Finite Math Examples

\begin{array}{c} x & y \\ 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8 \\ 9 & 10 \end{array}

$\begin{array}{c} x & y \\ 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8 \\ 9 & 10 \end{array}$

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}}

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

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}}

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

Step 3

Sum up the

x

$x$ values.

\sum_{}^{} x = 1 + 3 + 5 + 7 + 9

$\sum_{}^{} x = 1 + 3 + 5 + 7 + 9$

Step 4

Simplify the expression.

\sum_{}^{} x = 25

$\sum_{}^{} x = 25$

Step 5

Sum up the

y

$y$ values.

\sum_{}^{} y = 2 + 4 + 6 + 8 + 10

$\sum_{}^{} y = 2 + 4 + 6 + 8 + 10$

Step 6

Simplify the expression.

\sum_{}^{} y = 30

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

Step 7

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum_{}^{} x y = 1 \cdot 2 + 3 \cdot 4 + 5 \cdot 6 + 7 \cdot 8 + 9 \cdot 10

$\sum_{}^{} x y = 1 \cdot 2 + 3 \cdot 4 + 5 \cdot 6 + 7 \cdot 8 + 9 \cdot 10$

Step 8

Simplify the expression.

\sum_{}^{} x y = 190

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

Step 9

Sum up the values of

x^{2}

$x^{2}$ .

\sum_{}^{} x^{2} = {(1)}^{2} + {(3)}^{2} + {(5)}^{2} + {(7)}^{2} + {(9)}^{2}

$\sum_{}^{} x^{2} = {(1)}^{2} + {(3)}^{2} + {(5)}^{2} + {(7)}^{2} + {(9)}^{2}$

Step 10

Simplify the expression.

\sum_{}^{} x^{2} = 165

$\sum_{}^{} x^{2} = 165$

Step 11

Sum up the values of

y^{2}

$y^{2}$ .

\sum_{}^{} y^{2} = {(2)}^{2} + {(4)}^{2} + {(6)}^{2} + {(8)}^{2} + {(10)}^{2}

$\sum_{}^{} y^{2} = {(2)}^{2} + {(4)}^{2} + {(6)}^{2} + {(8)}^{2} + {(10)}^{2}$

Step 12

Simplify the expression.

\sum_{}^{} y^{2} = 220

$\sum_{}^{} y^{2} = 220$

Step 13

Fill in the computed values.

m = \frac{5 (190) - 25 \cdot 30}{5 (165) - {(25)}^{2}}

$m = \frac{5 (190) - 25 \cdot 30}{5 (165) - {(25)}^{2}}$

Step 14

Simplify the expression.

m = 1

$m = 1$

Step 15

Fill in the computed values.

b = \frac{(30) (165) - 25 \cdot 190}{5 (165) - {(25)}^{2}}

$b = \frac{(30) (165) - 25 \cdot 190}{5 (165) - {(25)}^{2}}$

Step 16

Simplify the expression.

b = 1

$b = 1$

Step 17

Fill in the values of slope

m

$m$ and y-intercept

b

$b$ into the slope-intercept formula.

y = 1 x + 1

$y = 1 x + 1$