Statistics Examples

$(- 3, - 28)$ , $(0, - 4)$ , $(4, 168)$ , $(- 5, - 174)$

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.

$\sum_{}^{} x = - 5 - 3 + 0 + 4$

Step 4

Simplify the expression.

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

Step 5

Sum up the $y$ values.

$\sum_{}^{} y = - 174 - 28 - 4 + 168$

Step 6

Simplify the expression.

$\sum_{}^{} y = - 38$

Step 7

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

$\sum_{}^{} x y = - 5 \cdot - 174 - 3 \cdot - 28 + 0 \cdot - 4 + 4 \cdot 168$

Step 8

Simplify the expression.

$\sum_{}^{} x y = 1626$

Step 9

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

$\sum_{}^{} x^{2} = {(- 5)}^{2} + {(- 3)}^{2} + {(0)}^{2} + {(4)}^{2}$

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 50$

Step 11

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

$\sum_{}^{} y^{2} = {(- 174)}^{2} + {(- 28)}^{2} + {(- 4)}^{2} + {(168)}^{2}$

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 59300$

Step 13

Fill in the computed values.

$m = \frac{4 (1626) + 4 \cdot - 38}{4 (50) - {(- 4)}^{2}}$

Step 14

Simplify the expression.

$m = 34.52173913$

Step 15

Fill in the computed values.

$b = \frac{(- 38) (50) + 4 \cdot 1626}{4 (50) - {(- 4)}^{2}}$

Step 16

Simplify the expression.

$b = 25.02173913$

Step 17

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

$y = 34.52173913 x + 25.02173913$