Statistics Examples

\begin{array}{c} x & p \\ 0 & 0.2 \\ 1 & 0.3 \\ 2 & 0.1 \\ 3 & 0.4 \end{array}

$\begin{array}{c} x & p \\ 0 & 0.2 \\ 1 & 0.3 \\ 2 & 0.1 \\ 3 & 0.4 \end{array}$

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 = 0 + 1 + 2 + 3

$\sum_{}^{} x = 0 + 1 + 2 + 3$

Step 4

Simplify the expression.

\sum_{}^{} x = 6

$\sum_{}^{} x = 6$

Step 5

Sum up the

y

$y$ values.

\sum_{}^{} y = 0.2 + 0.3 + 0.1 + 0.4

$\sum_{}^{} y = 0.2 + 0.3 + 0.1 + 0.4$

Step 6

Simplify the expression.

\sum_{}^{} y = 1

$\sum_{}^{} y = 1$

Step 7

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum_{}^{} x y = 0 \cdot 0.2 + 1 \cdot 0.3 + 2 \cdot 0.1 + 3 \cdot 0.4

$\sum_{}^{} x y = 0 \cdot 0.2 + 1 \cdot 0.3 + 2 \cdot 0.1 + 3 \cdot 0.4$

Step 8

Simplify the expression.

\sum_{}^{} x y = 1.7

$\sum_{}^{} x y = 1.7$

Step 9

Sum up the values of

x^{2}

$x^{2}$ .

\sum_{}^{} x^{2} = {(0)}^{2} + {(1)}^{2} + {(2)}^{2} + {(3)}^{2}

$\sum_{}^{} x^{2} = {(0)}^{2} + {(1)}^{2} + {(2)}^{2} + {(3)}^{2}$

Step 10

Simplify the expression.

\sum_{}^{} x^{2} = 14

$\sum_{}^{} x^{2} = 14$

Step 11

Sum up the values of

y^{2}

$y^{2}$ .

\sum_{}^{} y^{2} = {(0.2)}^{2} + {(0.3)}^{2} + {(0.1)}^{2} + {(0.4)}^{2}

$\sum_{}^{} y^{2} = {(0.2)}^{2} + {(0.3)}^{2} + {(0.1)}^{2} + {(0.4)}^{2}$

Step 12

Simplify the expression.

\sum_{}^{} y^{2} = 0.30000001

$\sum_{}^{} y^{2} = 0.30000001$

Step 13

Fill in the computed values.

m = \frac{4 (1.7) - 6 \cdot 1}{4 (14) - {(6)}^{2}}

$m = \frac{4 (1.7) - 6 \cdot 1}{4 (14) - {(6)}^{2}}$

Step 14

Simplify the expression.

m = 0.04

$m = 0.04$

Step 15

Fill in the computed values.

b = \frac{(1) (14) - 6 \cdot 1.7}{4 (14) - {(6)}^{2}}

$b = \frac{(1) (14) - 6 \cdot 1.7}{4 (14) - {(6)}^{2}}$

Step 16

Simplify the expression.

b = 0.18999996

$b = 0.18999996$

Step 17

Fill in the values of slope

m

$m$ and y-intercept

b

$b$ into the slope-intercept formula.

y = 0.04 x + 0.18999996

$y = 0.04 x + 0.18999996$

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