Finite Math Examples

\begin{matrix} x & y 8 & 4 14 & 3 14 & 4 15 & 6 15 & 10 15 & 3 16 & 6 16 & 10 \end{matrix}

$\begin{array}{c} x & y \\ 8 & 4 \\ 14 & 3 \\ 14 & 4 \\ 15 & 6 \\ 15 & 10 \\ 15 & 3 \\ 16 & 6 \\ 16 & 10 \end{array}$

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 = 8 + 14 + 14 + 15 + 15 + 15 + 16 + 16

$\sum_{}^{} x = 8 + 14 + 14 + 15 + 15 + 15 + 16 + 16$

Step 4

Simplify the expression.

\sum x = 113

$\sum_{}^{} x = 113$

Step 5

Sum up the

y

$y$ values.

\sum y = 4 + 3 + 4 + 6 + 10 + 3 + 6 + 10

$\sum_{}^{} y = 4 + 3 + 4 + 6 + 10 + 3 + 6 + 10$

Step 6

Simplify the expression.

\sum y = 46

$\sum_{}^{} y = 46$

Step 7

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum x y = 8 \cdot 4 + 14 \cdot 3 + 14 \cdot 4 + 15 \cdot 6 + 15 \cdot 10 + 15 \cdot 3 + 16 \cdot 6 + 16 \cdot 10

$\sum_{}^{} x y = 8 \cdot 4 + 14 \cdot 3 + 14 \cdot 4 + 15 \cdot 6 + 15 \cdot 10 + 15 \cdot 3 + 16 \cdot 6 + 16 \cdot 10$

Step 8

Simplify the expression.

\sum x y = 671

$\sum_{}^{} x y = 671$

Step 9

Sum up the values of

x^{2}

$x^{2}$ .

\sum x^{2} = {(8)}^{2} + {(14)}^{2} + {(14)}^{2} + {(15)}^{2} + {(15)}^{2} + {(15)}^{2} + {(16)}^{2} + {(16)}^{2}

$\sum_{}^{} x^{2} = {(8)}^{2} + {(14)}^{2} + {(14)}^{2} + {(15)}^{2} + {(15)}^{2} + {(15)}^{2} + {(16)}^{2} + {(16)}^{2}$

Step 10

Simplify the expression.

\sum x^{2} = 1643

$\sum_{}^{} x^{2} = 1643$

Step 11

Sum up the values of

y^{2}

$y^{2}$ .

\sum y^{2} = {(4)}^{2} + {(3)}^{2} + {(4)}^{2} + {(6)}^{2} + {(10)}^{2} + {(3)}^{2} + {(6)}^{2} + {(10)}^{2}

$\sum_{}^{} y^{2} = {(4)}^{2} + {(3)}^{2} + {(4)}^{2} + {(6)}^{2} + {(10)}^{2} + {(3)}^{2} + {(6)}^{2} + {(10)}^{2}$

Step 12

Simplify the expression.

\sum y^{2} = 322

$\sum_{}^{} y^{2} = 322$

Step 13

Fill in the computed values.

m = \frac{8 (671) - 113 \cdot 46}{8 (1643) - {(113)}^{2}}

$m = \frac{8 (671) - 113 \cdot 46}{8 (1643) - {(113)}^{2}}$

Step 14

Simplify the expression.

m = 0.45 ¯ 3

$m = 0.45\overline{3}$

Step 15

Fill in the computed values.

b = \frac{(46) (1643) - 113 \cdot 671}{8 (1643) - {(113)}^{2}}

$b = \frac{(46) (1643) - 113 \cdot 671}{8 (1643) - {(113)}^{2}}$

Step 16

Simplify the expression.

b = - 0.65 ¯ 3

$b = - 0.65\overline{3}$

Step 17

Fill in the values of slope

m

$m$ and y-intercept

b

$b$ into the slope-intercept formula.

y = 0.45 ¯ 3 x - 0.65 ¯ 3

$y = 0.45\overline{3} x - 0.65\overline{3}$

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