# How do you find the equation of the regression line for the given data?

## [(x:, -5, -3, 4, 1, -1, -2, 0, 2, 3, -4), (y:, -10, -8, 9, 1, -2, -6, -1, 3, 6, -8)]

Nov 10, 2017

$y = - 0.552 + 2.097 x$

#### Explanation:

The equation for the regression line is $y = a + b x , \left\{\begin{matrix}a = \setminus \overline{y} - b \setminus \overline{x} \\ b = \frac{{S}_{x y}}{{S}_{x x}}\end{matrix}\right\}$

$\setminus \overline{y} = \frac{\setminus \Sigma y}{n} = - \frac{16}{10} = - 1.6$

$\setminus \overline{x} = \frac{\setminus \Sigma x}{n} = - \frac{5}{10} = - 0.5$

${S}_{x x} = \setminus \Sigma {x}^{2} - \frac{{\left(\setminus \Sigma x\right)}^{2}}{n} = 85 - \frac{{\left(- 5\right)}^{2}}{10} = 82.5$

${S}_{x y} = \setminus \Sigma x y - \frac{\left(\setminus \Sigma x\right) \left(\setminus \Sigma y\right)}{n} = 181 - \frac{80}{10} = 173$

$b = \frac{{S}_{x y}}{{S}_{x x}} = \frac{173}{82.5} = 2.097$ $\left(\text{to 2d.p}\right)$

$a = \setminus \overline{y} - b \setminus \overline{x} = - 1.6 - 2.097 \left(- 0.5\right) = - 0.552$ $\left(\text{to 2d.p}\right\}$

$y = - 0.552 + 2.097 x$