Statistics Examples

$\begin{array}{c} x & y \\ 7 & 9 \\ 7 & 11 \\ 8 & 7 \\ 11 & 11 \\ 12 & 9 \\ 12 & 11 \\ 13 & 9 \end{array}$

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.

$\sum_{}^{} x = 7 + 7 + 8 + 11 + 12 + 12 + 13$

Step 4

Simplify the expression.

$\sum_{}^{} x = 70$

Step 5

Sum up the

$y$ values.

$\sum_{}^{} y = 9 + 11 + 7 + 11 + 9 + 11 + 9$

Step 6

Simplify the expression.

$\sum_{}^{} y = 67$

Step 7

Sum up the values of

$x \cdot y$ .

$\sum_{}^{} x y = 7 \cdot 9 + 7 \cdot 11 + 8 \cdot 7 + 11 \cdot 11 + 12 \cdot 9 + 12 \cdot 11 + 13 \cdot 9$

Step 8

Simplify the expression.

$\sum_{}^{} x y = 674$

Step 9

Sum up the values of

$x^{2}$ .

$\sum_{}^{} x^{2} = {(7)}^{2} + {(7)}^{2} + {(8)}^{2} + {(11)}^{2} + {(12)}^{2} + {(12)}^{2} + {(13)}^{2}$

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 740$

Step 11

Sum up the values of

$y^{2}$ .

$\sum_{}^{} y^{2} = {(9)}^{2} + {(11)}^{2} + {(7)}^{2} + {(11)}^{2} + {(9)}^{2} + {(11)}^{2} + {(9)}^{2}$

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 655$

Step 13

Fill in the computed values.

$m = \frac{7 (674) - 70 \cdot 67}{7 (740) - {(70)}^{2}}$

Step 14

Simplify the expression.

$m = 0.1$

Step 15

Fill in the computed values.

$b = \frac{(67) (740) - 70 \cdot 674}{7 (740) - {(70)}^{2}}$

Step 16

Simplify the expression.

$b = 8.\overline{571428}$

Step 17

Fill in the values of slope

$m$ and y-intercept

$b$ into the slope-intercept formula.

$y = 0.1 x + 8.\overline{571428}$

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