step 9

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

$\sum_{}^{} x^{2} = {(- 2)}^{2} + {(- 1)}^{2} + {(0)}^{2} + {(1)}^{2} + {(2)}^{2}$

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 10$

Step 11

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

$\sum_{}^{} y^{2} = {(4.2)}^{2} + {(4.3)}^{2} + {(4.4)}^{2} + {(4.5)}^{2} + {(4.6)}^{2}$

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 96.9$

Step 13

Fill in the computed values.

$m = \frac{5 (1) + 0 \cdot 22}{5 (10) - {(0)}^{2}}$

Step 14

Simplify the expression.

$m = 0.1$

Step 15

Fill in the computed values.

$b = \frac{(22) (10) + 0 \cdot 1}{5 (10) - {(0)}^{2}}$

Step 16

Simplify the expression.

$b = 4.4$

Step 17

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

$y = 0.1 x + 4.4$