Question

A population data set produced the following information. N=460, ∑x=3920, ∑y=2650, ∑xy=26,570, ∑x2=48,530 Find the population regression line. Round to three decimal places. Use the format as an example when submitting your equation 456.123 + 789.123x

Answer 1

Regression line is given in the form of: y = a + bx
Where b is the gradient

Working out 'b'

$b = \frac{S_{xy}}{S_{xx}}$
$S_{xy} =$Σxy - [ΣxΣy]/N
$S_{xx}=$ Σx² - [Σx]²/N

$S_{xy} = 26570 - \frac{(3920)(2650)}{460}= \frac{91710}{23} =3987.39$
$S_{xx}=48530- \frac{(3920)^2}{460}=15124.78$
$b= \frac{3987.39}{15124.78}=0.264$

Working out 'a'

a = [∑y/N] - b[∑x/N]
a = [2650/460] - 0.264[3920/460]
a = 5.86 - 2.25
a = 3.61

Regression line equation is 
y = 3.61 + 0.264x