Finite Math Examples

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

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.

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

Step 4

Simplify the expression.

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

Step 5

Sum up the

$y$ values.

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

Step 6

Simplify the expression.

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

Step 7

Sum up the values of

$x \cdot y$ .

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

Step 8

Simplify the expression.

$\sum_{}^{} x y = 40$

Step 9

Sum up the values of

$x^{2}$ .

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

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 30$

Step 11

Sum up the values of

$y^{2}$ .

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

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 54$

Step 13

Fill in the computed values.

$m = \frac{4 (40) - 10 \cdot 14}{4 (30) - {(10)}^{2}}$

Step 14

Simplify the expression.

$m = 1$

Step 15

Fill in the computed values.

$b = \frac{(14) (30) - 10 \cdot 40}{4 (30) - {(10)}^{2}}$

Step 16

Simplify the expression.

$b = 1$

Step 17

Fill in the values of slope

$m$ and y-intercept

$b$ into the slope-intercept formula.

$y = 1 x + 1$

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