Finite Math Examples Correlation and Regression

Find the Regression Line

$\begin{array}{c} x & y \\ 0 & 7 \\ 5 & 1 \\ 6 & 0 \\ 7 & 6 \\ 7 & 9 \\ 8 & 5 \\ 9 & 8 \end{array}$

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.

$\sum_{}^{} x = 0 + 5 + 6 + 7 + 7 + 8 + 9$

Step 4

Simplify the expression.

$\sum_{}^{} x = 42$

Step 5

Sum up the $y$ values.

$\sum_{}^{} y = 7 + 1 + 0 + 6 + 9 + 5 + 8$

Step 6

Simplify the expression.

$\sum_{}^{} y = 36$

Step 7

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

$\sum_{}^{} x y = 0 \cdot 7 + 5 \cdot 1 + 6 \cdot 0 + 7 \cdot 6 + 7 \cdot 9 + 8 \cdot 5 + 9 \cdot 8$

Step 8

Simplify the expression.

$\sum_{}^{} x y = 222$

Step 9

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

$\sum_{}^{} x^{2} = {(0)}^{2} + {(5)}^{2} + {(6)}^{2} + {(7)}^{2} + {(7)}^{2} + {(8)}^{2} + {(9)}^{2}$

Step 10

Simplify the expression.

$\sum_{}^{} x^{2} = 304$

Step 11

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

$\sum_{}^{} y^{2} = {(7)}^{2} + {(1)}^{2} + {(0)}^{2} + {(6)}^{2} + {(9)}^{2} + {(5)}^{2} + {(8)}^{2}$

Step 12

Simplify the expression.

$\sum_{}^{} y^{2} = 256$

Step 13

Fill in the computed values.

$m = \frac{7 (222) - 42 \cdot 36}{7 (304) - {(42)}^{2}}$

Step 14

Simplify the expression.

$m = 0.1\overline{153846}$

Step 15

Fill in the computed values.

$b = \frac{(36) (304) - 42 \cdot 222}{7 (304) - {(42)}^{2}}$

Step 16

Simplify the expression.

$b = 4.\overline{450549}$

Step 17

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

$y = 0.1\overline{153846} x + 4.\overline{450549}$

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Find the Regression Line

Correlation and Regression

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