Statistics Examples

\begin{matrix} x & y 9 & 10 9 & 11 11 & 12 13 & 15 14 & 12 \end{matrix}

$\begin{array}{c} x & y \\ 9 & 10 \\ 9 & 11 \\ 11 & 12 \\ 13 & 15 \\ 14 & 12 \end{array}$

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 = 9 + 9 + 11 + 13 + 14

$\sum_{}^{} x = 9 + 9 + 11 + 13 + 14$

Step 4

Simplify the expression.

\sum x = 56

$\sum_{}^{} x = 56$

Step 5

Sum up the

y

$y$ values.

\sum y = 10 + 11 + 12 + 15 + 12

$\sum_{}^{} y = 10 + 11 + 12 + 15 + 12$

Step 6

Simplify the expression.

\sum y = 60

$\sum_{}^{} y = 60$

Step 7

Sum up the values of

$x \cdot y$ .

$\sum_{}^{} x y = 9 \cdot 10 + 9 \cdot 11 + 11 \cdot 12 + 13 \cdot 15 + 14 \cdot 12$

Step 8

Simplify the expression.

$\sum_{}^{} x y = 684$

Step 9

Sum up the values of

$x^{2}$ .

$\sum_{}^{} x^{2} = {(9)}^{2} + {(9)}^{2} + {(11)}^{2} + {(13)}^{2} + {(14)}^{2}$

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 648$

Step 11

Sum up the values of

$y^{2}$ .

$\sum_{}^{} y^{2} = {(10)}^{2} + {(11)}^{2} + {(12)}^{2} + {(15)}^{2} + {(12)}^{2}$

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 734$

Step 13

Fill in the computed values.

$m = \frac{5 (684) - 56 \cdot 60}{5 (648) - {(56)}^{2}}$

Step 14

Simplify the expression.

$m = 0.5\overline{769230}$

Step 15

Fill in the computed values.

$b = \frac{(60) (648) - 56 \cdot 684}{5 (648) - {(56)}^{2}}$

Step 16

Simplify the expression.

$b = 5.\overline{538461}$

Step 17

Fill in the values of slope

$m$ and y-intercept

$b$ into the slope-intercept formula.

$y = 0.5\overline{769230} x + 5.\overline{538461}$

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