Finite Math Examples

$\begin{array}{c} x & y \\ 4 & - 2 \end{array}$

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.

$\sum_{}^{} x = 4$

Step 4

Simplify the expression.

$\sum_{}^{} x = 4$

Step 5

Sum up the $y$ values.

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

Step 6

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

$\sum_{}^{} x y = 4 \cdot - 2$

Step 7

Simplify the expression.

$\sum_{}^{} x y = - 8$

Step 8

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

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

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 16$

Step 10

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

$\sum_{}^{} y^{2} = {(- 2)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 4$

Step 12

Fill in the computed values.

$m = \frac{1 (- 8) - 4 \cdot - 2}{1 (16) - {(4)}^{2}}$

Step 13

Simplify the expression.

$m = N a N$

Step 14

Fill in the computed values.

$b = \frac{(- 2) (16) - 4 \cdot - 8}{1 (16) - {(4)}^{2}}$

Step 15

Simplify the expression.

$b = N a N$

Step 16

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

$y = N a N x + N a N$